Influence of wind direction, wind waves, and density stratification upon sediment transport in shelf edge regions: The Iberian shelf

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 107, NO. C8, 3101, 10.1029/2001JC000961, 2002 Influence of wind direction, wind waves, and density stratification upon sediment transport in shelf edge regions: The Iberian shelf Jiuxing Xing and Alan M. Davies Proudman Oceanographic Laboratory, Bidston Observatory, Birkenhead, UK Received 9 May 2001; revised 27 December 2001; accepted 15 January 2002; published 8 August 2002. [1] A prognostic baroclinic model including a suspended sediment transport module is used in cross-sectional form to examine processes, namely, internal tide, wind, and wind waves, which lead to cross-shelf sediment movement. Although the main focus is a process study to quantify the role of various mechanisms giving rise to ocean-shelf sediment exchange, the calculations are set in the context of the Iberian shelf. Eddy viscosity and diffusivity are computed from a turbulence energy submodel. Calculations with upwelling and downwelling favorable winds showed that friction velocity and turbulent mixing were a maximum in near-coastal regions. In these areas, suspended sediment concentration was a maximum. For upwelling favorable winds in homogeneous water, near-bed sediment was moved toward the coast where upwelling occurred. In this area, sediment was transported into the near-surface layer and advected offshore by the wind-driven flow. For the parameters considered here, advection in the near-surface layer exceeded vertical settling, and maximum sediment concentration occurred at the surface. For a downwelling favorable wind the strong surface currents are onshore, and hence any sediment in the surface layer is advected toward the coast. Although the bottom current is off-shelf, it is weak, and hence the off-shelf export of sediment in this layer is less than that found in the surface layer with an upwelling favorable wind. In stratified conditions, with an upwelling favorable wind the intensity of the stratification at the shelf edge increases. Associated with this, there is an increase in the vertical sediment concentration gradient. With downwelling favorable winds, rapid mixing occurs on the shelf, and a shelf front is formed. Sediment concentration on the shelf and at the shelf edge shows a similar distribution to that found under homogeneous conditions. When tidal forcing is included an internal tide is produced that interacts with the wind-driven flow in a nonlinear manner. Increased bed stress due to the internal tide and vertical circulation cells lead to enhanced sediment erosion above that found with wind forcing only. For an upwelling wind this leads to enhanced off-shelf sediment movement in the surface layer. For a downwelling wind a circulation develops that tends to inhibit off-shelf sediment transport. The effect of wind waves is to increase significantly sediment suspension on the shelf. Although the concentration of the sediment is influenced by the wind waves, its spatial distribution is determined by the wind and tidal flows. A detailed analysis of the terms in the sediment transport equation is used to quantify the effects of each process upon the sediment distribution in the water column. INDEX TERMS: 4255 Oceanography: General: Numerical modeling; 4544 Oceanography: Physical: Internal and inertial waves; 4568 Oceanography: Physical: Turbulence, diffusion, and mixing processes; 4211 Oceanography: General: Benthic boundary layers; KEYWORDS: shelf edge, wind, tide, sediment, waves, stratification 1. Introduction [2] In shallow sea regions there has been significant progress in understanding sediment movement under wind and wave conditions [e.g., Davies et al., 1988; Huntley and Hazen, 1988; Huntley et al., 1994; Heathershaw, 1981; Aldridge, 1997; Holt and James, 1999; Green et al., 1995; Gerritsen and Berentsen, 1998; Grant and Madsen, 1986]. Copyright 2002 by the American Geophysical Union. 0148-0227/02/2001JC000961 However, in shelf edge regions where the water is stratified, and internal waves, particularly internal tides [Baines, 1982; Craig, 1987; Holloway, 1996; Lamb, 1994; New, 1988; Sherwin, 1988; Gerkema and Zimmerman, 1995; Xing and Davies, 1997, 1998] are present very little modeling work has been performed, and the physical environment is very different to that in nearshore regions where currents are stronger (of order 1 m s 1 ) and water depths are shallow. In these regions tidally generated bed turbulence is large, and very often the water column remains well mixed. At times of major wind events when there is significant wind wave 16-1

16-2 XING AND DAVIES: IBERIAN SHELF SEDIMENT TRANSPORT activity, the water depth is sufficiently shallow that the wave orbital velocity is large at the seabed, leading to an enhancement in bed turbulence [Davies and Lawrence, 1994, 1995], associated stress and sediment suspension. Similarly turbulence generated at the sea surface by the imposed wind stress produces a surface Ekman layer of comparable thickness to the water depth. In close proximity to coastlines an upwelling/downwelling wind besides producing an offshore/onshore surface flow gives rise to an opposite flow in the near-bed region with an associated bottom Ekman layer. The shallowness of the water depths in the nearshore region is such that these two layers overlap and the water remains well mixed. This together with the highly turbulent environment in this area has a significant influence upon sediment movement, which is very different to that in shelf edge regions. [3] With recent advances in three-dimensional tidal modeling [Davies and Jones, 1990; Davies and Xing, 1995; Davies et al., 1997a, 1997b] an accurate description of tidal currents, bed stresses, and turbulence is now available in shallow water well-mixed regions. Also three-dimensional models of wind-induced flow taking account of enhanced bed stress due to wave effects and their influence on currents in shallow regions [Davies and Lawrence, 1995; Jones and Davies, 1998] can now provide an accurate flow field for coastal sediment movement during major wind events. [4] With significantly deeper water and weaker tidal currents at the shelf edge, there is a permanent thermocline at depth and a seasonal one extending onto the shelf. A consequence of the presence of the thermocline, and the deeper water is that surface and bottom boundary layers are well removed from each other [Huthnance, 1995]. When the stratification intersects the slope topography the on-shelf/ off-shelf tidal motion produces internal tides, which can lead to enhanced sediment erosion [Heathershaw, 1985; Heathershaw et al., 1987]. In the case of wind forcing in deep water, surface and bottom turbulence layers are well removed from each other, with a region of little vertical mixing separating the two layers. A situation very different from that found in shallow seas, and as we will show this has a significant influence upon sediment dynamics. During wind events, changes in the density field produced by the wind can significantly modify the internal tide [Xing and Davies, 1997], leading to major coupling between the two flows, which can modify the sediment distribution due to either the tide or the wind in isolation. [5] To date the number of comprehensive shelf edge data sets of sediment movement [Butman, 1988; Flagg, 1988] is limited. Recently, a detailed measuring programme was conducted off the west coast of Spain as part of an Ocean Margin Exchange (OMEX) project with a view to understanding the processes that control shelf edge sediment movement. Here we concentrate upon the role of the wind and wind wave effects upon sediment suspension and its transport. Also the influence of coupling between the winddriven circulation and the internal tide upon sediment movement is considered. [6] The first part of the paper briefly presents (with references to the literature for detail) a general-purpose three-dimensional model, which has been used in a range of shelf sea [Xing and Davies, 2001a] and shelf edge [Xing and Davies, 1998; Xing et al., 1999] full three-dimensional simulations. In the present study the model is used in crosssectional form with topography corresponding to that of the Iberian shelf at 42 40.5 0 N where measurements were made as part of OMEX. A full three-dimensional simulation of this region would require a detail description of the along-shelf topography, tides, winds, and waves together with the alongshelf flow at the time of the measurements with associated northern and southern open boundary conditions besides the oceanic boundary used here. Such a three-dimensional simulation is outside the scope of the present paper, but details of such applications is given by Davies and Xing [2001], Xing and Davies [1998, 2001a], and appropriate forms of across-shelf open boundary conditions by A. M. Davies et al. (Barotropic eddy generation by flow instability at the shelf edge: Sensitivity to open boundary conditions, inflow and diffusion, submitted to Journal of Geophysical Research, 2002, hereinafter referred to as Davies et al., submitted manuscript 2002) and Davies and Hall [2002]. In three-dimensional long-term simulations in which instabilities give rise to energetic eddies the across-shelf open boundary can be a problem [Davies and Hall, 2002], although a range of methods to overcome this is given by Davies et al. (submitted manuscript, 2002) with stable longterm integrations using appropriate boundaries by Xing and Davies [2001a] and Xing et al. [1999]. It is not the aim of the present paper to present a full three-dimensional simulation of sediment transport on the Iberian shelf, but to perform a process orientated study as described earlier. Besides giving details of the model, the turbulence energy submodel used to parameterize vertical mixing is also discussed, in the next section. Subsequent sections describe how sediment movement is controlled in shelf edge regions by tidal and wind events, and modified by wind waves. 2. Models [7] For completeness, the full three-dimensional model in Cartesian coordinates is presented here. Although in the application considered here the model is only used in cross-sectional form. The continuity equation, momentum equations, and transport equations for temperature and sediment concentration in flux form using s coordinates where s =(z z)/h are given by @Hu @t @Hv @t @z @t þr Z o 1 ðhvþds ¼ 0; þrðhuvþþ @Huw @z fhv ¼ gh @s @x þ BPF x þ 1 @ H 2 @s K @Hu m þ HF u ; @s þrðhvvþþ @Hvw @z þ fhu ¼ gh @s @y þ BPF y þ 1 @ H 2 @s K @Hv m þ HF v ; @s The time evolution of temperature T is given by @HT @t þrðhtvþþ @HTw @s ¼ 1 @ H 2 @s K v @HT @s þ HF T ; ð1þ ð2þ ð3þ ð4þ

XING AND DAVIES: IBERIAN SHELF SEDIMENT TRANSPORT 16-3 with a corresponding equation for the suspended sediment concentration C is given by @HC @t þrðhcv Þþ @HC ð w w s=hþ @s ¼ 1 H 2 @ @s K v @HC @s þ HF c ; [8] A simple equation of state was used to convert temperature into density, namely, r = r o [1 b(t T o )], where T o is a reference temperature corresponding to r o, and b = 0.0002/ C. In these equations, V =(u, v) and (u, v, w) are the velocity components corresponding to the (x, y, s) coordinates: r is density; T is the temperature; C the concentration, H = h + z is the total water depth; z is the elevation of the sea surface above the undisturbed level h; z is the water depth increasing vertically upward with z = z the free surface and z = h the seabed; f is the Coriolis parameter, g is the gravitational acceleration; t is time; F u, F v, F T, and F c are horizontal diffusions for the momentum, temperature and sediment concentration. Also K m and K v are the vertical eddy viscosity and diffusivity respectively, with w s the settling velocity which depends upon sediment size. In these equations the baroclinic pressure force terms (BPF x, BPF y ) are as given by Xing and Davies, [1999a, 1999b]. The pressure P at any depth s is given by @P @s ¼ rgh; with w the vertical velocity derived from the diagnostic form of the continuity equation. [9] At the sea surface, the vertical derivative of velocity was zero in tidal problems, while for wind-driven flows, the surface stress was set equal to the wind stress. At the seabed a quadratic friction law was applied. Heat flux was zero at sea surface and seabed. A zero flux condition was applied to sediment concentration at the surface, while at the bed a pick-up function was defined by K v H @C @s ¼ a u2 u2 c u 2 c ð5þ ð6þ! 3=2 ; ð7þ when u * u *c, otherwise zero, with a set at 0.001, u * friction velocity, and u *c its critical value. [10] At land boundaries the normal component of the current was set to zero while at offshore boundaries a radiation condition was applied. In the calculations involving tidal motion, forcing at the M 2 period was applied through the radiation condition. A range of open boundary radiation conditions for tidal and associated inflows is considered by Davies et al. [1997a, 1997b], with ones involving along-shelf instabilities and energetic eddy propagation [Davies and Xing, 2000] by Davies et al. (submitted manuscript, 2002). The problem of nesting models in shelf edge regions through radiation type boundary conditions is given by Davies and Hall [2002]. These open boundary conditions have proved very robust and long-term (of order a year) integrations using them are described by Xing and Davies [2001a] and Xing et al. [1999]. The nature of the tide in the Iberian shelf region described here is that besides an across-shelf component there is also a significant alongshelf component (T. J. Sherwin et al., personal communication, 2002). This along-shelf flow at the M 2 tidal period with maximum current in shallow water was applied by introducing an additional sinusoidal (with tidal period) forcing into the hydrodynamic equations. The spatial distribution of the forcing was adjusted to give a realistic distribution of tidal currents in the region. [11] A turbulence energy submodel was used to compute the eddy viscosity and diffusivity. This involved a predictive equation for turbulence energy E, namely, @HE @t þrðhev Þ ¼ K m H " @u 2 þ @v # 2 @s @s K m @HE @s þ g K m r þ b o H @ @s @r @s eh þ HF E; where HF E is horizontal diffusion of turbulence and the turbulence dissipation is given by e ¼ C 0 C 1 E 2 =K m ; with K v = K m = C 0 le 1/2, where b 0 = 1.0, C 0 = C 1/4, and C 1 = C 0 3, where C = 0.046. This turbulence model is just one of many that exists in the literature [e.g., Blumberg and Mellor, 1987; Baumert and Radach, 1992; Davies and Jones, 1991; Davies and Xing, 2000; Luyten et al., 1996; Oey and Chen, 1992a, 1992b] but has been very successful in numerous simulations. [12] In the calculations described later the sediment concentration was assumed to be so small that it did not affect the density which was determined by the temperature field. The mixing length was computed using an algebraic expression given by Xing and Davies [2001a]. As its formulation is standard it will not be repeated here. [13] In the calculations concerned with the influence of wind waves at swell periods, of order 15 20 s, the wave amplitude A w in the near-coastal region (depths of 100 m or less) was assumed to decay from its oceanic value A o, according to ð8þ h 2 A w ¼ A o ; h 100 m: ð9þ 100 [14] The drag coefficient in the quadratic friction law which related bed stress to bed current was modified using the wave-current interaction formulation of Davies and Lawrence [1994, 1995], based upon the work of Grant and Madsen [1979]. Consequently, when wave effects are present the drag coefficient increases, reflecting the additional turbulence due to the wind waves. This has the effect of changing the flow field and turbulence within the model and hence the computed bed stress and, consequently, the computed friction velocity u *f due to the flow. Under wave conditions there is an additional component of friction velocity u *w due to the waves, with the total friction velocity u * = u *f +u *w then being used in equation (7). Since u *w depends upon the wave orbital velocity at the bed which is a function of wave period, amplitude and water depth, then for swell waves, u *w often exceeds u *f in water depths less than 200 m and hence the pick up of sediment (equation (7))

16-4 XING AND DAVIES: IBERIAN SHELF SEDIMENT TRANSPORT Figure 1a. (i) Cross-shelf depth distribution and (ii) detailed shelf edge profile showing location of points (a)(b)(c) where current time series is examined in detail. can be significantly increased by the presence of wind waves. [15] As extensive details of the numerical methods used to solve the equations have been given previously [Xing and Davies, 1996, 1997] only a brief outline is presented here. A finite difference grid of 340 m resolution was used in the horizontal. The order of 60 sigma levels was used in the vertical, with enhanced resolution in the near-surface and near-bed regions in order to accurately resolve shear in these layers due to wind forcing and bed friction. [16] The equations were integrated through time using a time splitting method [Xing and Davies, 1996, 1997], and the total variation diminishing (TVD) advection scheme was used for temperature and sediment advection. This scheme has been shown [James, 1996; Xing and Davies, 1998], to retain high concentration gradients when material is advected over steep topography. To overcome inaccuracies in calculating baroclinic pressure and horizontal density diffusion in sigma coordinates in the presence of steep topography, these terms were computed on z surfaces, and results then interpolated onto sigma surfaces. 3. Wind Influence Upon Sediment Transport [17] In the calculations described here the model in crosssectional form is initially used to examine the across-shelf transport of suspended sediment due to wind-induced flow in the absence of tidal motion upon. Subsequently, tidal motion is added and the effect of both wind and tidal forcing is examined. In this series of calculations the sediment has a settling velocity w s =510 4 ms 1, with a critical bed shear stress for sediment pick up of 0.9 10 2 ms 1. [18] The depth distribution in the model is given in Figure 1a, which shows a shelf region (depths of less than 200 m), extending approximately 35 km offshore, with the shelf break area from 35 to 50 km offshore, where depths reach 1500 m, extending to oceanic depths (2000 m) at 60 km offshore. In the stratified calculations described subsequently, a climatic mean temperature profile, as employed previously in internal tide calculations [Xing and Davies, 1996] was used (Figure 1b). At water depths below 1200 m, the temperature was assumed constant at its 1200 m value. 3.1. Upwelling Favorable Wind With a Homogeneous Water Column (Calculation 1) [19] In an initial calculation (calculation 1, Table 1), the water was assumed homogeneous and an upwelling favorable along-shelf wind stress of 0.2 Pa was applied, giving an offshore surface current after 15 days of the order of 10 cm s 1 (Figure 2a), and a region of upwelling at the shelf edge. On the shelf an along-shelf flow of approximately 40 cm s 1 was produced, above a bottom layer with velocities of the order of 20 cm s 1. These flows produced an across-shelf distribution of friction velocity (Figure 2b), with a maximum on the shelf where currents are largest. In this region, the vertical diffusion is also strong, and hence a high sediment concentration can reach the surface winddriven flow region, and is advected offshore (Figure 2a). At Figure 1b. Profiles of temperature ( C) and square of Brunt Vaisalla frequency (10 6 s 2 ) for an idealized climatic situation.

XING AND DAVIES: IBERIAN SHELF SEDIMENT TRANSPORT 16-5 Table 1. Summary of Various Parameters Used in the Calculation Calculation Wind a Density Sediment Type b Wind Waves Tide 1 U homogeneous B 2 U stratified B 3 D homogeneous B 4 D stratification B 5 fixed stratification B yes 6 stratified B yes 7 U stratified B yes 7A U stratified B1 yes 7B U stratified B2 yes 7C U stratified B3 yes 8 D stratified B yes 9 U stratified B WR yes 10 D stratified B WR yes a U = upwelling, D = downwelling, and WR = wind waves with amplitude reduced in shallow water. b B: u *c =0.910 2 ms 1 and w s =510 4 ms 1 ; B1: w s =2.0w o s ; B2: w s =3.0w o s ; and B3: w s =4.0w o s, with w o s =510 4 ms 1. the shelf edge, the friction velocity is substantially less, as is the vertical diffusivity and hence sediment concentration is less in the near-bed region than close to the coast. However, the nature of the across-shelf flow (Figure 2a) is such that the sediment in the bottom boundary layer is moved toward the coast, while that near the surface is moved offshore. Since currents in the surface layer are stronger than those in the near-bed layer, and the greatest sediment concentration is near the coast, then the sediment movement is toward the ocean. Consequently, at a given location this produces a higher concentration in the upper part of the water column than the lower. Although this sediment will gradually settle, the low settling velocity and the high advection offshore, maintains the profiles shown in Figure 2a. 3.2. Upwelling Favorable Wind With Stratification (Calculation 2) [20] In the previous calculation the water was assumed homogeneous. However, in shelf edge regions stratification is present and its influence upon the wind-induced distribution of sediments was investigated in a subsequent calculation (calculation 2, Table 1). The temperature profile Figure 2a. Contours for the nearshore region of the model of (i) across-shelf velocity hui (cm s 1 ), (ii) along-shelf velocity hvi (cm s 1 ), (iii) across-shelf sediment concentration hci (mg L 1 ), and (iv) across-shelf sediment transport huci (10 3 Kg m 2 s 1 ) from calculation 1, a homogeneous sea region with an upwelling favorable wind (calculation 1). ( Note: in all contour plots, a solid contour indicates a positive value; the zero line is denoted by a dotted and dashed contour; the dashed line denotes a negative value.)

16-6 XING AND DAVIES: IBERIAN SHELF SEDIMENT TRANSPORT Figure 2b. A snapshot of across-shelf plot of the friction velocity u * (cm s 1 ). Figure 3b. A snapshot of across-shelf plot of the temperature ( C) field. given in Figure 1b was used in all calculations involving stratification effects. Obviously, it is not the absolute value of temperature but its gradient that is important in these calculations. [21] The across-shelf flow (Figure 3a) was comparable to that found previously (Figure 2a). The on-shelf flow in the bottom boundary layer, produces an upwelling of density surfaces (Figure 3b) at the shelf edge, with frictional effects and associated bed turbulence producing a vertically wellmixed bottom boundary layer (Figure 3b). Horizontal density gradients in the region of the shelf edge produce an along-shelf flow through the thermal wind relation, modifying the v component of velocity found previously (compare Figures 3a and 2a). [22] The existence of the high vertical density gradient (denoted by the close proximity of the 9.0 and 8.75 C isotherms between x = 33 and 22 km) due to upwelling of cold water, effectively suppresses the vertical diffusion of turbulence in this region. Consequently, sediment is confined to the near-bed region (Figure 3a). This is a very different situation than in the homogeneous case where sediment can diffuse to a greater height in the water column. In shallower water (depths less than 100 m) stratification is weak, vertical diffusion is strong and the sediment distribution is in close agreement with that found in calculation 1 (compare Figures 3a and 2a). As stated previously the off-shelf flow in the surface layer is similar to that found in the barotropic case. Also the nearshore distributions of sediment are comparable and are the main source of sediment for advection. Consequently, in the surface layer the sediment concentration is similar to that found in the homogenous case, and is mainly dominated by surface off-shelf advection. In the present calculation, in the shelf edge region, the location of the top of the Figure 3a. As Figure 2a but with climatic vertical stratification. (calculation 2).

XING AND DAVIES: IBERIAN SHELF SEDIMENT TRANSPORT 16-7 Figure 4. As Figure 2a but with a downwelling favorable wind. (calculation 3). turbulent bottom boundary layer (not shown), coincides with the transition from on shelf to off-shelf flow, and effectively a two-layer system exists with little or no vertical diffusion between layers. Consequently there is a strong vertical gradient in the sediment concentration at the position of near-zero flow. [23] Advective flow also has a major role in determining the vertical profile of sediment at the shelf edge. In the near- Figure 5a. As Figure 2a but with a downwelling favorable wind and stratification. (calculation 4).

16-8 XING AND DAVIES: IBERIAN SHELF SEDIMENT TRANSPORT Figure 5b. A snapshot of across-shelf plot of the temperature field ( C) and stream function (m 2 s 1 ) (solid is positive; dashed is negative) and contour intervals of 0.2 m 2 s 1 with a downwelling favorable wind and stratification. (calculation 4). bed region frictional effects reduce the on shelf flow below that higher in the water column, with flow reaching near zero at the level of the thermocline. This together with sediment pick up at the bed gives rise to the near-bed sediment layer shown in Figure 3a. In the upper layer, above the thermocline, velocity reduces with distance below the Figure 6b. Across-shelf contours of instantaneous sediment concentration (mg L 1 ) and friction velocity u * (cm s 1 ) at time t = 4 / 12 T, with T the M 2 tidal period (for calculation 5). surface wind-forced layer, giving rise to the linear variation in sediment concentration (Figure 3a). 3.3. Downwelling Favorable Homogeneous (Calculation 3) [24] Changing the direction of wind forcing, produces a downwelling flow at both coast and shelf edge (Figure 4). Figure 6a. As Figure 2a but with tidal forcing and a specified (fixed) stratification. (calculation 5).

XING AND DAVIES: IBERIAN SHELF SEDIMENT TRANSPORT 16-9 Figure 6c. Profiles of the u (contour interval 2.5 cm s 1 ) and v components of velocity (cm s 1 ), sediment concentration (C) (mgl 1 ) (contour interval 0.02mg L 1 ), and time series of friction velocity u * (cm s 1 ) at position (a) over two tidal cycles from calculation 5. The magnitudes and spatial distributions of the acrossand along-shelf flows, friction velocities (not given) were not significantly different from those found in the upwelling case (Figure 2a), except for the reversal in flow directions. [25] Without any vertical stratification to inhibit the upward diffusion of sediment, it can diffuse away from the bottom boundary layer and is advected toward the coast by the on-shelf surface current (Figure 4). Any offshore advection in the bottom boundary layer is small due to weaker currents in the bed region, and the rapid vertical diffusion of sediment out of this layer, into the surface layer where it is advected toward the coast. These processes explain the time averaged sediment concentration hci and transport huci shown in Figure 4. 3.4. Downwelling Favorable, Stratified (Calculation 4) [26] Although the initial stratification was identical to that used previously (calculation 2), the flow was induced by a downwelling favorable wind (calculation 4, Table 1). The main features of the across-shelf flow (Figure 5a) are comparable to those found in the homogeneous case, although there are differences in the shelf edge region. These arise because in this case, the warmer and consequently Figure 7a. Across-shelf contours of the temperature field ( C), sediment concentration (C) (mg L 1 ), stream function (m 2 s 1 ), and friction velocity u * (cm s 1 ) at time t = 4 / 12 T, for calculation 6.

16-10 XING AND DAVIES: IBERIAN SHELF SEDIMENT TRANSPORT Figure 7b. As Figure 2a but with only tidal forcing and a time-evolving density field (calculation 6). lighter surface water is advected on shelf where downwelling occurs followed by convective mixing producing a vertically well-mixed water column on the shelf, and a frontal system at the shelf edge (Figure 5b), which influences the along- and across-shelf flow in this region. On the shelf where the water is vertically well-mixed the alongshelf flow is comparable to that found in the homogeneous case (compare Figures 5a and 4). Although at the shelf edge it is substantially different due to internal pressure gradients associated with the density gradients in this area. Also on the shelf and at the shelf edge, the sediment concentration and across-shelf transport is similar to that found earlier (compare Figures 5a and 4), for the reasons discussed previously. 3.5. Tidal Influence With Fixed Stratification (Calculation 5) [27] Before considering how the internal tide influences the across-shelf wind-induced sediment transport, and the interaction between the wind and the internal tide [Xing and Davies, 1997] it is useful to examine sediment transport induced by the internal tide. In these calculations the model is forced by the M 2 barotropic tide at the oceanic open boundary, and an along-shelf flow at the tidal period as described earlier. The internal tide is generated by internal pressure gradients as the temperature field is advected over the shelf slope. In an initial calculation the temperature field was identical to that used previously (Figure 1b), but was maintained constant in time. Consequently, an internal tide was not produced, although the influence of the stratification upon the vertical diffusion of sediment was included. [28] In this calculation, as previously the model was integrated for 15 days, by which time the flow field was established. In the tidal case, in order to determine the residual movement of sediment it was necessary to remove the oscillatory component by harmonic analysis or in the case of a single constituent, by time averaging over a tidal period. In the absence of wind effects, and internal Figure 7c. As Figure 6c but only u and v current profiles (cm s 1 ) for calculation 6.

XING AND DAVIES: IBERIAN SHELF SEDIMENT TRANSPORT 16-11 Figure 8a. As Figure 2a, but with tidal and upwelling favorable wind forcing (calculation 7). pressure gradients produced by time evolving stratification, this is the tidal residual due to rectification by the nonlinear terms in the model [Tee, 1980, 1985, 1987; Xing and Davis, 2001b]. [29] Contours of the across-shelf (u) tidal residual show (Figure 6a) a weak (of order 1 cm s 1 ) on-shelf current at the surface, with a slightly larger (about 2.6 cm s 1 )offshelf current at the seabed. The along-shelf flow is much stronger with a shelf edge jet exceeding 15 cm s 1. [30] An instantaneous picture (at t = 4/12T, with T the M 2 tidal period) shows (Figure 6b) that the friction velocity is nearly constant across the shelf, with u * at this time Figure 8b. Across-shelf contours, (for the nearshore region of the model) of temperature ( C), stream function (m 2 s 1 ), sediment concentration (C) (mg L 1 ), and friction velocity u * (cm s 1 ) at time t = 4 / 12 T during the tidal cycle, from calculation 7.

16-12 XING AND DAVIES: IBERIAN SHELF SEDIMENT TRANSPORT maximum in the region approximately 20 30 km from the coast, giving rise to the time averaged maximum in sediment concentration, and bottom boundary layer thickness in this region (Figure 6a). Since the residual flow is offshelf in the near-bed region this produces the small offshelf transport shown in Figure 6a. This calculation shows that the barotropic tide in the region contributes little to sediment movement compared with the wind-induced circulation described earlier. 3.6. Internal Tidal Influence (Calculation 6) [31] In this calculation the boundary forcing and the initial temperature were as previously. However, the density stratification evolved with the flow field, thereby giving internal pressure gradients and an internal tide. The lateral oscillatory advection of the temperature field across the bottom boundary layer due to the on-shelf/off-shelf movement of the tide produces a well-mixed bottom boundary layer on the shelf [Chen and Beardsley, 1995] where u * is large. The presence of the tidal front (Figure 7a) leads to across-shelf pressure gradients which drive an along-shelf flow (Figure 7b) in addition to that produced by the tidal rectification [Tee, 1980, 1985, 1987; Ou and Maas, 1986, 1988; Xing and Davies, 2001b]. Also, an on-shelf/off-shelf circulation in the shelf edge region (Figure 7b), and associated sediment transport is produced. [32] Associated with the internal tide there are upwelling and downwelling regions on the shelf (Figure 7a), leading to a larger spatial variability in u * (Figure 7a) and suspended sediment (Figures 7a and 7b) than previously (Figures 6a and 6b). Although an internal tide is generated, the circulation and bed stress associated with it are weak and sediment concentration is not appreciably different than found previously (calculation 5). The presence of the internal tide can be seen in the time series of the u and v profiles of velocity at position (a) (Figure 7c). Figure 8c. Contours of the terms u@c/@x, w@c/@z, w s @C/@z, and (@/@z) [K v (@C/@z)] (mg L 1 s 1 ) averaged over a tidal cycle from calculation 7. exceeding u *c (taken as 0.9 cm s 1 ), and hence sediment is suspended on the shelf, although not along the shelf slope where u * is less than u uc (Figure 6b). The oscillatory nature of the tide means that u * varies over a tidal cycle, and to understand the dynamics of tidal sediment suspension it is necessary to examine this in detail before considering contours of cross-shelf sediment concentration and transport. Time series of the u and v components of velocity at position (a) (Figure 1a), show a uniform oscillatory flow above a frictionally retarded bottom boundary layer (Figure 6c), with u * reaching 1.0 cm s 1 ; a maximum value only slightly above that required to suspend the sediment. At times of maximum u * sediment is suspended in the near-bed layer. Vertical diffusion moves sediment higher in the water column, giving rise to a maximum concentration in this region at a later time than at the bed. Calculations showed that u * and vertical diffusivity was a 3.7. Internal Tide and Upwelling Wind (Calculation 7) [33] As discussed earlier, an upwelling favorable wind produces a significant vertical temperature gradient on the shelf and at the shelf slope. Such conditions significantly modify the internal tide due to increased density gradients in the near-bed region [Xing and Davies, 1997]. [34] The residual across-shelf velocity (Figure 8a) shows the same characteristics as in the wind-driven flow case (Figure 3a), although with more spatial variability in the shelf edge region. However, on the shelf in shallow water, the flow field is consistent with that found previously (Figure 3a). The reason for the change in the shelf edge region is that the upwelling has modified the density field in this area (Figure 8b), leading to a change in across- and along-shelf flow. At the coast stratification is comparable to that found in the absence of the tide (compare Figures 8b and 3b) and hence the flow is comparable to that found previously. Regions of upwelling and downwelling (Figure 8b) now occur on the shelf associated with the internal tide, which were not found in the upwelling wind only solution. These are similar to those found with the internal tide (calculation 6), although their magnitude has been increased. Associated with this circulation are areas of enhanced bottom current giving regions of increased, u * (Figure 8b).

XING AND DAVIES: IBERIAN SHELF SEDIMENT TRANSPORT 16-13 (I) Figure 8d. Contours of the temperature anomaly ( C), profiles of the u and v components of velocity (cm s 1 ), contours of log 10 of viscosity (m 2 s 1 ), sediment concentration (mg L 1 ), and time series of friction velocity u * (cm s 1 ) over two tidal cycles at Positions (a) (Figure 8d(i)), (b) (Figure 8d(ii)), and (c)(figure 8d(iii)) from calculation 7. [35] An instantaneous picture of the across-shelf sediment distribution (Figure 8b) shows similar characteristics to that found previously (Figure 3a). In particular, the large vertical gradient in the sediment distribution in the region between 20 and 30 km offshore where the vertical stratification is strong. Here the sediment concentration above the thermocline is larger than that below, due to offshore advection from the coastal region. As previously in the coastal region, the vertical stratification is weak, and sediment concentration is a maximum. [36] A significantly higher time averaged concentration (Figure 8a) occurs, than that found previously with just an upwelling wind (Figure 3a), or due to the internal tide alone (Figure 7a). Obviously this is in part due to the addition of both tidal and wind forcing. However, as shown by Xing and Davies [1997] an upwelling wind changes the stratification in such a way that the internal tide on the shelf is enhanced. The increased bed stress, and in particular the circulation cells associated with the internal tide (which were not present in the wind only induced circulation), produce an enhanced erosion of the sediment that is then advected in an off-shelf direction in the surface layer by the wind-driven mean flow (Figure 8a). [37] The fact that the wind changes the density field and hence influences the internal tide shows that there is a high degree of nonlinearity in the system, and the tidal flow and wind flow cannot be linearly superimposed. Also, the nonlinear terms produce a tidal residual flow Xing and Davies [2001b] which will contribute to the movement of sediment. A third source of residual flow is that due to the pressure gradients associated with the tidal fronts (Figure 8b). This flow will also influence the movement of sediment. [38] The relative importance of the lateral advection (u@c/@x), vertical advection (w@c/@z), settling ( w s @C/ @z) and diffusion ( (@/@z) (K v )(@C/@z)) averaged over a tidal cycle is given in Figure 8c. A nearly uniform offshore wind-driven advection of sediment occurs in the surface layer, with a maximum in the near-coastal region where surface current and sediment concentration are a maximum. Here there is a maximum on shore advection of sediment in the bottom boundary layer. In the nearshore region this is more spatially uniform than at the shelf edge, as the bottom advective velocity in this area is due to the upwelling wind. In the shelf edge region a more spatially variable distribution occurs, due to the residual flow produced by the internal tide. Similarly, the vertical advection terms show significant spatial variability in the shelf edge region, due to the residual flow induced by the upwelling and downwelling flows associated with the internal tide. This term shows a maximum at the location of maximum gradient in the

16-14 XING AND DAVIES: IBERIAN SHELF SEDIMENT TRANSPORT (II) (III) Figure 8d. (continued)

XING AND DAVIES: IBERIAN SHELF SEDIMENT TRANSPORT 16-15 Figure 8e. Contours of the terms @C/@t, u@c/@x, w@c/@z w s @C/@z, and (@/@z) [K v (@C/@z)] (mg L 1 s 1 ) over a tidal cycle at position (a) from calculation 7. concentration profile. Very close to the seabed, where there is a rapid decrease in sediment concentration, the settling term is a maximum. Above the bed the upwelling current, in the bottom boundary layer advects lower concentration sediment water into the region, producing a lower sediment concentration than in the upper part of the water column. [39] In the surface layer the sediment concentration has increased due to the horizontal advection of sediment into the region. Consequently, the sign of the concentration gradient and hence the settling term changes. Although the magnitude of the settling term is a maximum at the position of maximum sediment concentration gradient, material is settling at a slower rate than it is being advected into the region by the surface current and consequently sediment concentration will increase in the surface layer until a dynamic balance is obtained. The vertical diffusion term will also contribute to this balance. However because the diffusion coefficient in the offshore region is small, due to the influence of stratification, the effect of this term is small despite the high sediment concentration gradient. In the near-coastal region, the water column is well mixed, and consequently the vertical diffusion coefficient increases and this term becomes more important. Above the near-bed region where settling is important, the main balance is between lateral advection and vertical diffusion. [40] The dynamics of the temporal and spatial variability of the sediment can be appreciated by considering time series at a number of locations from shelf edge (location (a), h = 200 m) to midshelf (location (b), h = 125 m) to a near coastal (location (c), h = 95 m) (Figure 1a). Comparing the time series of current profiles at location (a) with that found previously, it is evident that the uniform flow in the vertical, above a frictionally retarded bottom boundary layer, found in the tidal calculation has been modified by the presence of the internal tide leading to a maximum u-velocity close to the bed (see the 15 cm s 1 contour Figure 8d(i)), and higher in the water column. The flow has also been modified by the across-shelf component of the wind-driven circulation. The along-shelf flow is dominated by the wind-driven current, but is modulated by the tidal velocity. Internal pressure gradients associated with the bottom tidal fronts also contribute to this flow. The friction velocity shows a mean value modulated by changes produced by the tide. The near-bed sediment concentration shows a slight increase at times of maximum friction velocity, although the concentration in this region is small compared to that in the upper part of the water column, due to the surface advection of sediment from the nearshore region. [41] As described previously in connection with Figure 8b, at this location there is a well-mixed surface layer where vertical mixing due to the wind is large (Figure 8b) below which there is a sharp thermocline where turbulence is suppressed. The location of this thermocline and its intensity changes with time as the internal tide propagates on and off the shelf as shown by the temperature anomaly plot (Figure 8d(i)). Associated with the internal tide are large vertical velocities that can produce significant vertical displacements in the sediment concentration at the level of the thermocline (Figure 8d(i)). [42] As discussed in the case of wind-induced flow only, the mean position of the thermocline approximates the boundary between on shelf and off-shelf flow, and it is the off-shelf flow at this location that contributes to the high sediment concentration above the thermocline. To understand this high sediment concentration which has originated in the nearshore region we examine the time series at location (b) (Figure 8d(ii)). [43] At position (b) the vertical stratification is weaker, and occurs at approximately mid-water. An intensification

16-16 XING AND DAVIES: IBERIAN SHELF SEDIMENT TRANSPORT Figure 8f. Contours of across-shelf sediment concentration hci (mg L 1 ), and across shelf sediment transport huci (10 3 Kg m 2 s 1 ) from calculation 7A (w s =2w o s ) (Figure 8f(i)), calculation 7B (w s = 3 w o s ) (Figure 8f(ii)) and calculation 7C (w s =4w o s ) (Figure 8f(iii)). of the cross-shelf current occurs at approximately mid-water at times of on shelf flow, associated with a rise in the temperature anomaly surfaces at mid-depth due to internal tide propagation. In the region of the thermocline diffusivity is reduced, and the gradient of the sediment concentration is a maximum. A significant displacement (of order 20 m) at the level of the thermocline in both the contours of viscosity and concentration occurs as the internal tide propagates through the region. [44] In shallower water ( position (c)) there is a linear variation in temperature (Figure 8d(iii), temperature anomaly distribution) and consequently no mid-water thermocline to support a decrease in turbulence, or internal wave propagation. At times of maximum u * sediment is suspended at the bed, and moved toward the coast in the bottom boundary layer by the onshore bottom current at these times. Maximum sediment concentration in the surface layer occurs at different times to that in the bed layer and is associated with the time of maximum offshore current which advects sediment into the region. The phase difference between times of maximum offshore transport and peak u * and onshore flow explains the wave-like time variation in the sediment concentration profile and its absence in the temperature field, which has little horizontal gradient at this location. This is a different process to that which occurred in the region of the thermocline at position (b), although it is responsible for the differences in time between maximum sediment concentration in the near-surface and near-bed regions. [45] To understand the various dynamic balances, contours through the vertical and over the last tidal cycle, of terms (@C/@t), (u@c/@x), (w@c/@z), ( w s @C/@z), and (@)/ (@z)[k v (@C/@z)] (over the last tidal cycle shown in Figure 8d(i)) at position (a), are given in Figure 8e. [46] The @C/@t term shows a rapid change in the first part of the tidal cycle, as the position of maximum sediment concentration moves down in the water column due to the downwelling (term w@c/@z) event as the tide propagates through the region. At this time the u component of velocity is off shelf, and hence the term u@c/@x is negative in the upper part of the water column. Subsequently, when the flow reverses this term becomes positive. Also, there is an upwelling event in the bottom boundary layer. However, the time derivative becomes negative, suggesting that sediment is being advected out of this region. The settling velocity and diffusion terms are small over the majority of the water

XING AND DAVIES: IBERIAN SHELF SEDIMENT TRANSPORT 16-17 column, reaching a maximum in the region of maximum concentration gradient. 3.8. Sensitivity to Settling Velocity (Calculations 7A 7C) [47] To examine the influence of settling velocity upon sediment concentration the previous calculation was repeated with w s =2w o s,3w o s, and 4w o s, (calculations 7A 7C) where w o s =5 10 4 ms 1, the settling velocity used previously. Since the sediment concentration does not affect the dynamics the flow fields and mixing were as previously. However, as the settling velocity was increased, the time averaged sediment concentration in suspension is rapidly reduced (Figures 8f(i) 8f(iii)). The main features of the vertical profile, namely, an enhanced concentration in the near-surface layer are maintained, as is the concentration contour (although with reduced magnitude) at the top of the bottom boundary layer. [48] Although the time variation of the sediment concentration at position (a) (Figures 8g(i) 8g(iii)), is similar to that found previously (Figure 8d(i)), the effect of increasing the settling velocity is to reduce the concentration of the suspended sediment in the water column (compare Figures 8g(i) 8g(iii)). This reduces the sediment concentration gradient at the top of the bottom boundary layer (Figures 8g(i) 8g(iii)). Since it is the product of this gradient and the settling velocity that determines the rate of deposition from the surface layer, this term is also reduced. A consequence of this is that any sediment in the surface layer can be advected farther offshore. This is evident in the surface location of the 2 mg L 1, concentration contour (Figures 8f(i) 8f(iii)). [49] The time variation of @C/@t, u@c/@x, w@c/@z, w s @C/@z, and @/@z(k V @C/@z) (not shown) are similar to those shown previously, although their maximum values occur closer to the bed reflecting the reduced sediment concentration in the upper part of the water column. This calculation shows that as the settling velocity increases more sediment remains in the near-bed region and the concentration in the water column decreases. Also the concentration in the upper part of the water column remains higher than that below, even with a four fold increase in w s and is advected farther offshore. This illustrates that the horizontal as well as the vertical distribution of sediments will depend upon their settling velocity. Figure 8g. Contours of the profile of sediment concentration (C) (mg L 1 ) over two tidal cycles at position (a) for (i) w s =2w o s (calculation 7A), (ii) w s =3w o s (calculation 7B), (iii) w s =4w o s (calculation 7C). 3.9. Internal Tide and Downwelling Wind (Calculation 8) [50] Since a well-mixed region on the shelf (Figure 5b) is produced by a downwelling favorable wind any internal tide generated at the shelf slope cannot be supported on the shelf. The time-averaged across-shelf current (Figure 9a), shows a similar distribution on the shelf to that found without the tide, although in the shelf slope region, where stratification intersects the topography (Figure 9b), the difference in stream function (compare Figures 5b and 9b) indicates the presence of an internal tide. The along-slope flow in the shelf edge region contains a contribution from the across-shelf density gradient (Figure 9b). [51] The spatial distribution of the friction velocity on the shelf is consistent with that due to the barotropic tide and a downwelling wind (Figure 9b). Also, it is significantly larger than that due to the upwelling wind and the internal tide (compare Figures 9b and 8b, note differences in scale). To compare the two cases and before, we consider the time averaged sediment concentration and transport, we will consider the magnitude and spatial distributions of the various terms during the downwelling wind event as opposed to the upwelling situation. The time averaged horizontal advection of sediment term (Figure 9c), shows an onshore advection of sediment in the surface layer, increasing close to the coastline where sediment concentration is a maximum. A comparable offshore advection occurs in the near-bed region. In the shelf edge region there is a small on shelf advection of sediment at depth associated with the residual produced by the internal tide in this region. In this area the vertical velocity is significant and the vertical advection term is nonzero. Elsewhere, except close to the coast where downwelling is important the vertical advection term is negligible. Unlike in the upwelling case, sediment concentration at all locations decreases with height above the seabed (compare Figures 9a and 8a), and hence the settling velocity term is significantly larger than the other terms, with its largest magnitude in the near-bed and near-coastal regions where sediment concentration is a maximum (Figure 9a).