MICHAEL W. STACEY. Department of Physics, Royal Military College of Canada, Kingston, Ontario, Canada S. POND

Transcription

1 2366 JOURNAL OF PHYSICAL OCEANOGRAPHY Dependence of Currents and Density on the Spring Neap Cycle and the Diurnal Inequality in Burrard Inlet, British Columbia: Simulations and Observations MICHAEL W. STACEY Department of Physics, Royal Military College of Canada, Kingston, Ontario, Canada S. POND Department of Earth and Ocean Sciences, The University of British Columbia, Vancouver, British Columbia, Canada (Manuscript received 2 August 2002, in final form 20 May 2003) ABSTRACT Observations of the circulation in a hole near a constriction in Burrard Inlet are simulated using a twodimensional (i.e., laterally integrated) numerical model. The model uses a level-2 version of the Mellor Yamada turbulence closure scheme. During spring tides, when mixing is at its most intense, the density in the hole decreases (increases) during the large (small) floods, and there is an up-inlet current pulse into the hole during each flood regardless of the flood s strength. During the large floods in particular, the simulation is significantly improved if the explicit influence of horizontal spatial variations on the production of turbulent kinetic energy is taken into account. During neap tides the simulated density is much less variable, and the currents in the hole are much weaker, in agreement with the observations. The model differs from the observations in that the simulated current pulses are significantly weaker than the observed pulses, possibly because the cross-channel averages computed by the model may not be a good estimate of the observed currents. 1. Introduction Burrard Inlet (Fig. 1) is about 20 km long and is never deeper than about 65 m. At two of its shallowest locations, First and Second Narrows, the water depth is 15 and 19 m below datum, respectively. The western end of Burrard Inlet opens out into the Strait of Georgia. Its eastern end connects to Indian Arm, which is a fjord about 20 km long, 2 km wide, and with a maximum depth of about 220 m. Currents as large as about 2 m s 1 can occur in First and Second Narrows on large tides. Much of the net, M 2 barotropic energy flux into Burrard Inlet can be explained by frictional dissipation over First and Second Narrows (de Young and Pond 1989). About 18% of the available barotropic energy entering Burrard Inlet is dissipated directly by friction, with about 9% being dissipated at each narrows. Freshwater runoff into Indian Arm/Burrard Inlet is quite small. The largest discharge is at the Buntzen Power Stations (Fig. 1) with an annual average discharge of about 20 m 3 s 1. The total annual average discharge from all sources is about 40 m 3 s 1. The runoff has a Corresponding author address: Dr. Michael W. Stacey, Department of Physics, Royal Military College of Canada, P.O. Box 17000, Stn Forces, Kingston, ON K7K 7B4, Canada. stacey-m@rmc.ca noticeable influence on the circulation however. In addition to the surface outflow, the stratification caused by the runoff can influence the strength of the internal tide in Indian Arm (Stacey et al. 1991) and may influence the timing of renewal events into Indian Arm (de Young and Pond 1988). Deepwater renewal of Indian Arm has been observed to occur (or be enhanced) during neap tides (de Young and Pond 1988) when tidal mixing in Burrard Inlet is at a minimum. Less surface water is mixed downward during neap tides, and therefore water entering Indian Arm from Burrard Inlet is denser and more likely to sink to the bottom during neap tides. Stacey et al. (2002) successfully simulated this fortnightly enhancement of the deep-water inflows by using a Mellor Yamada level- 2 turbulence closure scheme (Mellor and Yamada 1982) and very fine spatial resolution. The closure scheme is described in some detail in section 3a of this paper. It was found that the simulation of the subtidal circulation in Indian Arm was improved by including the explicit influence of horizontal spatial variations in the flow field on the rate of turbulent kinetic energy production [see the second term on the rhs of Eq. (5b) in section 3a]. The simulated increase with time in bottom density in Indian Arm, caused by the renewal events, was improved by the inclusion of this horizontal spatial dependence. Also, the strength of the near-surface subtidal outflow in Indian Arm was better simulated because the 2003 American Meteorological Society

2 NOVEMBER 2003 STACEY AND POND 2367 FIG. 1. Plan view of Burrard Inlet and Indian Arm. The mooring locations are QB, 66, and 48. Stations 66 and 48 are located in holes just up-inlet of First and Second Narrows, respectively. The dashed line shows the location of the sill separating Burrard Inlet and Indian Arm [adapted from Fig. 1 of Isachsen and Pond (2000)]. extra mixing in Burrard Inlet caused by inclusion of this horizontal dependence resulted in a larger outward nearsurface pressure gradient force. With the goal of investigating mixing in Burrard Inlet, field experiments were mounted in 1995 and 1997 (Isachsen 1998; Isachsen and Pond 2000). In 1995 between the beginning of March and the end of June, moorings were deployed at three locations: outside First Narrows and at the deepest points inside First and Second Narrows (Figs. 1 and 4). At each mooring, S4s (electromagnetic current meters) were deployed 6 and 16 m above the bottom (about 20 and 30 m below datum at Station QB and about 50 and 60 m below datum at Stations 66 and 48). In 1997, acoustic Doppler current profiler (ADCP) measurements were made near Second Narrows. In this paper, the observations made in 1995 will be compared with results from the numerical model described by Stacey et al. (2002). The observations have robust properties that can be simulated by the model as long as due consideration is given to the parameterization of the diffusion terms and to the turbulence production downstream of the Narrows. 2. The observations Figures 2 and 3 are taken from Isachsen and Pond (2000). Figures 2a and 2c show that during the spring tides there is greater temporal variability in the density field than during the neap tides, the variability being greatest inside Second Narrows. Figures 2a and 2b show that during the spring tides there are strong up-inlet current pulses into the holes up-inlet of First and Second Narrows, but that during the neap tides the pulses are much less intense or do not occur at all. Figure 3 shows the detailed response in the hole inside Second Narrows during a particular spring tide. One sees that there are strong, up-inlet current pulses during flood tides [i.e., while the surface height is increasing (Fig. 3a)] but that the density in the hole (Fig. 3c) increases during small floods and decreases during large floods. During the small floods, denser water from down-inlet flows into the hole; during the large floods, even though there is still inflow from down-inlet, tidal mixing is strong enough to decrease the density in the hole. Isachsen and Pond (2000) showed that during spring tides the tendency for the density to increase (decrease) during small (large) floods is quite general inside Second Narrows, although the magnitudes of the increases (decreases) exhibited considerable variation. They attributed the extra mixing during the large floods to complex turbulent motions (hydraulic jumps, etc.) on the lee side of Second Narrows. The ADCP observations made in 1997 showed that the motion on the lee side of Second Narrows during strong floods was complex and unordered, suggesting the presence of boils extending throughout the water column. During small floods there was no extensive mixing over the entire water column and the water column remained highly stratified. Isachsen and Pond

3 2368 JOURNAL OF PHYSICAL OCEANOGRAPHY FIG. 2. Observations recorded by Isachsen and Pond (2000) for their whole measurement period: (a) the water level at Station 66; (b) the horizontal speeds from the deeper current meters at Station QB (top), Station 66 (middle), and Station 48 (bottom); (c) same as (b) but for sigma t. [This figure is the same as Fig. 2 of Isachsen and Pond (2000).] suggested that mixing in the lee of the sill must be accounted for if the temporal dependence of the circulation near Second Narrows, and probably near First Narrows also, is to be accurately simulated. 3. The model The model used here is described in Stacey et al. (2002) and the references listed therein. It is two-dimensional (i.e., laterally integrated), nonlinear, and hydrostatic. Temperature and salinity are not solved for separately, but rather an initial density field (calculated from temperature and salinity) is prescribed and then allowed to evolve. The model can include the influences of freshwater input, the winds, and the tides, although for the study presented here the winds are not taken into account. As noted by Isachsen and Pond (2000), the complex geometry and stratification of Burrard Inlet may limit the applicability of simple models when it comes to simulating the circulation in the region of First and Second Narrows. Visual observation (by S. Pond) of surface disturbances in the lee of Second Narrows suggests significant cross-channel variability. However, it will be shown that this model can simulate important aspects of the circulation as long as particular attention is paid to the mixing terms, which are now described in much the same way that they were presented by Stacey et al. (2002). a. The eddy diffusion terms The vertical diffusion coefficients for momentum and density, A V and K V, are expressed as AV lqsm and KV lqs H, (1) where S M and S H are flow-dependent, dimensionless parameters (Mellor and Yamada 1982), l is a length scale, and q is a velocity scale, where k q 2 /2 is the turbulent kinetic energy divided by the water density. The prescribed length scale [ l l erf (H z) ] max (H ) [ ] (z ) erf (2) (H ) [where 0.4 is von Kármán s constant, H(x) isthe mean water depth, and (x, t) is the surface displacement] gives l the form appropriate for a logarithmic

4 NOVEMBER 2003 STACEY AND POND 2369 FIG. 3. Observations for a 4-day period during a spring tide in May 1995 at Station 48: (a) water level, (b) temperature, (c) sigma t, (d) east west velocity, and (e) north south velocity. The thin line is for 16 m above the bottom, and the thick line is for 6 m above the bottom; 16 May (i.e., 16/5) is yearday 136. [This figure is the same as Fig. 3 of Isachsen and Pond (2000). They note that these raw data at 15-min intervals have not had the salinity and density corrected for offsets, and the few comparisons with CTD data suggest that the salinity and hence the density values from the current meter 16 m off the bottom are low. Thus the densities at the two levels are closer after the large floods than shown in the figure; CTDs show them to be the same after strong floods.] layer near the surface and the bottom. The upper bound on l (l max ) is defined as l max L H (H ), where the constant L H is the proportionality constant between l max and the total water depth. Stacey et al. (2002) used L H 0.2 whereas previous publications (e.g., Stacey et al. 1995) used L H The rationale for this change came from Burchard et al. (1998) who found that a triangular shape for l produces better estimates of vertical mixing than does a parabolic shape, at least for channel flows. Examination of these two shapes shows that for the parabolic (triangular) shape L H 0.1 (0.2). An additional limit put on l is that it cannot be larger than the Osmidov length scale. That is, k 2 l 0.56, (3) where N is the Brunt Väisälä frequency. This limit was found to be particularly important in Indian Arm so as to prevent l from becoming unrealistically large. Other N 2 authors (e.g., Galperin et al. 1988) have also found it necessary to impose this limit on l. It is assumed that the local production of turbulent kinetic energy is balanced by local dissipation so that the velocity scale q is determined from the algebraic equation Ps PB, (4) where the dissipation rate and the shear and buoyancy production rates P S and P B are q 3, (5a) Bl 1 U U 2 PS uw u, and z x (5b) gkv PB, z (5c)

5 2370 JOURNAL OF PHYSICAL OCEANOGRAPHY FIG. 4. The model grid, for the density grid points. Stations 48 and 66 are labeled. The open boundary of the model is to the right on the figure. where B ; u and w are the turbulent velocity fluctuations in the along-channel and vertical directions, respectively; and and U are the water density and along-channel velocity, respectively (Mellor and Yamada 1982). The Reynolds stresses are expressed as (Mellor and Yamada 1982) U uw A and (6a) V z 2 q 3A1l U 2 2 u 2uw, (6b) 3 q z 3 where A The second term on the rhs of (5b), which is usually not taken into account, was included by Stacey et al. (2002) and found to have a noticeable influence on the circulation in Indian Arm. Note that the term is positive when U/ x 0, and so it will enhance turbulent energy production on the lee side of sills and will therefore tend to increase the rate of mixing there, as observed by Isachsen and Pond (2000) for Second Narrows. A lower bound of the form (A V, K V) an (7) is imposed on the mixing coefficients, where a 0 is a sitespecific constant, in order to crudely account for the influence of breaking internal waves of high frequency. Stacey et al. (2002) used a ( ) m 2 s 5/2 for Burrard Inlet (Indian Arm) based on values estimated from observations by Isachsen and Pond (2000) (deyoung and Pond 1988). To keep A V and K V bounded, the lower bound was never allowed to be larger than the value (7) would have with N s 2. FIG. 5. The initial sigma t field. b. The model grid and the inputs The model grid (Fig. 4) has the same number of grid points (a maximum of 99 in the vertical and 200 in the horizontal) and covers the same geographic region as in Stacey et al. (2002), but the grid density is now highest in the region of Second Narrows. The horizontal (vertical) spacing is as small as 40 (0.8) m. Note the hole up-inlet of Second Narrows, about 23 km from the head of Indian Arm. It is the observations from this hole (station 48) with which the model will be compared. The initial density field is shown in Fig. 5. It was constructed from the CTD profiles that were collected when the S4s were serviced about 10 days before the observations shown in Fig. 3 were collected. Freshwater inputs were included for the Capilano and Seymour Rivers and for the Buntzen Power Stations (Fig. 1). The tides were input by prescribing the surface height at the open boundary of the model using the tidal constituents listed in Table 1. The same constituents were used by Stacey et al. (2002). The density at the open boundary was prescribed using the data from the nearest CTD station. CTD profiles were made at approximately monthly intervals, when the S4s were being serviced. Values for the density between these times were estimated by linear interpolation. Starting with zero initial velocity, each simulation was spun up by holding the density constant for 2 days of simulation time. Then the density was allowed to vary and the simulation continued for a further 15 days. 4. The results a. Simulations during a spring tide Figure 6 shows the simulated tidal height, the density (expressed as sigma t) and the velocity at depths of TABLE 1. Tidal constituents from Point Atkinson used to force the numerical model. Constituent 1) S 2 2) M 2 3) N 2 4) K 1 5) P 1 6) O 1 Period (h) Amplitude (m) Greenwich phase ( )

6 NOVEMBER 2003 STACEY AND POND 2371 FIG. 6. (a) The tidal height, (b) the simulated density (expressed as sigma t), and (c) the along-channel velocity at Station 48 when the extra production term in (5b) is included. For (b) and (c) the dashed line is for a depth of 40 m, the thin solid line is for 50 m, and the thick solid line is for 60 m. The simulated output has been plotted at hourly intervals, which is the interval at which the model output was saved. 40, 50, and 60 m in the hole (station 48) just up-inlet of Second Narrows, when the extra term, u 2 U/ x in (5b), is included. Figure 7 shows the simulated circulation when the extra term in (5b) is not included. The time period plotted includes the time period covered by the observations shown in Fig. 3. The simulated sigma t and velocity at 40-m depth are shown because the simulations exhibit temporal variability at 40 m that is more like that of the observations from the deeper depths 50 and 60 m. The simulations allow water that is somewhat too dense to enter the hole, presumably then confining the variability to the shallower-than-observed depths. The distinctive dependence of the density at 50 and 60 m on the state of the tide (Figs. 3a,c) is much the same as that of the simulation at 40 m when the extra term in (5b) is included (Figs. 6a,b). During the small (large) floods the simulated density increases (decreases) quite abruptly. The simulated velocity at 40 m (Fig. 6c) shows distinctive, up-inlet pulses during the small floods, although they are only about one-tenth to onefifth as strong as those observed at 50 and 60 m (Figs. 3d,e). During the large floods the simulated pulses are FIG. 7. As in Fig. 6 but the extra term in (5b) is not included. weaker and less distinct even though they are very clear in the observations. When the extra term in (5b) is not included, the temporal dependence of the density on the state of the tide (Figs. 7a,b) exhibits noticeably less variability. This simulation differs from the observations more than does the simulation that includes the extra term. There is a somewhat abrupt increase in the simulated density at 40 m during the small floods, but the decrease in the density during the large floods is more gradual than observed. At 50 and 60 m there is not much variability in the density field at all. Note also that the mean density (i.e., the density about which the fluctuations tend to occur) is even further from the observations when the extra term is not included (cf. Figs. 3c, 6b, and 7b). The velocity (Fig. 7c) is the same as before (Fig. 6c) in that the pulses at 40 m tend to be most noticeable during the small floods, but their magnitude is even smaller and therefore even further from the observations. The simulated mean density in the hole near Second Narrows is too high primarily because of dense water coming into Burrard Inlet over First Narrows. The initial density field (Fig. 5) shows that the water is significantly denser outside First Narrows than inside. It was felt therefore that putting the open boundary of the model inside First Narrows might reduce the simulated density in the hole. We tried this by placing the open boundary at Station 66, located at the hole just inside of First Narrows (Figs. 1 and 5). The CTD observations from

7 2372 JOURNAL OF PHYSICAL OCEANOGRAPHY FIG. 8. As in Fig. 6 but the extra term in (5b) has been multiplied by a factor of 5. FIG. 9. As in Fig. 6 but the extra term in (5b) has been multiplied by a factor of 10. station 66 provided the density at the open boundary. We found that the simulated mean density in the hole near Second Narrows did indeed decrease and become much closer to the observations. We also found, however, that the density exhibited much less temporal variability and that the velocity pulses became much more intermittent. It is clear that what happens over First Narrows influences the details of the circulation in the hole near Second Narrows, even though significant mixing occurs in the approximately 10 km between the two locations. When the extra term in (5b) is included, the simulation is noticeably better. The dependence of the density on the stage of the tide is qualitatively reproduced and so are the current pulses (those that occur during the small floods at least), although these flow characteristics do not occur in the simulation at the correct depth. The observations and the simulation still differ in a number of aspects, however, and a possible reason for these differences is that the model is laterally integrated. Tidal jets flowing over the sills will not necessarily cover the entire width of the inlet and may therefore have velocities that are larger than the lateral average. To crudely account for the extra mixing that these larger velocities would cause, we have multiplied the extra term, u 2 U/ x in (5b), by a factor of 5 (Fig. 8) and then a factor of 10 (Fig. 9). Figure 8 shows that when the extra term is multiplied by a factor of 5 the simulation is closer to the observations. Now at 60-m depth, and therefore in closer agreement with the observations, the density increases (decreases) abruptly during the small (large) floods (Figs. 8a,b). The simulated mean density is smaller than before and is closer to, although still larger than, that of the observations. There are now distinct current pulses into the hole during both large and small floods (Fig. 8c), and these pulses are stronger than they were before (Figs. 6c and 7c). Figure 9 shows the density and currents when the extra term in (5b) is multiplied by a factor of 10. Now, the simulated mean density has decreased even more but the density s temporal dependence no longer resembles that of the observations. During the large floods the simulated density at times actually increases, which is opposite to the observed behavior of the density. There are still current pulses during both large and small floods (Fig. 9c) but they tend not to be much larger than those shown in Fig. 8c. Based on the temporal dependence of the density in particular, there is likely too much mixing occurring in this simulation. A simulation was done with L H 0.1 but the mean density increased and the strength of the current pulses decreased. In agreement with Burchard et al. (1998), we find that L H 0.2 is the better parameter to use. The influence of a 0 was investigated by setting a m 2 s 5/2 everywhere, but this change had much

8 NOVEMBER 2003 STACEY AND POND 2373 FIG. 10. As in Fig. 8 but for the entire simulation time, not including the two days of spinup during which the density was held constant. (Also, the simulated results from 40 m are not shown in this figure.) the same effect as changing L H to 0.1. When a 0 was increased by a factor of 10 in the regions of First and Second Narrows, the abrupt density changes became fewer and, when there was an abrupt change, it was usually an increase in density during a large flood, contrary to the observed behavior. The current pulses were fewer and generally quite weak. Additional values for a 0 were tried but no improvement was found comparable to that resulting from inclusion and augmentation of the extra term in (5b). When the lower bound on N 2 in (7) was decreased by a factor of 10, to 10 7 s 2, the mean density increased and the current pulses decreased in magnitude. The changes to the empirical constants that were tried generally resulted in somewhat or much worse simulations. A number of perturbations were tried to the initial density field also, with little appreciable change in the accuracy of the simulation. b. The spring neap cycle Figure 10 shows, for the entire simulation time, the simulated tidal height, and the simulated density and velocity at 50 and 60 m. The extra term in (5b), multiplied by a factor of 5, has been included. We see that the temporal variations in the density are largest during the spring tide and that the current pulses tend not to occur during the neap tide, in agreement with the observations (see Fig. 2). The most noticeable differences between the observations and the simulation are, as already mentioned, that the simulated mean density tends to be too high and that the magnitude of the current pulses during the spring tide is too small. Once the density is allowed to vary in the model, after about two days there is a pulse of dense water into the hole during a large flood that significantly increases the density there. This pulse appears to be a primary reason why the simulated density in the hole tends to be too high. Three possible reasons for this pulse are 1) mixing throughout the model domain is still not being completely accounted for (particularly mixing linked to cross-channel variations in the flow field, and perhaps to limited resolution around First Narrows), 2) possibly the model could have been spun up in a better way, and 3) there are certainly uncertainties in the initial density field even though it was carefully constructed from the available observations along the inlet. (Only one CTD profile was available downstream of First Narrows, and the reader is reminded of the influence that the flow across First Narrows has on the simulated density in the hole.) We feel that if wind forcing was included in the model the flows being studied here would not be significantly better simulated. Generally the winds are weak and their effects are confined to the near surface. The qualitative spring neap behavior of the model when the extra term in (5b) is included but not multiplied by 5, or when the extra term is not included at all, is similar to what is shown in Fig. 10. Note that the circulation under consideration here is quite different from, but not inconsistent with, what de Young and Pond (1988) observed. They observed that the much larger scale renewal events into Indian Arm occurred only during neap tides. 5. Discussion and conclusions A laterally integrated hydrostatic numerical model that uses a Mellor Yamada level-2 turbulence closure scheme can reproduce a number of the features of the circulation observed in Burrard Inlet by Isachsen (1998) and Isachsen and Pond (2000). During spring tides, during both the large and small semidiurnal floods, current pulses flow up-inlet into the hole located just up-inlet of Second Narrows. During the large (small) floods the density in the hole decreases (increases) in a quite abrupt manner. During the small floods, the rate of mixing is smaller than during the large floods, and water denser than what is already in the hole flows up-inlet into it, increasing its density. During the large floods, the mixing is more intense and actually causes the water density in the hole to decrease, even though there is still a current pulse into it. When the term u 2 U/ x in the expression for the production of turbulent kinetic energy is included in the model, the abrupt changes in the density that occur during the floods during the spring tides are better simu-

9 2374 JOURNAL OF PHYSICAL OCEANOGRAPHY lated. However, the simulated changes occur at a shallower depth than do the observed changes. When the extra production term is multiplied by a factor of 5 to roughly account for lateral variability, the simulated density changes occur at the correct depth. The current pulses that are observed to occur during the small floods during the spring tides also occur in the simulation, even when the extra production term is not included, but they are much smaller in magnitude in the simulation. The pulses that are observed to occur during the large floods during the spring tides do not occur in the simulation unless the extra production term (multiplied by a factor of 5) is included. Inclusion of this augmented production term also causes the magnitude of the current pulses to increase, but they are still significantly weaker than the observed pulses. Increasing the extra production term by a factor of 10 causes the simulation to become worse. During neap tides the current pulses are observed to be much weaker or not to occur at all, and they are much weaker in the simulation also. It may be that the extra production term needs to be augmented because the model underestimates the magnitude of the current pulses. The extra production term [see (5b)] depends on the cube of the horizontal velocity, and so (aside from possible errors in accurately representing the relevant horizontal length scales) the factor of 5 would be required if the velocity scale, where mixing is important, is about 1.7 times that estimated by the model. This factor is actually somewhat less than the factor by which the model tends to underestimate the current pulses. One could use the same reasoning to argue that other terms in the turbulence closure should also be augmented, but we have refrained from considering this possibility so that the scheme, except for inclusion of the extra term, will remain unmodified. Our basic premise is that mixing in the lee of the sill has a significant influence on the circulation in the hole near Second Narrows and that this extra mixing can be accounted for by including the explicit influence of horizontal variations in the flow field on the production of turbulent, kinetic energy. Cross-channel variability may be the reason why the laterally averaged model underestimates the magnitude of the current pulses. It is possible that the tidal jets that flow away from the sills of First and Second Narrows during flood tides do not span the entire width of the channel. Observation by eye (made by S. Pond) of surface disturbances caused by the subsurface flow near Second Narrows suggests that there is significant crosschannel variability. Confirmation of this suggestion, however, requires more observations and the application of a three-dimensional model. The degree to which a cross-channel average underestimates the maximum current at a given location obviously depends on the specifics of the location, but the underestimate found here for Second Narrows is not unprecedented. Tinis and Pond (2001) for example found that the maximum currents over the sill of Sechelt Inlet were 4.2 times the cross-channel average. It is possible (even likely) that increased mixing linked to lateral variations in the flow field has an influence on the circulation well beyond the lees of the sills and that therefore there are implications regarding the applicability of laterally integrated models to systems like Burrard Inlet and Indian Arm. We are presently investigating these implications using a different dataset. Acknowledgments. This work was supported by DND Academic Research Program (ARP) grants to M. Stacey and by Natural Sciences and Engineering Council (NSERC) grants to S. Pond. We thank the officers and crew of the research vessels of the Institute of Ocean Sciences for their assistance with the data collection. We also thank Mr. Igor Astapov and Mr. Terry Hutchinson for producing most of the figures. REFERENCES Burchard, H., O. Petersen, and T. P. Rippeth, 1998: Comparing the performance of the Mellor Yamada and the k two-equation turbulence models. J. Geophys. Res., 103, de Young, B., and S. Pond, 1988: The deepwater exchange cycle in Indian Arm, British Columbia. Estuarine, Coastal Shelf Sci., 26, , and, 1989: Partition of energy loss from the barotropic tide in fjords. J. Phys. Oceanogr., 19, Galperin, B., L. H. Kantha, S. Hassid, and A. Rosati, 1988: A quasiequilibrium turbulent energy model for geophysical flows. J. Atmos. Sci., 45, Isachsen, P. E., 1998: The influence of the spring neap tidal cycle on currents and density in Burrard Inlet (Vancouver Harbour), British Columbia, Canada. Ph.D. thesis, University of British Columbia, 185 pp., and S. Pond, 2000: The influence of the spring neap tidal cycle on currents and density in Burrard Inlet, British Columbia, Canada. Estuarine, Coastal Shelf Sci., 51, Mellor, G., and T. Yamada, 1982: Development of a turbulent closure model for geophysical fluid problems. Rev. Geophys. Space Phys., 20, Stacey, M. W., S. Pond, and A. N. Cameron, 1991: The comparison of a numerical model to observations of velocity and scalar data in Burrard Inlet and Indian Arm, British Columbia. J. Geophys. Res., 96, ,, and Z. P. Nowak, 1995: A numerical model of the circulation in Knight Inlet, British Columbia, Canada. J. Phys. Oceanogr., 25, , R. Pieters, and S. Pond, 2002: The simulation of deepwater exchange in a fjord: Indian Arm, British Columbia, Canada. J. Phys. Oceanogr., 32, Tinis, S. W., and S. Pond, 2001: Tidal energy dissipation at the sill of Sechelt Inlet, British Columbia. J. Phys. Oceanogr., 31,