INTERACTION OF BOTTOM TURBULENCE AND COHESIVE SEDIMENT ON THE MUDDY ATCHAFALAYA SHELF, LOUISIANA, USA

Transcription

1 INTERACTION OF BOTTOM TURBULENCE AND COHESIVE SEDIMENT ON THE MUDDY ATCHAFALAYA SHELF, LOUISIANA, USA By ILGAR SAFAK A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2010

2 c 2010 Ilgar Safak 2

3 To Besiktas 3

4 ACKNOWLEDGMENTS I would like to thank my advisor Dr. Alex Sheremet to give me the opportunity to work with him at the University of Florida. His expertise, readiness for advising, and suggestions made everything much easier for me. I have also learned from him the real scientific approach to all sorts of problems, including those in daily life. For me, this is as valuable as the research work. This research was supported by Office of Naval Research funding of Contracts No. N and N Dr. Tian-Jian Hsu from the University of Delaware is greatly acknowledged for agreeing to share with me the boundary layer model he developed. My research has benefited substantially from this model and through his guidance. He was initially an internal member in my committee, but unfortunately he had to be taken out, as he left the University of Florida. Special thanks go to Sergio Jaramillo, who is now in the University of Hawaii at Manoa, and especially Bilge Tutak, who have never hesitated to leave their works aside to be able to give me a hand for my work. Dr. Mead A. Allison from the University of Texas, Austin provided extremely valuable data, help, and guidance at every level of this study. My committee members Dr. Arnoldo Valle-Levinson, Dr. Jane Mckee Smith, Dr. Peter N. Adams, and Dr. Donald N. Slinn spent their valuable time to evaluate the progress of my research work. Dr. Valle-Levinson is further acknowledged for introducing me some oceanographic concepts that I was not very familiar with. The data set, used in this study, was collected during a field experiment that benefited from the efforts of Viktor B. Adams, Sidney Schofield and Jimmy Joiner from our Coastal Engineering Laboratory, Daniel D. Duncan from the University of Texas, Austin, and the field support group of LUMCON. Sergio Jaramillo, Uriah M. Gravois, and Jungwoo Lee also assisted in the deployment and retrieval of the instruments. 4

5 Dr. Clinton D. Winant from Scripps Institution of Oceanography spent his valuable time on tutoring me and the other graduate students towards our Ph.D. qualifying tests in While it is not in the scope of this dissertation, I have had the opportunity to work on dissipation of surface wave energy while propagating over muddy seafloors, using a comprehensive data set that was kindly provided by Dr. Steve Elgar and Dr. Britt Raubenheimer from Woods Hole Oceanographic Institution. Tracy J. Martz, Chelsea L. Sydow, and Chloe D. Winant kindly agreed to proofread this dissertation. I would like to thank my dear friend Hande Caliskan, who graduated from our program in 2006, and Dr. Aysen Ergin, my advisor during my M.S. studies at Middle East Technical University. Dr. Ergin made me contact with Hande for applying to University of Florida, and Hande s guidance throughout the entire application process helped substantially. Although being far away from me, knowing that Irmak Yesilada, Ozan Gokler and Murat Dilman - the co-starrings if a desperate director would make a biographical sketch of my life one day- are somewhere in this world always helps me to enjoy life, and get along with all sorts of difficulties easily. Cihat and Sukran, you GUYS are the best! 5

6 TABLE OF CONTENTS page ACKNOWLEDGMENTS LIST OF TABLES LIST OF FIGURES ABSTRACT CHAPTER 1 INTRODUCTION Cohesive Sediments in Marine Environment Turbulence in Combined Wave-Current Flow Interaction of Turbulent Flow with Cohesive Sediments Objectives of This Study FIELD EXPERIMENT Experiment Site Instrumentation General Conditions DATA ANALYSIS METHODS Wave Spectral Calculations Estimation of Reynolds Stresses in the Presence of Surface Waves Definition of Reynolds stress Wave bias in Reynolds stress estimates Two-sensor methods to reduce wave bias Logarithmic Law of the Wall OBSERVATIONS General Overview The LISST Data Set from BOTTOM BOUNDARY LAYER MODELING Introduction Governing Equations Momentum balance Sediment concentration balance Turbulent kinetic energy balance and balance of turbulent kinetic energy dissipation rate Sediment definition

7 5.3 Analytical Flocculation Model Application Model Sensitivity to Floc Size CONCLUSION APPENDIX A DIRECT ESTIMATION OF REYNOLDS STRESSES REFERENCES BIOGRAPHICAL SKETCH

8 Table LIST OF TABLES page 2-1 Location, mean depth, and retrieval dates of the instrumented platforms Numerical coefficients in the k ɛ closure

9 Figure LIST OF FIGURES page 1-1 Noncohesive sand grains and cohesive fluid mud Comparison of spectral evolution of waves over muddy and sandy seafloors Gulf of Mexico Bathymetry of the Atchafalaya Shelf and the locations of the instrumented platforms A typical instrumentation platform The synchronized ADVs and the OBS-5 on the platform before the deployment Configuration of the instrument array Wind, wave, and near-bed conditions on the Atchafalaya Shelf throughout the 2008 experiment Examples of ogive curves as a function of the dimensionless wavenumber Tidal variations during the experiment A one-minute segment of the flow velocity, recorded by the ADV array Wind, wave, and current conditions on the Atchafalaya Shelf throughout the 2-week experiment Bulk spectral characteristics of waves, and the measurements of suspended sediment concentration Reynolds stress estimates versus the quadratic drag relation Reynolds stress estimates, and the measurements of suspended sediment concentration Wave and current observations during the 2006 experiment Examples of logarithmic layer fits, and grain size distributions from the 2006 experiment Observations of particle size distribution and wave-turbulence conditions in An example of time-series in the model simulations Comparison of the observations and the model results Analysis of the model representation of the turbulent kinetic energy balance

10 5-4 Effect of varying floc size D on the model calculations

11 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy INTERACTION OF BOTTOM TURBULENCE AND COHESIVE SEDIMENT ON THE MUDDY ATCHAFALAYA SHELF, LOUISIANA, USA By Ilgar Safak August 2010 Chair: Alexandru Sheremet Major: Coastal and Oceanographic Engineering Interaction of near-bed wave-induced turbulence and cohesive sediments in muddy environments is studied based on field observations and a bottom boundary layer model. Wave, current, and sediment observations were collected with a suite of acoustic and optical instrumentation at approximately 5-m depth on the muddy Atchafalaya clinoform, Louisiana, USA. Low wave-bias estimates of near-bed Reynolds stresses are obtained by a method that is based on differencing and filtering of velocities from two sensors. The event that is focused on in this study is characterized by moderate waves with high steepness, currents with speeds sometimes reaching 30 cm/s near bed, and Reynolds stresses and suspended sediment concentrations reaching to their maximum values throughout the experiment (0.4 Pa, 3 g/l). In general, Reynolds stresses are found to be correlated with short-wave near-bed accelerations and suspended sediment concentration, as previously observed on sandy beaches, where accelerations have been associated with bed fluidization and sediment transport. A detailed numerical analysis of the observations is performed with a one-dimensional bottom boundary layer model for small scale turbulence and sediment transport processes on cohesive beds. The model accounts for the coupling between the fluid and the cohesive sediment phases, and uses a floc size that is constant in time and space. A representative floc size is selected for the experiment site, based on two independent sources that show consistency. Direct estimates of size distribution of 11

12 suspended sediments in the vicinity of the experiment site show a remarkably stable floc mode peak under varying wave and turbulence conditions. Indirect estimates of equilibrium floc size are obtained through calculations of an analytical flocculation model that uses observation-based parameters. With a floc size input based on the observations, the model reproduces currents and suspended sediment concentrations accurately; modeled Reynolds stresses match the low wave-bias estimates, with better agreement for cases of stronger currents and smaller wave-orbital velocities. The numerical simulations suggest that sediment-induced stratification effects are the same order of magnitude as turbulent dissipation, and thus play a significant role in the turbulent kinetic energy (TKE) balance within the tidal boundary layer. However, inside the wave boundary layer, the ratio of stratification to shear-induced turbulence production (i.e., gradient Richardson number) decreases significantly; shear-induced turbulence production and turbulent dissipation dominate the TKE balance. For these observations, model results show that the vertical structures of currents and Reynolds stresses are relatively insensitive to the exact floc size. Future efforts should include analysis of wider range of conditions (especially events with higher near-bed concentrations), and comparison of model results with a more detailed vertical structure of suspended sediment concentration. 12

13 CHAPTER 1 INTRODUCTION 1.1 Cohesive Sediments in Marine Environment Marine sediment transport is a coastal process that affects shoreline change, methods of coastal protection, design of coastal and offshore structures (see Sterling and Strohbeck (1973) for an example of failure of oil platforms due to wave-induced seafloor movements), underwater detection, navigation, water quality, and fate of pollutants and biomatter due to settling of sediment from surface to deep sea (Hill, 1998). In the conventional scheme, bed sediment is entrained into the water column by surface waves and is advected by currents. Recently, waves in shallow water were also noted to cause a net sediment transport (e.g., Hoefel and Elgar, 2003; Hsu and Hanes, 2004). According to the presence of cohesion between particles, sediments are classified into two categories: cohesive, which is also commonly known as mud (silt and clay with primary particle size smaller than 63 µm), and non-cohesive such as sand grains and coarser particles (Figure 1-1). Mehta (2002) defines mud as a mixture of water and sediment particles that are predominantly cohesive, which exhibits a rheological behavior that is poroelastic or viscoelastic when the mixture is particle-supported, and is highly viscous and non-newtonian when it is in a fluid-like state. The majority of the coasts around the world are covered mostly with sand. However, there are numerous muddy coasts dominated by cohesive sediments, especially at river mouths, such as the Atchafalaya Shelf in the Gulf of Mexico (Allison et al., 2000), continental shelf off the Eel River in Northern California (Traykovski et al., 2000), southwest coast of India (Jiang and Mehta, 1996), east coast of China (Jiang and Mehta, 2000), on the Amazon Delta (Cacchione et al., 1995), Po prodelta in the Adriatic (Traykovski et al., 2007), etc. In muddy environments, there is strong evidence of coupling between boundary layer turbulence and suspended sediment processes 13

14 (Trowbridge and Kineke, 1994; Allison et al., 2000; Traykovski et al., 2000; Sheremet and Stone, 2003; Sheremet et al., 2005; Allison et al., 2005; Kineke et al., 2006; Traykovski et al., 2007; Jaramillo et al., 2009). Waves which generate shear stresses at the bed greater than the bed strength cause liquefaction of a layer in the muddy bed with a thickness depending on the properties of the bed material and the wave conditions (Winterwerp et al., 2007). If the resulting cohesive sediment suspension near the bed reaches a volume concentration of unity, a space-filling network with both fluid and solid properties develops (Mehta, 1989). In the literature, cohesive sediment suspensions with mass concentrations exceeding 10 g/l are commonly classified as fluid mud layers, and this state is called structural density (Winterwerp and van Kesteren, 2004). The internal friction within the fluid mud layer can dissipate the surface wave-generated internal waves at the mud-water interface (Winterwerp et al., 2007). In the presence of currents, fluid mud (formed and entrained by waves) is transported in the upper water column, which otherwise remains just above the bed (Mehta, 1989). On the Eel River continental shelf in Northern California (Traykovski et al., 2000; Wright et al., 2001), on the Po prodelta in the Adriatic (Traykovski et al., 2007) and on the Yellow River mouth in the Gulf of Bohai, China (Wright et al., 2001), wave induced fluid mud layers of thickness on the order of the wave boundary layer thickness were observed to flow downslope (offshore) in the form of gravity currents. Turbulence, necessary to prevent deposition of the advected material by this mechanism, was generated by the flow itself. On the shallow Atchafalaya Shelf, bed liquefaction and sediment resuspension by surface gravity waves also result in the formation of fluid mud layers. These layers were observed to flow in the form of a turbidity current (Jaramillo, 2008; Jaramillo et al., 2009). Beyond the scope of this study, another mechanism through which mud affects large scale nearshore ocean dynamics is the significant dissipation of wave energy while propagating over muddy seafloors in shallow waters. Recent studies showed that fluid mud layers dissipate wave energy not only within the swell band but also within 14

15 the short-wave band. This is due to nonlinear energy transfers from high-frequency bands towards low-frequency bands, which interact with the seafloor more significantly (Sheremet and Stone, 2003; Sheremet et al., 2005; Kaihatu et al., 2007; Elgar and Raubenheimer, 2008; Jaramillo, 2008; Sheremet et al., 2010). Figure 1-2 shows a comparison of numerical simulation of wave field propagation on sandy and muddy seafloors. Nonlinear interactions across spectrum are not accounted for. An idealized case of unidirectional propagation over a distance of 5-km with constant 5-m depth is set. An initial spectrum is selected based on the parameterizations obtained from the directional wave measurements during the Joint North Sea Wave Project, i.e., JONSWAP (Hasselmann et al., 1980). A significant wave height of 2 m, and a peak frequency of 0.1 Hz is selected (thick line in Figure 1-2). The material on the sandy seafloor is represented by 0.2 mm grains. The muddy seafloor is set to have a 15-cm thick viscous fluid mud layer, with a density of 1.1 g/cm 3 and a kinematic viscosity of 10 3 m 2 /s (Kaihatu et al., 2007; Winterwerp et al., 2007). Bottom friction by the sandy bed (Jonsson, 1966; Kamphuis, 1975; Dean and Dalrymple, 1991) causes visible dissipation at only five frequencies around the spectral peak (thin line with squares in Figure 1-2) and the resulting significant wave height is 1.8 m. The calculations, based on a formulation which assumes the layer is a viscous fluid (Ng, 2000) show that the muddy seafloor causes a more significant collapse in the wave field s energy, in a wide range of frequencies (dashed line with dots in Figure 1-2). The resulting significant wave height for this case is 0.6 m. Therefore, while bottom friction by the sandy bed dissipates 19% of the initial energy of the wave field, the muddy seafloor, characterized by the parameters given above, dissipates 91% of the initial energy. In terms of small scale ocean bottom boundary layer processes, interaction of turbulent flow with sediment is more challenging to study in muddy environments than in sandy environments because of the complicated physics related to cohesive sediments. In a cohesive sediment suspension, rather than bouncing away from each other as 15

16 sand grains do, the collision of sediment particles results in the formation of aggregates called flocs. These flocs are characterized by high water content (Winterwerp and van Kesteren, 2004) and a fractal geometry with dimension close to 2 (Kranenburg, 1994). The flocculation process is discussed in more detail in the following sections. The settling velocity of sand grains can be calculated as a function of grain size and fluid viscosity through Stokes law (e.g., Nielsen, 1992). However, changes in the water content, geometry and, therefore, density of cohesive sediment flocs cause their settling velocity to be temporally varying, and higher than those obtained for primary particles, by Stokes law. Therefore, a cohesive sediment sample needs to be considered site-specific and event-specific in the sense that flocs in each sample may have varying physical properties such as size, density, and settling velocity (Mehta, 1989). Gases and organic particles in cohesive sediments (Winterwerp and van Kesteren, 2004) should also be considered in the analysis of cohesive sediments interacting with fluid flow. In fact, the interest of the U.S. Navy in the hydrodynamics in muddy environments has recently increased due to the fact that available Navy models for waves and circulation were mostly developed for sandy environments but do not work well with mud. 1.2 Turbulence in Combined Wave-Current Flow Flow-generated turbulence is a major mechanism in large scale processes such as momentum balance in the surf zone (e.g., Trowbridge and Elgar, 2001) and small scale sediment transport processes (Winterwerp, 1998). Numerical models for ocean bottom boundary layer turbulence are often based on two-equation turbulence closures and validated with laboratory experiments (e.g., Winterwerp, 2001; Hsu et al., 2007, 2009). On shallow continental shelves, surface wave-induced orbital velocities at the bed generate a wave boundary layer of a few centimeters thick, much thinner than the current boundary layer that scales with water depth (e.g., Fredsoe and Deigaard, 1992). Waves cause currents to experience a bottom drag above the wave boundary 16

17 layer larger than that associated with the bottom roughness, deviating from the logarithmic vertical structure and having a reduced vertical shear near the bed (e.g., Grant and Madsen, 1979, 1986). The resulting non-linear friction processes and the differences in the characteristic length and time scales of waves and currents complicate modeling of turbulence and sediment transport processes in the bottom boundary layers (e.g., Styles, 1998; Styles and Glenn, 2000, 2002; Hsu et al., 2009). This is a major research area in oceanographic studies because sediment entrainment from the bed is controlled by wave boundary layers where a significant amount of energy is being dissipated (Trowbridge and Agrawal, 1995) and exchanges of heat and momentum occur. The flow parameters in these boundary layer models (e.g., eddy viscosity, see Winterwerp (2001) and references therein) are modified by the turbulence-damping effect of density-induced stratification, i.e., vertical gradient of suspended sediment concentration. The turbulence closures on which these models are built have yet to be evaluated in detail against high-resolution field observations of combined wave-current flows and sediment transport processes. 1.3 Interaction of Turbulent Flow with Cohesive Sediments Hydrodynamic properties of cohesive sediments, which differ significantly from those of the primary particles (e.g., settling velocity, Section 1.1), result in stratification effects on vertical mixing that are specific to cohesive sediments (e.g., hindered settling, formation of near-bed fluid mud layers). In hypothetical cases of cohesive sediment suspensions in tidal flow, Winterwerp (2001) numerically simulated the formation of these fluid mud layers when the concentration of suspension exceeded the sediment-carrying capacity of the flow. Simulations in that study showed that stratification modifies vertical structures of velocity and turbulent flow parameters at depth-averaged concentrations as low as 0.1 g/l, as long as near-bed fluid mud layers of at least a few centimeters thick are formed. The one-dimensional boundary layer model, used by Winterwerp (2001), was validated with data from laboratory experiments 17

18 of cohesive sediment suspensions of depth averaged concentrations of 1 g/l in tidal flow (Winterwerp, 2006). Model calculations of Winterwerp (2006) agreed with the measured velocity and suspended sediment concentration; the model also captured the decreasing trend of vertical eddy viscosity (estimated through measured data) with increasing sediment concentration. In other related studies on steady currents in the tidal boundary layer, field observations (e.g., Trowbridge and Kineke, 1994), laboratory experiments (e.g., Gratiot et al., 2005), and models (e.g., Trowbridge and Kineke, 1994; Michallet and Mory, 2004) seem to agree that turbulence is significantly affected by cohesive sediment in the vicinity of a steep vertical gradient of suspended sediment concentration. These gradients are commonly known as a lutocline, which separates a high concentration layer with a mixed and comparatively low concentration layer (e.g., Parker and Kirby, 1982; Mehta, 1989; Vinzon and Mehta, 1998). Flocculation is a combined process of aggregation (floc formation due to collision of particles by turbulent motions) and floc breakup (disruption of flocs by turbulent shear), which is governed by turbulent eddies scaled by the Kolmogorov microscale (Berhane et al., 1997). While the importance of flocculation in altering the flow-sediment interaction through stratification is well established (Winterwerp, 2001), the role of the floc size (and therefore settling velocity of the floc) is less understood. Dyer (1989) hypothesized that floc structure is a function of turbulence levels and availability of sediment, i.e., suspended sediment concentration. The argument was that flocs should grow as the concentration of primary particles increases, due to increased probability of particle collisions. Turbulence (low to moderate shear stresses) is needed to promote collisions; however, high turbulence levels (high shear stresses) are expected to break the flocs and limit their size. In turn, floc structure should affect the hydrodynamic properties of flocs (e.g., settling velocity) with direct effects on the residual time of the flocs in the water column and, therefore, the vertical structure of suspended sediment concentration. Following the hypothesis that increasing turbulent shear stress first 18

19 increases and then decreases floc size (Dyer, 1989), simplified analytical expressions for equilibrium values of floc size and settling velocity were proposed by Winterwerp (1998), for a constant fractal dimension of 2. The formulation of Winterwerp (1998) was later modified by Son and Hsu (2009) to include variable fractal dimension and variable floc yield strength. The simplified formulation using the floc fractal dimension 2 was used to model cohesive sediment transport in the boundary layer of a tidal channel (Winterwerp, 2002). Winterwerp (2002), however, did not discuss the details of the turbulence kinetic energy balance. The flocculation models discussed above were calibrated for cohesive sediment transport in the laboratory with simple shear flow or homogeneous turbulence and applied to a tidal boundary layer condition. Their applicability to wave-induced fluid mud transport is unclear. Moreover, turbulence may not be the governing mechanism that controls flocculation at every condition. Based on field observations, Hill (1998) proposed a flocculation mechanism with a different dependence on turbulence: at low turbulent energy, disruptive stresses on flocs due to sinking in the fluid may exceed turbulence-induced stresses and limit floc size. 1.4 Objectives of This Study In this study, the interaction between turbulence induced by combined wave-current flow and suspended cohesive sediments in bottom boundary layers of muddy environments is studied based on observations collected during spring of 2006 and 2008, on the Atchafalaya inner shelf, Louisiana, USA. Wave and current parameters are calculated using standard data assimilation methods and spectral analysis. In addition, near-bed Reynolds stresses are estimated through the data with the most advanced of a series of methods recently proposed to reduce wave bias in turbulence estimates (Feddersen and Williams, 2007). This is a challenging task, especially in wave-energetic environments (Trowbridge, 1998). Having Reynolds stress estimates provides the advantage of designating, merely by analyzing the observations, the events when turbulent fluxes in the boundary layer are likely to be significant. Based on these observations, small-scale 19

20 turbulent flow and sediment transport processes are modeled using a one-dimensional bottom boundary layer model for cohesive beds (Hsu et al., 2007, 2009). The model uses a constant floc size, and therefore a constant settling velocity, in contrast with other models (e.g., Winterwerp, 2002) that predict a settling velocity varying over a tidal cycle. While this may lead to errors when used to simulate the vertical structure of suspended sediment concentration, the constant floc size assumption seems to be consistent with the field observations, which suggest a weak relationship between turbulence and floc size, at least in relatively dilute suspensions. Direct observations of floc size distribution (but not co-located with these particular hydrodynamic measurements) are used to estimate a representative floc size. The values used here are of the same order of magnitude as the equilibrium floc sizes calculated with the model proposed by Winterwerp (1998) using the observed primary particle size, suspended sediment concentration and estimated Reynolds stresses. The description of the field experiment, the details of instrumentation and sampling schemes, an overview of the sedimentological characteristics of the experiment site, typical atmospheric and flow conditions for the site, and a brief summary of the wave and near-bed flow observations during the entire experiment period are presented in Section 2. In Section 3, the data analysis methods used are presented. A general overview of the observations during the experiment studied herein is given in Section 4, together with the details of a 1-day event which is characterized by the highest amount of suspended sediment recorded near bed. Why a relatively stronger local turbulence-cohesive sediment interaction is expected during this event is discussed. The bottom boundary layer model is presented in Section 5, together with the governing equations, description of its execution procedures, and discussions on the selection of the floc size input based on two independent sources. Capabilities of the model are tested first by comparing the model results with the measurements. Model calculations of Reynolds stress are compared with the observation-based 20

21 estimates. The contribution of different terms in the turbulence kinetic energy balance and sensitivity of this balance on floc size are evaluated. The results are summarized and discussed in Section 6. 21

22 Figure 1-1. Noncohesive sand grains and cohesive fluid mud. (a) Sand grains; and (b) mud sample collected at the Atchafalaya Shelf, Louisiana (Photo courtesy: K. T. Holland, Naval Research Laboratory at the Stennis Space Center). 22

23 10 1 flux spectral density (m 3 ) frequency (Hz) Figure 1-2. Comparison of spectral evolution of waves over muddy and sandy seafloors. Initial JONSWAP spectrum (thick continuous line), resulting spectra after propagating 5-km in 5-m depth over a flat bottom covered with 0.2 mm sand (thin continuous line with squares), and 15-cm thick viscous fluid mud layer (dashed line with dots). 23

24 CHAPTER 2 FIELD EXPERIMENT 2.1 Experiment Site The main data set on which this study is based was collected from March 25th to April 7th, This was the last two-week interval of an experiment which started on February 22nd, 2008 on the muddy inner shelf fronting Atchafalaya Bay, Louisiana, USA, in the north-central Gulf of Mexico (Figures 2-1 and 2-2). This experiment was part of a larger scope study of wave, turbulence and sediment transport processes in shallow muddy environments that started in Four instrumented platforms were deployed on February 22nd by the University of Florida and the University of Texas (Figure 2-2). Platforms 1-3 were put in a cross-shore transect and Platform 4 was located in an alongshore transect with the shallow platform 3. Platform 5 was near Fresh Water Bayou about 60 miles west of the Atchafalaya Bay, near the center of a transect of current-meters, deployed by the group led by Dr. Steve Elgar and Dr. Britt Raubenheimer from Woods Hole Oceanographic Institution (Safak et al., 2010b). The coordinates and retrieval dates of the platforms are given in Table 2-1, together with the mean depth at the location of the platforms (average of the data collected throughout the experiment). The experiment site was revisited for each two-week period to retrieve data and change the batteries of the instruments deployed at platforms 1-4. Therefore, the three periods February 22nd - March 8th, March 8th - March 25th and March 25th -April 7th were named as experiments A,B and C, respectively. The focus of this study is the observations collected at Platform 2 near the 5-m isobath during Experiment C. The experiment site is located on the topset of the Atchafalaya sub-aqueous feature, which is defined as a clinoform of up to 3-m thick mud layer. The clinoform extends out to the 8-m isobath at tens of kilometers offshore (Allison et al., 2000; Neill and Allison, 2005). Since the 1940s, the muddy Atchafalaya inner continental shelf receives about 30% of the discharge of the Mississippi River, which is the largest river 24

25 on the North American continent (Mossa, 1996; Allison et al., 2000; Neill and Allison, 2005). The Atchafalaya River leaves the main course 320 km upstream of the Gulf of Mexico near Simmesport, Louisiana. The annual sediment discharge by the Atchafalaya River is estimated to be 84 million metric tons. The suspended sediment load into the bay and the inner shelf is identified by fine grains with median particle diameter D 50 =2-6 µm, however, includes 17% sand, as well (Allison et al., 2000). West of Marsh Island (92.5 degrees longitude West), D 50 was estimated to be between µm (Allison et al., 2005). Sheremet et al. (2005) measured D 50 =6.34 µm on the inner shelf, about 20 km offshore of Marsh Island. These data suggest that D 50 =2-7 µm is representative for the area. Size distribution of suspended sediments is available from the previous experiments and is investigated in the following sections. The Atchafalaya River is different than the major distributary of the Mississippi 180 km to the east in the sense that the Atchafalaya Shelf is shallower with a milder slope (e.g., low-gradient where the 10-m isobath is approximately 40 km offshore) and more wave-energetic. This region is interesting for sediment transport studies due to the fact that over the last few decades, the coastline has been prograding seaward with rates of O(10 m/yr) and land accretes vertically at rates reaching O(1 cm/yr) due to the sediment discharge of the Atchafalaya River in spite of rising sea levels. However, much of the rest of the Louisiana coastline and the Mississippi Delta are experiencing significant erosion (Allison et al., 2000; Draut et al., 2005; Neill and Allison, 2005; Kineke et al., 2006). Despite these high sediment accumulation rates, it is unlikely that the outer Atchafalaya Bay and the clinoform topset area will accrete to sea level, since atmospheric conditions force the hydrodynamics to distribute sediments away from these areas (Neill and Allison, 2005). Wind is the major forcing that controls circulation, sediment transport, water level, and salinity changes over the Atchafalaya Shelf. The wave climate is dominated between December and April (coinciding with the period of high sediment discharge in 25

26 the Atchafalaya River) by wave fields associated with storms and cold fronts passing through the area on 3-7 day time scales (Allison et al., 2000; Walker and Hammack, 2000). These fronts are characterized by pre-frontal onshore winds, strong wave activity and coastal setup, followed by post-frontal offshore winds, set-down, and formation of large sediment plumes (Allison et al., 2000; Walker and Hammack, 2000). At the experiment site, these perturbations can generate swells in excess of 1-m height lasting for several days. In shallow water, such intense wave activity causes significant variations of the bed state throughout a storm, in a sequence of breaking down stratification, triggering bed liquefaction, increasing sediment resuspension and turbidity throughout the water column (Allison et al., 2000), followed by the formation of fluid mud layers within 1-m near the bed due to settling, and finally consolidation to a soft bed (Jaramillo et al., 2009). These high concentration fluid mud layers can be transported over the shelf in different directions by various mechanisms: westward by residual currents of about 10 cm/s which may account for advection of more than half of the sediment discharge into the shelf (Wells and Kemp, 1981; Allison et al., 2000); onshore by coastal upwelling (Kineke et al., 2006); and offshore in the form of a turbidity current of about 5 cm/s, which is maintained in suspension by wave-induced turbulence (Jaramillo et al., 2009). On the other hand, the contribution of extreme events such as tropical cyclones and hurricanes (e.g., Hurricane Lili in 2002) to sediment transport and organic matter deposition may exceed the input by the Atchafalaya River (Allison et al., 2005; Goni et al., 2006). Together with the studies on nearshore circulation and sediment transport processes discussed above, the broad-spectrum wave-energy dissipation effect of muddy seafloors has been studied extensively on the Atchafalaya Shelf and near Fresh Water Bayou in the last decade (Sheremet and Stone, 2003; Sheremet et al., 2005; Elgar and Raubenheimer, 2008; Jaramillo, 2008). A recent finding from these wave-mud interaction studies is that maximum mud-induced dissipation rates are observed not 26

27 during the input of highest wave energy into the system but in the wane of the storm. During that period, the seafloor is characterized either as a viscous fluid or a viscoelastic material, and the boundary layer is expected to be laminar (Jaramillo, 2008; Sheremet et al., 2010). 2.2 Instrumentation A typical platform in 2006 and 2008 experiments is shown in Figure 2-3. Currents in the upper water column and the directional surface wave field were monitored by upward-pointing Acoustic Doppler Current Profilers (ADCP, Teledyne RD Instruments, 1200 khz, Figure 2-3 label A). Velocity and backscatter within 1-m of the bed were continuously measured by downward-pointing Pulse Coherent-Acoustic Doppler Profilers (PC-ADP, Sontek/YSI, 1500 khz, Figure 2-3 label B) in bins of either 1.6- or 3.2-cm continuously with sampling rates of either 1- or 2-Hz. The PC-ADPs are also equipped with built-in pressure sensors. Acoustic Backscatter Profilers (ABS, Aquatec, Figure 2-3 label C) provided a more detailed profile of the near-bed backscatter at bins smaller than 1 cm. Optical backscatterance sensors (OBS-3s and OBS-5s, D & A Instruments, Figure 2-3 label D) measured turbidity. Operational principles of these acoustic and optical instruments can be found in Lhermitte and Serafin (1984) and Downing et al. (1981), respectively. Conductivity-Temperature sensors (CT, SeaBird Electronics) provided salinity estimates and temperature measurements. At the location of Platform 1, a pressure sensor, located 1-2 m below the surface, sampled at 4-Hz throughout the entire 7-week experiment. At the location of Platform 3, an Onset, Inc., HOBO micro-station located at an elevation of 7-m above the sea surface, provided 30-min averages of wind speed and direction. The instrumentation used in this analysis comprised a vertical array of two synchronized Acoustic Doppler Velocimeters (ADV, SonTek/YSI Hydra 5-MHz), and an OBS-5. An ADV is a pointwise velocity sensor, and it has been tested in laboratories to estimate turbulence parameters (Voulgaris and Trowbridge, 1998) and to measure 27

28 instantaneous velocities in concentrated fluid mud (Gratiot et al., 2000). A photograph of the instrumentation on the platform before the deployment and a schematic of the platform showing the locations of the instruments are shown in Figures 2-4 and 2-5, respectively. The sampling volume of the lower ADV (ADV-1) was located at 17 cmab (cm above bed); the higher ADV (ADV-2) sampled in a volume at 145 cmab. Based on the measurements in a wave-free environment (Trowbridge et al., 1999), Shaw and Trowbridge (2001) suggested that two vertically-stacked sensors are optimally configured to yield uncorrelated cross-sensor turbulent covariances if the distance between the sensors is greater than 5 times the height of the lower sensor above the bed. For the application of the two-sensor method of wave-bias reduction from the Reynolds stress estimates (see Section 3.2.3), the configuration of the ADVs (Figure 2-5) follows this recommendation. Each ADV was equipped with a built-in pressure sensor, located at about 60 cm from its sampling volume. The ADVs sampled pressure and three-dimensional flow velocity (converted to East-North-Up coordinates in post-processing) at 10 Hz, in 10-min measurement bursts, one burst every hour, for the entire two-week duration of the experiment. A burst duration of 10-min allows the ADVs to run for two weeks with a shared battery pack, spans about 75 swell periods (for a swell period of 8 s, which is typical for the site), and is long enough to provide a stable mean current estimate (Soulsby, 1980). The OBS-5 was mounted at 12 cmab, and recorded 1-min averages of backscatter at a rate of 2 Hz. The backscatter signal from the OBS-5 was calibrated in the laboratory with in-situ sediment and water samples collected at the site surveys during the deployment and retrieval of the platforms. Through this calibration, the turbidity records were converted to suspended sediment concentration estimates. For the directional wave measurements, the data collected by the ADCP at Platform 3, located 4 km onshore of the experiment site (Figure 2-2) was used. The ADCP transducer head was located at 1.3 mab and measured pressure, acoustic surface track, and velocity profiles at 2 Hz, in 40-min measurement bursts, one 28

29 burst every hour. Wave data were processed using the Teledyne RDI software packages WavesMon and WaveView, with a frequency resolution of Hz and an angular resolution of 4 degrees. The ADCP also provided 10-min averaged current profiles in bins of 20 cm. For this analysis, the only information about the size distribution of suspended sediments on the Atchafalaya Shelf was available from a LISST-100X Type-C (Laser In Situ Scattering Transmissometer, Sequoia Scientific). LISST records the small-angle scattering distribution of particles in water, which is inverted into size spectra. For further operational principles, see Agrawal and Pottsmith (1994). Two sets of observations (Allison et al., 2010) were collected, one from the 2006 experiment between February 28th and March 14th (Jaramillo et al., 2009) at the location of Platform 3 (Figure 2-2) and one from the 2008 experiment A between February 22nd and March 8th, at Platform 4 (Figure 2-2). As both data sets have time offsets with the analyzed experiment, the 2006 data set was preferred because it was collected at a location closer to the location of the data set used in the analysis herein. The LISST background was calibrated using filtered water at the deployment site. The path of the LISST measurements (which determines the upper limit of sediment concentration at which reliable data can be obtained) is reduced with an 80% path reduction module. With this setting, the threshold sediment concentration is about 1 g/l, and reliable data were collected at 120 cmab between March 1st and March 9th, The instrument estimates size distributions of suspended particulates (flocs and primary) in 32 class ranges between µm size. However, in this experiment, the data is unreliable above 350 µm, and not reproduced here. The grain-size distribution was recorded every minute (an average of 100 samples at 2 Hz) in 30-min bursts each hour. On the same platform with the LISST, a downward-pointing PC-ADP measured velocity and backscatter profiles, and pressure. The PC-ADP sampled at 2 Hz sampling in 60 bins of 1.6 cm, following a 10-cm blanking distance. A 10-min burst was started every 30-min. The PC-ADP 29

30 measurements were missing velocity profiles once in every three or four samples, due to an unknown instrumentation problem. Therefore, the 2 Hz velocity measurements were burst-averaged to calculate the vertical structure of mean currents and then estimate the bottom friction velocity by using the logarithmic law of the wall (Section 3.3). These estimates, and the spectral wave calculations based on the PC-ADP pressure sensor data, present a general picture of the variation of size distribution records of LISST under varying wave and bottom turbulence conditions (Sections 3.3 and 4.2). 2.3 General Conditions Before focusing on the experiment of interest and the presentation of the related data analysis methods, a general overview of the conditions (winds, near-bed flows, and surface waves) throughout the entire seven-week experiment duration is presented in Figure 2-6. For this, the wind and the PC-ADP data measured at Platform 3 (Figure 2-2), where the local depth was about 3.8 m, and the pressure data from the pressure sensor near Platform 1 (Figure 2-2), where the local depth was about 7.4 m, are used. The PC-ADP on Platform 3 was the only near-bed profiler that sampled throughout the entire experiment, except the retrievals for re-deployments between experiments A-B and B-C. The pressure sensor near Platform 1 was the only wave gauge which sampled continuously throughout the entire experiment. In the wave spectral calculations, which are detailed in the next section, swell (low frequency) and sea (high frequency) bands are decomposed using a cutoff frequency of f c =0.2 Hz. This arbitrary value is selected based on the similar evolution trends of spectral wave energy at frequencies larger than this value, and wind speed. Figures 2-6a and b show that sea waves (black curve in Figure 2-6b) closely follow the trend of wind speed, which sometimes exceeded 15 m/s and generated sea waves of significant heights exceeding 1.5 m (see the peaks on February 28th, March 4th, March 8th, and March 20th). Increasing swell energy seems to be triggered by shifts in wind direction from onshore winds to offshore winds on February 27th, March 4th, March 8th, and especially March 18th (see the variation 30

31 in the wind-direction representing color code in Figure 2-6a, from cyan-green sector, i.e., northward winds, to red-magenta sector, i.e., southward winds). During all four of these events, near-bed activity was observed in the sense that the location of the maximum backscatter is recorded to be closer to the PC-ADP sensor head compared to its initial location at the beginning of the experiment (Figure 2-6c). This indicates the formation of a high concentration, i.e., fluid mud layer above the consolidated bed. The backscatter is also showing an increase througout the water column during these events. The strongest swell event throughout the experiment was recorded on March 18th when swells reached 1.5 m and the near-bed observations indicate formation of a fluid mud layer of about 20 cm thickness. During the third and last 2-week interval of this experiment, experiment C, the data set for studying turbulence-cohesive sediment interaction herein was collected. During that experiment, swell heights were mostly less than 0.5 m at 7.4 m depth and the backscatter records are not indicating formation of any fluid-mud layers at 3.8 m depth. 31

32 Table 2-1. Location, mean depth, and retrieval dates of the instrumented platforms Platform Latitude(North) Longitude (West) Depth (m) Retrieval date 1 29 o o March 25th 2 29 o o April 10th 3 29 o o April 10th 4 29 o o April 10th 5 29 o o March 25th 32

33 31 Latitude (deg.) Louisiana Transect 2 Transect 1 Gulf of Mexico Florida Atlantic Ocean Longitude (deg.) Figure 2-1. Gulf of Mexico. The platforms along Transect 1 and Transect 2 were containing instrumentation deployed by the field support groups of the University of Florida-the University of Texas, and the University of Florida-Woods Hole Oceanographic Institution, respectively. 33

34 30.0 Louisiana 29.8 Latitude (deg.) Gulf of Mexico 5 30 m Trinity shoal Marsh Island 10 m 20 m Atchafalaya Bay Atchafalaya River Longitude (deg.) m Figure 2-2. Bathymetry of the Atchafalaya Shelf and the locations of the instrumented platforms. This bathymetry was based on a data set collected before the 2008 experiment and is showing differences with the 2008 bathymetry. The numbered red stars indicate the platform locations. The main data set on which this study is based was collected at Platform 2. Also from Platform 3 which is located 4 km onshore of Platform 2, directional wave measurements, wind data, and information on size distribution of suspended sediments in the area are investigated. 34

35 Figure 2-3. A typical instrumentation platform. The platforms were equipped with an upward-pointing ADCP (A), a downward-pointing PC-ADP (B), a downward-pointing ABS (C), and pointwise turbidity sensors (D). 35

36 Figure 2-4. The synchronized ADVs and the OBS-5 on the platform prior to the deployment. 36

37 Figure 2-5. Configuration of the instrument array. Circles mark the location of the sampling volumes. 37

38 Figure 2-6. Wind, wave, and near-bed conditions on the Atchafalaya Shelf throughout the seven-week experiment in Spring (a) Wind speed and direction (the color code shows where the wind flow is towards) measured near Platform 3 where the local depth is 3.8 m; (b) significant wave height in sea (black) and swell (red) bands, measured by the near-surface pressure sensor at Platform 1 where the local depth is 7.4 m; and (c) near-bed acoustic backscatter (normalized such that the maximum backscatter is shown by dark red and the minimum backscatter by dark blue) measured by the PC-ADP at Platform 3. The gaps in the backscatter data on March 8th and March 25th correspond to the intervals between the experiments A-B and B-C, when the data sets from the instruments were being retrieved, and the batteries and memory cards were being replaced. 38

39 CHAPTER 3 DATA ANALYSIS METHODS 3.1 Wave Spectral Calculations A wave mode with amplitude a and frequency f has a total average energy (sum of kinetic and potential energies) per unit surface area (Dean and Dalrymple, 1991): E(f ) = ρg a2 2, (3 1) where ρ is the fluid density and g is the acceleration caused by gravity. In the frequency domain, wave energy is usually represented as: S(f ) = a2 2 df, (3 2) where S(f ) is the energy spectral density of the mode with frequency f, and df is the frequency resolution. The wave field during the analyzed experiment is defined by statistical parameters which are obtained through spectral calculations. Also, the cross-spectrum of horizontal and vertical velocity measurements is calculated to estimate Reynolds stresses (Section 3.2). Therefore, a brief discussion of spectral analysis is given here. Spectral analysis is used to decompose a time-varying quantity x(t) into a sum of sine and cosine functions, and calculate the distribution of energy at modes of different frequencies (Priestley, 1981). For a stochastic process, the auto-correlation function describes the general dependence of the data values at one time on the values at another time (Bendat and Piersol, 1971). It is defined as: R xx (τ) = x(t) x (t + τ)dt, (3 3) where t is the time and asterisk denotes the complex conjugate. Fourier transform of x(t) at frequency f is: 39