1. Introduction
Turbulence is believed to have a dominant effect on flows and sediment transport in the surf zone. For example, often it is assumed that a balance between bottom stress and cross-shore gradient of wave-induced radiation stress controls the alongshore flow driven by breaking waves (e.g., Battjes 1988) and that the effect of bottom stress is transmitted through the water column by turbulence with scales much smaller than the water depth (e.g., Svendsen and Putrevu 1994). Breaking-induced turbulence dominates wave energy dissipation in the surf zone (Thornton and Guza 1986). Many models of sediment transport are based on the assumptions that near-bottom turbulent shear stress controls the entrainment of sediment from the seafloor (e.g., Glenn and Grant 1987) and that turbulence maintains suspended sediment in the water column (e.g., Fredsoe and Deigaard 1992; Nielsen 1992).
Despite the importance of turbulence in conceptual and mathematical models of surf zone processes, direct measurements of surf zone turbulence have been rare. Separation of turbulence from waves is difficult because turbulent velocity fluctuations typically are two to three orders of magnitude less energetic than wave motions. As a result, previous surf zone turbulence measurements have focused on velocity fluctuations at frequencies far higher than those of the waves, resulting in estimates of dissipation, but not stress (George et al. 1994), or they have have been obtained in laboratory basins (e.g., Ogston et al. 1995; Ting and Kirby 1996), where phase-averaging techniques appropriate for monochromatic waves, which are not applicable in random ocean waves, are used to separate waves from turbulence. Most estimates of nearshore turbulence statistics have been obtained indirectly from measurements of waves and winds. For example, depth-integrated dissipation has been estimated as the residual in a wave energy balance (Thornton and Guza 1986; Kaihatu and Kirby 1995; Elgar et al. 1997; Herbers et al. 2000), and bottom stress has been estimated as the residual in an alongshore momentum balance (Thornton and Guza 1986; Whitford and Thornton 1996; Feddersen et al. 1998; Lentz et al. 1999).
In (1)–(4), x, y, and z are coordinates in a right-handed system with x positive onshore, y positive alongshore, and z positive upward, where z = −h and z = η represent the seafloor and water surface, respectively. The quantity ρ0 is a fixed reference density, (u, υ, w) is the velocity vector, primes denote turbulent fluctuations, −ρ0
2. Methods
a. Measurements
The turbulence measurements, described in detail by Fredericks et al. (2001), were acquired between 25 August (yearday 236) and 21 November (yearday 324) of 1997 on a sandy Atlantic beach near Duck, North Carolina, at the U.S. Army Corps of Engineers Field Research Facility. An array of five upward-looking Sontek acoustic Doppler velocimeters (ADVs) was mounted on a low-profile frame (Fig. 1). The ADVs measure the three-dimensional velocity vector in a sample volume with a spatial scale of approximately 0.01 m (e.g., Voulgaris and Trowbridge 1998) and perform well in the surf zone (Elgar et al. 2001). The array included three of the field version of Sontek's acoustic Doppler velocimeter (ADVF) and two of the more rugged ocean version (ADVO), one of which was fitted with pressure, temperature, pitch, and roll sensors, as well as compass. The ADVOs shared a common logger that sampled the two sensors simultaneously at 7 Hz in one burst of 25 minutes each hour. The ADVFs shared a separate common logger that sampled the three sensors simultaneously at 25 Hz in one burst of 10 minutes each hour. The ADV frame was approximately 300 m from the shoreline and 300 m north of the Field Research Facility (FRF: Fig. 2). The ADVs occupied an on–offshore line along the frame's northern edge, upstream of the frame itself, relative to the predominantly southerly wind- and wave-driven flows. The bathymetry near the measurement site is approximately uniform in the alongshore direction on scales of kilometers (Birkemeier et al. 1985; Lentz et al. 1999), although there is a cross-shore channel approximately 100 m wide and 1 m deep beneath the pier (Fig. 2).
Other instrumentation included 12 Setra pressure sensors making up “compact arrays” 6 and 7 (CA6 and CA7), centered approximately 40 m onshore and 80 m offshore of the ADV frame, respectively (Herbers et al. 2000, submitted to J. Phys. Oceanogr.) two Marsh–McBirney two-axis electromagnetic current meters, located near the centers of CA6 and CA7; a Solent sonic anemometer, located on a mast at the end of the FRF pier approximately 20 m above the water surface; and a Sontek 3-MHz acoustic Doppler profiler (ADP), located approximately 170 m north of the ADV frame (Fig. 2). The pressure sensors and two-axis velocimeters were sampled nearly continuously at 2 Hz, the sonic anemometer was sampled continuously at 21 Hz, and the ADP sampled continuously in 0.25-m range bins at 25 Hz.
The ADV array experienced several problems. Estimates of wave angles indicate that the head of the offshore ADVF began rotating intermittently immediately after deployment. Approximately six days after deployment, the offshore ADVO began malfunctioning, and intermittently produced invalid data, characterized by intervals with velocities of precisely zero or poor correlation with velocities measured by the other ADVO. The ADVO measurements of acoustical backscatter intensity are clipped (i.e., do not exceed a fixed maximum value) during strong flows, which precludes use of this measurement to infer sediment concentration. Approximately ten days after deployment, the two onshore ADVFs were destroyed by large waves and strong currents. Divers reported that a scour hole with a depth of roughly 0.2 m formed beneath the ADV frame within a few days of deployment and that sand worms colonized the frame during the final two weeks, terminating useful data on approximately 27 October (yearday 299).
b. Analysis
The analysis focuses on data produced by the ADVOs and the two onshore ADVFs during the first six days of the measurement period, when these four sensors functioned well, and on the remainder of the records produced by the ADVOs during intervals when the offshore ADVO produced valid data. To identify valid segments in the record produced by the offshore ADVO [see Fredericks et al. (2001) for details], the ADVO records were divided into 100-sample blocks, and the squared correlation coefficient r2 between cross-shore velocities at the two ADVOs was calculated for each block. Data from the intermittently functioning ADVO were assumed valid for blocks with r2 > 0.90. Thresholds of r2 = 0.90 and r2 = 0.80 produced nearly identical results.
The estimates of dissipation are based on several considerations. Measured spectra are consistent with the model assumptions that Pww is noise-free and that Puu + Pυυ has a constant noise level (section 3; see also Elgar et al. 2001). The model fit is restricted to frequencies between 1 and 2 Hz because the measurements indicate applicability of (6) and (7) in this range (section 3) and because estimates of the spatial scales of turbulence corresponding to this range of frequencies, combined with atmospheric velocity spectra (Kaimal et al. 1968), indicate applicability of the inertial-range model. Equations (6) and (7) were not applied to ADVF data because, in contrast to the ADVO data, ω5/3 times spectral density minus noise for ADVF measurements was not constant at high frequency, instead exhibiting one or more peaks suggesting input of energy by flow disturbances produced by sensor supports and electronics, which were not far below the ADVF sample volumes (Fig. 1). High-frequency noise problems similarly precluded use of (6) and (7) with the offshore ADVO data.
Hour-averaged estimates of sea surface elevation variance, energy flux, and radiation stress in the wind wave frequency band (0.04 < f < 0.31 Hz) were obtained from the arrays of bottom-mounted pressure sensors using linear wave theory and a directional-moment-estimation technique (Elgar et al. 1994; Herbers et al. 1995; Herbers et al. 1999). Estimates obtained from the pressure arrays are well correlated and consistent in magnitude with independent estimates using linear theory from collocated measurements of pressure and velocity.
Hour-averaged estimates of τwy were determined from covariances of horizontal and vertical velocities computed from demeaned and detrended 10-min records from the sonic anemometer. These estimates are well correlated (r2 = 0.85) and consistent in magnitude (b = 1.35 ± 0.04) with independent estimates from a nearby mechanical anemometer (Fredericks et al. 2001).
Estimates of ∂
3. Results
During most of the measurement period, winds were weak, waves were small, and the 4.5-m-depth ADV site was seaward of the surf zone. During a few events, however, the alongshore wind stress approached 0.5 Pa (Fig. 3a), the significant wave height reached or exceeded 2 m (Fig. 3b), and shoreward-propagating waves lost energy flux (Fig. 3c) and produced a cross-shore gradient of wave-induced radiation stress (Fig. 3d), presumably because of breaking. The strong winds and breaking waves forced strong alongshore currents (Fig. 4b), in some cases accompanied by strong cross-shore currents (Fig. 4a), particularly during three events centered on days 246, 263, and 292. During these events,
Velocity spectra indicate energetic wave motions at cyclic frequencies f between approximately 0.05 and 0.5 Hz (Fig. 5a). At higher frequencies, spectra of horizontal and vertical velocity are consistent with isotropic inertial-range turbulence, as described by (6) and (7), because f5/3Pww and (12/21)f5/3(Puu + Pυυ − noise level) are nearly independent of f and nearly equal to each other (Fig. 5b). Cospectra of differences between alongshore and vertical velocities measured by the two ADVOs (Fig. 5c), which illustrate the frequency content of dual-sensor estimates of turbulent Reynolds shear stress based on (5), indicate significant contributions to stress between approximately 0.01 and 1.0 Hz. The spectra and cospectra in Fig. 5 are representative of the first six days of the record, when four ADVs functioned well, waves were unbroken, and flows were weak. Spectral shapes for periods with breaking waves are similar. Cospectra of Δυ and Δw during breaking waves were not computed because of short records caused by intermittent malfunctioning of the offshore ADVO (section 2).
Measurements from the beginning of the record, when both ADVOs and the onshore pair of ADVFs functioned well, permit a comparison of redundant stress estimates. The four single-sensor estimates −ρ0
Time series of the terms in (1)–(4) are dominated by a few brief events when strong winds and waves forced energetic flows. Estimates of the left and right sides of (1) (Figs. 7a and 7b) are well correlated (r2 = 0.63), but the turbulent Reynolds stress is approximately half the sum of the wave and wind forcing (b = 0.51 ± 0.03). In (2), dissipation and shear production are well correlated (r2 = 0.70) and consistent in magnitude (b = 1.1 ± 0.1), even though dissipation was large while shear production was small during an event centered on day 270 (Figs. 8a and 8b). Dissipation and shear production are two orders of magnitude smaller than the depth-averaged rate at which the shoaling waves lose energy to breaking (Fig. 8c). Estimates of −ρ0
Acoustical measurements of bedform geometry on the same isobath as the ADV frame (Hanes and Alymov 2000, submitted to J. Geophys. Res.) indicate short ripples, with heights up to 0.02 m and lengths up to 0.25 m, and long ripples, with heights up to 0.06 m and lengths up to 2 m. The heights and inverse wavenumbers of these bedforms are smaller than the ADV measurement heights, indicating that local flow distortions by bedforms had a negligible effect on the ADV measurements.
The results in Figs. 7–9 did not depend sensitively on the rate at which the malfunctioning ADVO produced valid data (Fig. 4d), because the correlation coefficients and regression slopes are not systematic functions of percent of valid data collected.
4. Discussion
a. Momentum balance
The factor of 2 difference between the left and right sides of the momentum balance (1) (Fig. 7) might be caused by inaccurate estimates of dSxy/dx or −ρ0
The differences between the left and right sides of (1) might also be caused by omitted terms in the alongshore momentum balance, including divergence of a shoreward flux of alongshore momentum by shear waves (Oltman-Shay et al. 1989; Bowen and Holman 1989), an alongshore pressure gradient, or advective acceleration of the hour-averaged flow. Velocity fluctuations at frequencies below the wind wave band contributed negligibly to shoreward fluxes of alongshore momentum at the ADV frame, indicating that shear waves had a small effect on the alongshore momentum balance. The pressure term neglected in (1) is O(ρ0gh∂
b. Energetics, velocity profile, and drag laws
Figure 8 indicates that a balance between shear production and dissipation controlled the energetics of near-bottom turbulence at the ADV frame and that breaking-induced dissipation associated with the shoreward decrease of wave-induced energy flux did not penetrate to the depth of the ADVs. These observations are similar to results in wall-bounded turbulent shear flows in which shear production balances dissipation near the wall (e.g., Tennekes and Lumley 1972). The observations are inconsistent with the simplest model of surf zone turbulence (Battjes 1975), in which breaking-induced dissipation is assumed to be distributed uniformly over the water depth, and they also are inconsistent with empirical results for locally forced waves in deep water (e.g., Terray et al. 1996), which indicate penetration of breaking-induced turbulence to depths of a few times the significant wave height, which exceeds the water depth in the surf zone. However, the observations are qualitatively consistent with Svendsen's (1987) analysis of laboratory measurements, which indicates that only a small fraction (2%–5%) of the dissipation associated with breaking waves in the surf zone occurs below trough level.
The drag coefficient estimated from (4) for unbroken waves [cd = (1.9 ± 0.2) × 10−3] is consistent with a previous nearshore estimate seaward of the surf zone (Feddersen et al. 1998). However, the smaller drag coefficient determined for breaking waves [cd = (0.71 ± 0.03) × 10−3] is smaller than other estimates obtained in the surf zone (Thornton and Guza 1986; Whitford and Thornton 1996) and contradicts studies that produced larger estimates of drag coefficients under breaking waves than under nonbreaking waves (Feddersen et al. 1998; Lentz et al. 1999). A reduced cd under breaking waves is plausible because large wave-induced velocities destroyed bedforms (Hanes and Alymov 2000, submitted to J. Geophys. Res.), and breaking-induced turbulence did not penetrate to the measurement depth (Fig. 8). In addition, stable stratification by suspended sediments may have occurred near the seafloor, increasing ∂
5. Summary and conclusions
Measurements of turbulence, waves, currents, and wind permit examination of 1) an approximate alongshore momentum balance between wind stress, cross-shore gradient of wave-induced radiation stress, and near-bottom turbulent Reynolds stress; 2) an approximate turbulence energy balance, in which dissipation balances the sum of shear production and the depth-averaged rate at which breaking extracts energy from the shoaling wave field; 3) the Prandtl–von Kármán representation of the velocity profile in a wall-bounded shear flow; and 4) a quadratic drag law. The results are dominated by three events when large winds and waves forced strong flows, and the sensors were in the outer part of the surf zone. Estimates of near-bottom turbulent Reynolds shear stress are smaller than the sum of wind and wave forcing by a factor of approximately 2. In the turbulent energy balance shear production balances dissipation, and both are two orders of magnitude smaller than the depth-averaged rate of energy loss by the shoaling wave field, suggesting that breaking-induced turbulence did not extend to the measurement depth. Near-bottom velocity gradients are larger by approximately 50% than indicated by the Prandtl–von Kármán logarithmic velocity law, given estimates of bottom stress. The bottom drag coefficient for unbroken waves is similar to a previous nearshore estimate outside of the surf zone, but the drag coefficient for breaking waves is smaller than values from previous results based on indirect estimates of bottom stress.
The reasons for the imbalances in the momentum equation and the Prandtl–von Kármán velocity profile are not known. However, turbulent Reynolds shear stress was central to these balances, and the technique for estimation of stress is based on the explicit assumption that the spatial scales of the stress-carrying near-bottom motions are smaller than the height above bottom. The present measurements are not sufficient to test this assumption. Determining the spatial scales of the stress-carrying motions in wave-driven nearshore flows is an important question for future research. Other unresolved questions include the adequacy of linear theory to estimate the cross-shore gradient of wave-induced radiation stress in breaking waves, the role of nonlinear advective terms and pressure gradient in the alongshore momentum balance, the effect of bedforms and suspended sediments on nearshore flows, and the vertical structure of dissipation in the surf zone.
Acknowledgments
Staff from the Field Research Facility, Duck, NC, and the Center for Coastal Studies, Scripps Institution of Oceanography, deployed, maintained, and recovered the instruments in harsh surf zone conditions. R. T. Guza, T. H. C. Herbers, B. Raubenheimer, and W. C. O'Reilly helped design and manage the field experiment and provided high-quality processed measurements of wave statistics and currents. P. Howd planned, obtained, and processed the ADP measurements. J. Fredericks, G. Voulgaris, and A. Williams obtained the ADV measurements, and J. Fredericks processed the ADV data. J. Edson obtained and processed the wind measurements. S. Lentz and F. Feddersen provided useful comments on the manuscript. Funding was provided by the Office of Naval Research, the National Science Foundation, the Mellon Foundation, and the Woods Hole Oceanographic Institution's Rinehart Coastal Research Center.
REFERENCES
Abramowitz, M., and I. A. Stegun, 1972: Handbook of Mathematical Functions. Natl. Bur. of Stand., 1046 pp.
Batchelor, G. K., 1967: The Theory of Homogeneous Turbulence. Cambridge University Press, 197 pp.
Battjes, J. A., 1975: Modeling of turbulence in the surf zone. Symp. on Modelling Techniques, MODELING75, Vol. 2, San Francisco, CA, American Society of Civil Engineers, 1050–1061.
Battjes, J. A., 1988: Surf-zone dynamics. Annu. Rev. Fluid Mech, 20 , 257–293.
Birkemeier, W. A., H. C. Miller, S. D. Wilhelm, A. D. DeWall, and C. S. Gorbics, 1985: A user's guide to the Coastal Engineering Research Center's (CERC's) Field Research Facility. Instr. Report CERC-85-1, U.S. Army Corps of Engineers Waterways Experiment Station, Coastal Engineering Research Center, Vicksburg, MS, 136 pp.
Bowen, A. J., 1969: The generation of longshore currents on a plane beach. J. Mar. Res, 27 , 206–215.
Bowen, A. J., and R. A. Holman, 1989: Shear instabilities of the mean longshore current. 1. Theory. J. Geophys. Res, 94 , 18 023–18 030.
Businger, J. A., J. C. Wyngaard, Y. Izumi, and E. F. Bradley, 1971: Flux–profile relationships in the atmospheric surface layer. J. Atmos. Sci, 28 , 181–189.
Elgar, S., T. H. C. Herbers, and R. T. Guza, 1994: Reflection of ocean surface gravity waves from a natural beach. J. Phys. Oceanogr, 24 , 1503–1511.
Elgar, S., R. T. Guza, T. H. C. Raubenheimer, and E. Gallagher, 1997: Spectral evolution of shoaling and breaking waves on a barred beach. J. Geophys. Res, 102 , 15 797–15 805.
Elgar, S., B. Raubenheimer, and R. T. Guza, 2001: Current meter performance in the surf zone. J. Atmos. Oceanic Technol., in press.
Feddersen, F., R. T. Guza, S. Elgar, and T. H. C. Herbers, 1998: Alongshore momentum balances in the nearshore. J. Geophys. Res, 103 , 15 667–15 676.
Fredericks, J. J., J. H. Trowbridge, and G. Voulgaris, 2001: Turbulence in the shallow nearshore environment during SandyDuck 97. Woods Hole Oceanographic Institution, Tech. Rep., WHOI-2001-02, Woods Hole, MA, 45 pp.
Fredsoe, J., and R. Deigaard, 1992: Mechanics of Coastal Sediment Transport. World Scientific, 369 pp.
Garcez Faria, A. F., E. B. Thornton, T. P. Stanton, C. V. Soares, and T. C. Lippmann, 1998: Vertical profiles of longshore currents and related bed shear stress and bottom roughness. J. Geophys. Res, 103 , (C2). 3217–3232.
George, R., R. E. Flick, and R. T. Guza, 1994: Observations of turbulence in the surf zone. J. Geophys. Res, 99 , 801–810.
Glenn, S. M., and W. D. Grant, 1987: A suspended sediment stratification for combined wave and current flows. J. Geophys. Res, 92 , 8244–8264.
Gradshteyn, I. S., and I. M. Ryzhik, 1965: Table of Integrals, Series, and Products. Academic Press, 1160 pp.
Grant, H. L., R. W. Stewart, and A. Moilliet, 1962: Turbulence spectra from a tidal channel. J. Fluid Mech, 12 , 241–263.
Herbers, T. H. C., S. Elgar, and R. T. Guza, 1995: Generation and propagation of infragravity waves. J. Geophys. Res, 100 , 24 863–24 872.
Herbers, T. H. C., S. Elgar, and R. T. Guza, 1999: Directional spreading of waves in the nearshore. J. Geophys. Res, 104 , 7683–7693.
Herbers, T. H. C., N. R. Russnogle, and S. Elgar, 2000: Spectral energy balance of breaking waves within the surf zone. J. Phys. Oceanogr, 30 , 2723–2737.
Hogstrom, U., 1988: Non-dimensional wind and temperature profiles in the atmospheric surface layer: A re-evaluation. Bound.-Layer Meteor, 42 , 55–78.
Jeffreys, H., 1974: Cartesian Tensors. Cambridge University Press, 92 pp.
Kaihatu, J., and J. Kirby, 1995: Nonlinear transformation of waves in finite water depth. Phys. Fluids, 7 , 1903–1914.
Kaimal, J. C., J. C. Wyngaard, and D. A. Haugen, 1968: Deriving power spectra from a three-component sonic anemometer. J. Appl. Meteor, 7 , 827–837.
Lentz, S., R. T. Guza, S. Elgar, F. Feddersen, and T. H. C. Herbers, 1999: Momentum balances on the North Carolina inner shelf. J. Geophys. Res, 104 , 18 205–18 226.
Longuet-Higgins, M. S., 1970: Longshore currents generated by obliquely incident sea waves. Part 1 and 2. J. Geophys. Res, 75 , 6790–6801.
Lumley, J. L., and E. A. Terray, 1983: Kinematics of turbulence convected by a random wave field. J. Phys. Oceanogr, 13 , 2000–2007.
Mei, C. C., 1983: The Applied Dynamics of Ocean Surface Waves. McGraw-Hill, 740 pp.
Monin, A. S., and A. M. Yaglom, 1971: Statistical Fluid Mechanics. The MIT Press, 769 pp.
Nielsen, P., 1992: Coastal Bottom Boundary Layers and Sediment Transport. World Scientific, 257 pp.
Ogston, A. S., C. R. Sherwood, and A. E. Asher, 1995: Estimation of turbulence dissipation rates and gas-transfer velocities in a surf pool: Analysis of the results from WABEX-93. Air–Water Gas Transfer: Selected Papers from the Third International Symposium on Air–Water Gas Transfer, Heidelberg University, B. Jahne and E. C. Monahan, Eds., AEON Verlag, 255–268.
Oltman-Shay, J., P. A. Howd, and W. A. Birkemeier, 1989: Shear instabilities of the mean long-shore current. Part 2. Field data. J. Geophys. Res, 94 , 18 031–18 042.
Stauble, D. K., 1992: Long-term profile and sediment morphodynamcis: Field Research Facility case history. Tech. Rep. CERC-92-7, U. S. Army Corps of Engineers Waterways Experiment Station, Coastal Engineering Research Center, Vicksburg, MS, 252 pp.
Svendsen, I. A., 1987: Analysis of surf zone turbulence. J. Geophys. Res, 92 , 5115–5124.
Svendsen, I. A., and U. Putrevu, 1994: Nearshore mixing and dispersion. Proc. Roy. Soc. London, 445A , 561–576.
Taylor, P. A., and K. A. Dyer, 1977: Theoretical models of flow near the bed and their implications for sediment transport. The Sea. Vol. 6: Marine Modeling, E. D. Goldberg, I. N. McCave, J. J. O'Brien, and J. H. Steele, Eds., Wiley and Sons, 579–601.
Tennekes, H., and J. L. Lumley, 1972: A First Course in Turbulence. The MIT Press, 300 pp.
Terray, E. A., M. A. Donelan, Y. C. Agrawal, W. M. Drennan, K. K. Kahma, A. J. Williams, P. A. Hwang, and S. A. Kitaigorodskii, 1996: Estimates of kinetic energy dissipation under breaking waves. J. Phys. Oceanogr, 26 , 792–807.
Thornton, E. B., and R. T. Guza, 1986: Surf-zone longshore currents and random waves: Field data and models. J. Phys. Oceanogr, 16 , 1165–1178.
Ting, F. C. K., and J. T. Kirby, 1996: Dynamics of surf-zone turbulence in a spilling breaker. Coastal Eng, 27 , 131–160.
Trowbridge, J. H., 1998: On a technique for measurement of turbulent shear stress in the presence of surface waves. J. Atmos. Oceanic Technol, 15 , 290–298.
Voulgaris, G., and J. H. Trowbridge, 1998: Evaluation of the acoustic Doppler velocimeter (ADV) for turbulence measurements. J. Atmos. Oceanic Technol, 15 , 272–289.
Whitford, D. J., and E. B. Thornton, 1996: Bed shear stress coefficients for longshore currents over a barred profile. Coastal Eng, 27 , 243–262.
APPENDIX
Model of High-Frequency Turbulent Velocity Spectra
Array of near-bottom acoustic Doppler current meters deployed in about 4.5-m water depth approximately 300 m from the shoreline. ADVF and ADVO are SonTek field and ocean probes, respectively
Citation: Journal of Physical Oceanography 31, 8; 10.1175/1520-0485(2001)031<2403:TMITSZ>2.0.CO;2
Array of near-bottom acoustic Doppler current meters deployed in about 4.5-m water depth approximately 300 m from the shoreline. ADVF and ADVO are SonTek field and ocean probes, respectively
Citation: Journal of Physical Oceanography 31, 8; 10.1175/1520-0485(2001)031<2403:TMITSZ>2.0.CO;2
Array of near-bottom acoustic Doppler current meters deployed in about 4.5-m water depth approximately 300 m from the shoreline. ADVF and ADVO are SonTek field and ocean probes, respectively
Citation: Journal of Physical Oceanography 31, 8; 10.1175/1520-0485(2001)031<2403:TMITSZ>2.0.CO;2
Locations of instruments (labeled) and contours of water depth (in m below mean sea level every 0.5 m) for yearday 226. Each compact array (CA6 and CA7) contained six accurately (±0.5 m) surveyed bottom-mounted pressure sensors (small filled circles) and one current meter located about 0.5 m above the bottom near the center of the array (not shown) (Herbers et al. 2000, submitted to J. Phys. Oceanogr.). The shoreline location was centered approximately at cross-shore location = 125 m, with ≃ ±10 m cross-shore fluctuations caused by the 1-m tidal range. The bathymetry seaward of about 3.5-m depth did not change significantly during the experiment
Citation: Journal of Physical Oceanography 31, 8; 10.1175/1520-0485(2001)031<2403:TMITSZ>2.0.CO;2
Locations of instruments (labeled) and contours of water depth (in m below mean sea level every 0.5 m) for yearday 226. Each compact array (CA6 and CA7) contained six accurately (±0.5 m) surveyed bottom-mounted pressure sensors (small filled circles) and one current meter located about 0.5 m above the bottom near the center of the array (not shown) (Herbers et al. 2000, submitted to J. Phys. Oceanogr.). The shoreline location was centered approximately at cross-shore location = 125 m, with ≃ ±10 m cross-shore fluctuations caused by the 1-m tidal range. The bathymetry seaward of about 3.5-m depth did not change significantly during the experiment
Citation: Journal of Physical Oceanography 31, 8; 10.1175/1520-0485(2001)031<2403:TMITSZ>2.0.CO;2
Locations of instruments (labeled) and contours of water depth (in m below mean sea level every 0.5 m) for yearday 226. Each compact array (CA6 and CA7) contained six accurately (±0.5 m) surveyed bottom-mounted pressure sensors (small filled circles) and one current meter located about 0.5 m above the bottom near the center of the array (not shown) (Herbers et al. 2000, submitted to J. Phys. Oceanogr.). The shoreline location was centered approximately at cross-shore location = 125 m, with ≃ ±10 m cross-shore fluctuations caused by the 1-m tidal range. The bathymetry seaward of about 3.5-m depth did not change significantly during the experiment
Citation: Journal of Physical Oceanography 31, 8; 10.1175/1520-0485(2001)031<2403:TMITSZ>2.0.CO;2
(a) Alongshore wind stress, (b) significant wave height, (c) cross-shore gradient of wave-induced energy flux, and (d) cross-shore gradient of wave-induced radiation stress vs time
Citation: Journal of Physical Oceanography 31, 8; 10.1175/1520-0485(2001)031<2403:TMITSZ>2.0.CO;2
(a) Alongshore wind stress, (b) significant wave height, (c) cross-shore gradient of wave-induced energy flux, and (d) cross-shore gradient of wave-induced radiation stress vs time
Citation: Journal of Physical Oceanography 31, 8; 10.1175/1520-0485(2001)031<2403:TMITSZ>2.0.CO;2
(a) Alongshore wind stress, (b) significant wave height, (c) cross-shore gradient of wave-induced energy flux, and (d) cross-shore gradient of wave-induced radiation stress vs time
Citation: Journal of Physical Oceanography 31, 8; 10.1175/1520-0485(2001)031<2403:TMITSZ>2.0.CO;2
(a) Cross-shore velocity (negative is offshore-directed flow), (b) alongshore velocity (positive is flow toward the south), (c) cross-shore gradient of alongshore velocity, and (d) percent of valid data from the malfunctioning ADVO vs time
Citation: Journal of Physical Oceanography 31, 8; 10.1175/1520-0485(2001)031<2403:TMITSZ>2.0.CO;2
(a) Cross-shore velocity (negative is offshore-directed flow), (b) alongshore velocity (positive is flow toward the south), (c) cross-shore gradient of alongshore velocity, and (d) percent of valid data from the malfunctioning ADVO vs time
Citation: Journal of Physical Oceanography 31, 8; 10.1175/1520-0485(2001)031<2403:TMITSZ>2.0.CO;2
(a) Cross-shore velocity (negative is offshore-directed flow), (b) alongshore velocity (positive is flow toward the south), (c) cross-shore gradient of alongshore velocity, and (d) percent of valid data from the malfunctioning ADVO vs time
Citation: Journal of Physical Oceanography 31, 8; 10.1175/1520-0485(2001)031<2403:TMITSZ>2.0.CO;2
Energy density spectra from (a) velocity time series and (b) modified according to (6) and (7). Solid curves are Puu + Pυυ and dashed curves are Pww. (c) Integral of cospectrum of velocity differences vs frequency. Data are from 25-min-long ADVO records obtained at 12:00 (EST) on yearday 236. The burst-averaged cross-shore and alongshore currents were −0.02 and 0.10 m s−1, respectively, and the significant wave height was 1.0 m
Citation: Journal of Physical Oceanography 31, 8; 10.1175/1520-0485(2001)031<2403:TMITSZ>2.0.CO;2
Energy density spectra from (a) velocity time series and (b) modified according to (6) and (7). Solid curves are Puu + Pυυ and dashed curves are Pww. (c) Integral of cospectrum of velocity differences vs frequency. Data are from 25-min-long ADVO records obtained at 12:00 (EST) on yearday 236. The burst-averaged cross-shore and alongshore currents were −0.02 and 0.10 m s−1, respectively, and the significant wave height was 1.0 m
Citation: Journal of Physical Oceanography 31, 8; 10.1175/1520-0485(2001)031<2403:TMITSZ>2.0.CO;2
Energy density spectra from (a) velocity time series and (b) modified according to (6) and (7). Solid curves are Puu + Pυυ and dashed curves are Pww. (c) Integral of cospectrum of velocity differences vs frequency. Data are from 25-min-long ADVO records obtained at 12:00 (EST) on yearday 236. The burst-averaged cross-shore and alongshore currents were −0.02 and 0.10 m s−1, respectively, and the significant wave height was 1.0 m
Citation: Journal of Physical Oceanography 31, 8; 10.1175/1520-0485(2001)031<2403:TMITSZ>2.0.CO;2
Estimates of near-bottom stress using (a) single and (b) dual sensors vs time. (b) Estimates from the pair of ADVOs and ADVFs are shown as solid and dashed curves, respectively
Citation: Journal of Physical Oceanography 31, 8; 10.1175/1520-0485(2001)031<2403:TMITSZ>2.0.CO;2
Estimates of near-bottom stress using (a) single and (b) dual sensors vs time. (b) Estimates from the pair of ADVOs and ADVFs are shown as solid and dashed curves, respectively
Citation: Journal of Physical Oceanography 31, 8; 10.1175/1520-0485(2001)031<2403:TMITSZ>2.0.CO;2
Estimates of near-bottom stress using (a) single and (b) dual sensors vs time. (b) Estimates from the pair of ADVOs and ADVFs are shown as solid and dashed curves, respectively
Citation: Journal of Physical Oceanography 31, 8; 10.1175/1520-0485(2001)031<2403:TMITSZ>2.0.CO;2
(a) Sum of wind and wave forcing and (b) near-bottom turbulent Reynolds shear stress vs time
Citation: Journal of Physical Oceanography 31, 8; 10.1175/1520-0485(2001)031<2403:TMITSZ>2.0.CO;2
(a) Sum of wind and wave forcing and (b) near-bottom turbulent Reynolds shear stress vs time
Citation: Journal of Physical Oceanography 31, 8; 10.1175/1520-0485(2001)031<2403:TMITSZ>2.0.CO;2
(a) Sum of wind and wave forcing and (b) near-bottom turbulent Reynolds shear stress vs time
Citation: Journal of Physical Oceanography 31, 8; 10.1175/1520-0485(2001)031<2403:TMITSZ>2.0.CO;2
(a) Shear production of turbulent kinetic energy, (b) dissipation of turbulent kinetic energy, and (c) depth-averaged rate of energy extraction from the shoaling wave field vs time. The vertical scale in (c) is different than in (a) and (b)
Citation: Journal of Physical Oceanography 31, 8; 10.1175/1520-0485(2001)031<2403:TMITSZ>2.0.CO;2
(a) Shear production of turbulent kinetic energy, (b) dissipation of turbulent kinetic energy, and (c) depth-averaged rate of energy extraction from the shoaling wave field vs time. The vertical scale in (c) is different than in (a) and (b)
Citation: Journal of Physical Oceanography 31, 8; 10.1175/1520-0485(2001)031<2403:TMITSZ>2.0.CO;2
(a) Shear production of turbulent kinetic energy, (b) dissipation of turbulent kinetic energy, and (c) depth-averaged rate of energy extraction from the shoaling wave field vs time. The vertical scale in (c) is different than in (a) and (b)
Citation: Journal of Physical Oceanography 31, 8; 10.1175/1520-0485(2001)031<2403:TMITSZ>2.0.CO;2
(a) Covariance, (b) log profile, and (c) drag law estimates of turbulent Reynolds shear stress vs time
Citation: Journal of Physical Oceanography 31, 8; 10.1175/1520-0485(2001)031<2403:TMITSZ>2.0.CO;2
(a) Covariance, (b) log profile, and (c) drag law estimates of turbulent Reynolds shear stress vs time
Citation: Journal of Physical Oceanography 31, 8; 10.1175/1520-0485(2001)031<2403:TMITSZ>2.0.CO;2
(a) Covariance, (b) log profile, and (c) drag law estimates of turbulent Reynolds shear stress vs time
Citation: Journal of Physical Oceanography 31, 8; 10.1175/1520-0485(2001)031<2403:TMITSZ>2.0.CO;2
Woods Hole Oceanographic Institution Contribution Number 10275.
