Showing papers in "Journal of Physical Oceanography in 1988"

A Method for the Routine Analysis of Pitch-and-Roll Buoy Wave Data

Abstract: A simple, computationally efficient method is proposed as a standard procedure for the routine analysis of pitch-and-roll buoy wave data. The method yields four directional model-free parameters per frequency: the mean direction, the directional width, the skewness, and the kurtosis of the directional energy distribution. For most applications these parameters provide sufficient directional information. The estimation procedure and error characteristics of the parameter estimates are discussed and illustrated with computer simulated data. An optional interpretation of the combination of skewness and kurtosis as an indicator of uni-modality of the directional energy distribution is suggested and illustrated with field observations.

A General Circulation Model for Upper Ocean Simulation

Abstract: A general circulation model (GCM) of the ocean that emphasizes the simulation of the upper ocean has been developed. This emphasis is in keeping with its future intent, that of an air-sea coupled model. The basic model is the primitive equation model of Bryan and Cox with the additions, of optional usage, of the Mellor-Yamada level 2.5 turbulence closure scheme and horizontal nonlinear viscosity. These modifications are intended to improve the upper ocean simulations, particularly sea surface temperature and heat content. The horizontal grid spacing is 1° latitude × 1° longitude and is global in domain. The equatorial region between 10°N and 10°S is further refined in the north–south direction to ⅓° resolution. There are 12 vertical levels, with six levels in the top 70 m. The model incorporates varying bottom topography. Prior to coupling the ocean model to an atmospheric GCM, experiments have been carried out to determine the ocean GCM's performance using atmospheric forcing from observed data....

A study of an intense density front in the eastern Alboran Sea: the Almeria-Oran front

Abstract: Studies of satellite imagery and space shuttle photographs of the western Mediterranean have indicated that the main path of inflowing Atlantic Water is around two large anticyclonic gyres in the Alboran Sea and along the Algerian Coast. These studies have also shown that a strong ocean front is present between Almeria, Spain, and Oran, Algeria, which is part of the easternmost segment of the Eastern Alboran Gyre. Based on these satellite studies, the first in situ investigation of the front, called here the Almeria–Oran Front, was conducted in March 1986 as part of the winter campaign of the Western Mediterranean Circulation Experiment (WMCE). Analyses of the resulting data show that the Almeria–Oran Front is a large-scale density front, formed by the convergence of two distinct water masses and controlled by the geographic position and strength of the Eastern Alboran Gyre. Physical and biochemical data indicate that the front is limited to the upper 300 m, with a strong southward baroclinic jet...

The Retroflection of the Agulhas Current

Abstract: A description of the nature and kinematics of the Agulhas Current termination is given based on satellite infrared imagery and selected hydrographic measurements collected over the past decade On average the Agulhas retroflection lies between 16° and 20°E longitude and has a loop diameter of 340 km During the period of the investigation the retroflection loop protruded into the South Atlantic at intervals of slightly more than one month, shedding a pinched-off Agulhas ring with a diameter of about 320 km at its most westerly extension Rings drift away at about 12 cm s−1 and can be observed by their distinctive thermal characteristics at the sea surface as far west as 5°E and as far south as 46°S, well south of the subtropical convergence The shedding rate of rings and their subsequent drift may play an important role in the dynamics of the South Atlantic Ocean

Wave Propagation in a Solid Ice Pack

Abstract: The analysis presented in this paper was inspired by the report that the R/V Polarstern has encountered surface waves of large amplitude hundreds of kilometers inside the ice pack in the Weddell Sea. This paper presents analysis of processes that affect waves in an ice pack, namely the refraction of waves at the pack edge, the effects of pack compression on wave propagation, wave train stability and buckling stability in the ice pack. Sources of pack compression and interaction between wave momentum and pack compression are discussed. Viscous damping of propagating waves are also studied. Significant results include the conditions for total reflection of waves at the pack edge, the strong effect of pack compressive stress on wave group speed, with the concomitant possibility of extreme local concentration of wave energy. The result that compressive stress in the pack leads to very rapid development of wave packets, through changes in the parameters for weakly nonlinear modulational instability of...

Modeling the Seasonal Cycle of the Upper Ocean

Abstract: The parameterization of the turbulence used in one-dimensional oceanic mixed layer models is briefly reviewed, focusing on the long-term response of these models. Particular attention is directed towards the parameterization of turbulent dissipation. A general parameterized form is proposed that provides a useful guideline to devise new parameterizations and to compare existing ones. Different models of the classical Niiler–Kraus type are first tested by simulating four years (1969–72) of the upper ocean evolution at Ocean Station Papa. In the results, distinction is made between the errors inherent in the model and those due to changes in the upper ocean heat content not explained by the surface heat fluxes. It appears that, after a needed empirical calibration, all models systematically overestimate the sea surface temperature (SST) in summer and underestimate it during fall. In absolute value, the maximum error on the monthly-mean predicted SST reaches about 1 K. In an attempt to reduce this e...

River-Forced Estuarine Plumes

Abstract: The development, maintenance, and dissipation of river-forced estuarine plumes with and without seaward sloping bottom are studied by use of a three-dimensional, primitive-equation model. Inside the estuary, discussion is focused on how the Coriolis force induces lateral asymmetries in the circulation. Four physical processes dictate the transient as well as the quasi-steady circulation in moderately stratified estuaries: 1) upper-layer convergence during the transient spinup phase, 2) upward entrainment leading to the two-layer steady circulation pattern, 3) upward stretching of the lower-layer vortex during the spindown period, and 4) in the presence of a seaward bottom slope, the left-bounded tendency of the landward undercurrent for all phases of development. Deviations from the laterally averaged circulation pattern caused by these processes are discussed. Over the shelf, various types of plumes are defined according to the visual appearance of the surface salinity field. The four types of p...

Wind-Driven Motion of Estuarine Plumes

Abstract: The effect of wind forcing on existing estuarine plumes in a coupled estuary-shelf environment is studied here using a three-dimensional primitive-equation model. The emphasis is on wide estuaries so that the Coriolis force cannot be ignored. Over the shelf, the plume responds mostly to the wind-induced surface Ekman drift. Under downwelling-favorable wind, an additional downwind coastal jet occurs that elongates the plume along the shore. For cross-shelf winds, the nearshore Ekman drift is considerably retarded by the sea level setup or setdown. The retardation is particularly effective when the stratification increases. These properties of wind-driven coastal circulations determine the first-order plume responses. Inside the estuary, the down estuary wind reinforces the gravitational circulation, but the up-estuary wind opposes it. Both winds are effective local forcings that make the remotely forced signals from the shelf unlikely to be detected. Compared to longitudinal winds, cross-estuary w...

Potential Vorticity Distribution in the North Pacific

Abstract: Vertical sections and maps of potential vorticity ρ−1f∂ρ/∂z for the North Pacific are presented. On shallow isopycnals, high potential vorticity is found in the tropics, subpolar gyre, and along the eastern boundary of the subtropical gyre, all associated with Ekman upwelling. Low potential vorticity is found in the western subtropical gyre (subtropical mode water), in a separate patch near the sea surface in the eastern subtropical gyre and extending around the gyre, and near sea-surface outcrops in the subpolar gyre; the last is analogous to the subpolar mode water of the North Atlantic and Southern Ocean. Meridional gradients of potential vorticity are high between the subtropical and subpolar gyres at densities which outcrop only in the subpolar gyre; lateral gradients of potential vorticity are low in large regions of the subtropical gyre on these isopycnals. On slightly denser isopycnals which do not outcrop in the North Pacific, there are large regions of low potential vorticity gradients ...

Variability of Structure and Transport of the Florida Current in the Period Range of Days to Seasonal

Abstract: Current measurements with five repeated moored arrays were carried out from April 1982 to June 1984 across the Florida Current between West Palm Beach and Grand Bahama Island; a reduced sixth array was continued until June 1985. Transport were calculated directly by vertical integration of the 40-hour low-passed northward current components and extrapolation to the surface using the mean vertical shears ova the extent of the mooring. These transports compared well with 96 transport sections measured by PEGASUS and with transports determined by cable voltage measurements. During 1982–84 the transport variations ranged between 20 and 40 Sv (Sv = 106 m3 s−1) with a mean of 30.5 Sv and standard deviations of the 40-hour low-passed data of ±3 Sv. However, monthly mean deviations from the mean annual cycle were only of order ± 1 Sv, indicating that the climate relevant long-period variations of this current are fairly small. The volume transport shows a continuous spectrum with no particularly energeti...

Observations of 20-Day Period Meridional Current Oscillations in the Upper Ocean along the Pacific Equator

Abstract: Prominent oscillations of the meridional current, with a mean period of approximately 20 days, have been observed in the upper ocean over several years from May 1979 to October 1985 using moored current measurements along the Pacific equator at 95°, 110°, 124°,140°W and 152°W, as well as off (but near) the equator at 110° and 140°W. The fluctuations are relatively narrowband (±0.005 cpd) in frequency. A 95% statistically significant peak in power spectra of meridional current occurred at 110°, 124° and 140°W, but not at 95° and 152°W where the spectral peaks were smaller. The dominant wave period decreased by about 4% from 110° to 140°W. Maximum amplitude was measured at 124°W; the amplitude above 80 m was maximum at the equator and decreased poleward from the equator. At 15 m the annual averaged root-mean-square amplitude was about 20.5 cm s−1, and individual peak-to-trough values reached 150 cm s−1. The wave amplitude decreased with depth and the wave was essentially confined to the upper 80 m....

Radar Returns from the Sea Surface—Bragg Scattering and Breaking Waves

Abstract: Recent ideas on the structure of the equilibrium range of wind-generated ocean waves are applied to the question of radar backscattered returns from the sea surface. It is shown that the backscattering cross section can be represented as the sum of separate contributions from Bragg-scattering and from individual breaking events:where θ is the angle of incidence, ϕ is the direction of observation relative to the wind, u* is the friction velocity and κ the radar wavelength; the Bragg-scattering contribution increases linearly with u* and the sea spike contribution cubically. The number of sea spikes per unit time per unit surface area for a given threshold of spike intensity or duration is proportional to g−1u*3. Calibrated radar measurements of median values of σ0, which tend to suppress sea spike contributions, have been made by Guinard et al. over a range of radar wavelengths from 70 to 3.4 cm. These scale consistently with the parameter (u*2κ/g)½ over angles of incidence greater than 30°, and a...

Dynamics of Seasonal and Intraseasonal Variability in the Eastern Equatorial Pacific

Abstract: Time series measurements from surface moored buoys in the eastern equatorial Pacific are analyzed for the period 1983–86. The data, collected as part of the EPOCS and TROPIC HEAT programs, consist of currents, temperatures, and winds on the equator at 110°, 124.5° and 140°W. The purpose is to examine the dynamics of seasonal and intraseasonal variability in the upper 250 m from a diagnosis of the depth integrated zonal momentum (i.e., transport) equation. The principal conclusions of this paper are that 1) there is an approximate balance between mean zonal wind stress and depth integrated pressure gradient; nonlinear advection is significantly nonzero however and leads to an enhancement of eastward transport along the equator, 2) there is an interannual change in zonal wind stress and pressure gradient in which both approximately double over the record length; 3) at the annual cycle, zonal wind stress and depth integrated pressure gradient tend to balance, though the uncertainties are large and o...

Instability Waves in the Equatorial Atlantic Ocean

Abstract: Evidence is presented for the generation of planetary waves by barotropic instability within the cyclonic shear region of the Atlantic Ocean's South Equatorial Current (SEC). Immediately following the springtime intensification of the southeast trade wind, which accelerates the SEC westward, a packet of waves with central periodicity of around 25 days is observed lasting for about three cycles. Independent wavenumber analyses on 1983 and 1984 data give newly identical zonal wavelengths and phase speed estimates of around 1100 km and −50 cm s−1. The waves are anisotropic and spatially inhomogeneous with generation confined primarily to the mixed layer. An energetics analysis using 1983 data centered upon the equator at 28°W shows a rapid increase in total perturbation energy (TPE) reaching values of 2000 erg cm−3 within two weeks. The subsequent decrease in TPE at this location is due primarily to meridional pressure-work divergence. Baroclinic instability is negligible because both the meridional...

Currents, Water Masses, Eddies and Jets in the Mediterranean Levantine Basin

Abstract: Hydrographic measurements in the southeastern Levantine basin are analyzed, and the climatological water masses of the region and their seasonal variations are identified. We observe the formation of the salty and warm Levantine Surface Water Layer (LSW); we characterize the subsurface Atlantic Water Layer (AW); and we describe the properties of the thermocline waters, called Levantine Intermediate Waters (LIW). The baroclinic dynamical modes are computed for the climatological stratification parameters. The empirical orthogonal function (EOF) analysis of the vertical shear profiles shows that considerable energy is contained in the second EOF at the thermocline and deep levels. Maps of the baroclinic streamfunction field referred to 700 meters are displayed: 16 instantaneous flow field realizations show an intense mesoscale eddy file never revealed before in the region. The space scales of the eddies are about 100 km and a smaller scale (60–70 km) variability is also evident. The eddies are pres...

Variations of whitecap coverage with wind stress and water temperature

Abstract: Results of whitecap coverages from five previously reported oceanic experiments by Monahan and coinvestigators have been analyzed; the fractional coverage of the sea surface(W) was shown to follow a power law, W = 2U3.7510, where U10 is the wind velocity at 10 m above the mean sea surface. Attempts were then made to associate the coverage with the wind-friction velocity (u*) deduced from the wind velocity and air–sea temperature differences as W = 0.2u3*. Finally, we discuss effects of the water temperature on the coverage.

Bottom Stress Estimates from Vertical Dissipation Rate Profiles on the Continental Shelf

Abstract: Measurements of the near-bottom distribution of the turbulent dissipation rate on the continental shelf west of Vancouver Island are used to calculate bottom stress. A free-failing vertical profiler with microstructure shear probes was used to measure the dissipation rate, from near the surface to within 0.15 m of the bottom. The shear probes measure velocity gradients at scales within the viscous subrange of the turbulence and therefore directly measure the rate at which kinetic energy is dissipated by viscosity. Friction velocities are computed from the formula uast; = (ϵκz/ρ)⅓, where the dissipation rate ϵ is measured in the constant stress layer. The technique is more reliable than estimates of the dissipation rate obtained by fitting spectral slopes to velocity spectra at scales in the inertial subrange. Near-bottom current measurements indicate that the bottom stress values obtained from the turbulent measurements are well correlated with the current magnitude. An estimate of the drag coeff...

The Effect of Salinity on Tropical Ocean Models

Abstract: The effect of horizontal salinity gradients on the tropical ocean circulation has not previously been evaluated. It is shown that there are noticeable differences between the dynamic height field calculated with and without the inclusion of salinity variations. Hence salinity has a significant contribution to the geostrophic velocity field. This conclusion is illustrated by running two identical Indian Ocean models:. one initialized using a climatological salinity field while the other has no horizontal salinity gradients. The differences in the temperature and velocity fields after 110 days are of the order of 0.5°C and 10 cm s−1 over some regions of the ocean. Further experiments using the same model for data updating studies showed that the absence of salinity data greatly reduces the usefulness of temperature data. It is concluded that for an accurate simulation of the tropical ocean the salinity field needs to be included.

Analysis of an Internal Tide Observed on the Malin Shelf, North of Ireland

Abstract: Evidence of an internal tide on the eastern side of the Rockall Trough is derived from recording current meters and thermistor chains sited at the edge and near the center of the Malin Shelf. Although the barotropic tidal currents are small (M2 is 0.13 m s−1), temperature contour plots revealed significant semidiurnal oscillations at both sites. From an analysis of the data it appears that there was a linear, predominantly mode-1, internal tide which was coherent with the barotropic tide over the spring-neap cycle and which had a mean energy of 452 J m−2 at the shelf edge. The onshore flux (estimated to be 104 W m−1) was about twice that predicted by the Baines model for subcritical slopes but, in view of the simplifications that are made, the comparison is considered reasonable. For the model to be applicable, most of the energy must be generated in the deep water of the Rockall Trough, propagating eastward over a marginally subcritical slope and onto the shelf. The energy dissipated at about 10...

Hydraulic Jump and Undular Bore Formation on a Shelf Break

Abstract: The evolution of the semidiurnal internal tide as it propagates across the Australian North West Shelf is discussed analytically. As the tide is of long wavelength and small amplitude, this evolution is described by a perturbed extended Korteweg-de Vries equation. It is found that the flow is dominated by nonlinearity, and hence is hydraulic, except in the neighborhood of any shocks predicted by hydraulic theory. Hydraulic theory predicts the formation of two shocks in each period of the tide. The inclusion of dispersion in boundary layers around the shocks results in one of these shocks breaking up into an undular bore. Good agreement is found with observations by Holloway of the semidiurnal internal tide on the Australian North West Shelf.

The Water Masses of the Central North Atlantic in 1983—84

Abstract: Hydrographic surveys carried out in 1983–84 along both sides of the Mid-Atlantic Ridge between 24° and 53°N provide a detailed description of the well-known North Atlantic water masses with particular emphasis on their meridional distribution and zonal dissymetry. In the upper layers the dense horizontal sampling resolves the several narrow Gulf Stream extensions into the ocean interior, giving the image, in the Central Water density range, of a mosaic of mode waters separated by fronts. At intermediate depths a vertical shear in the distributions of the Mediterranean Water and Labrador Sea Water stands out, both water masses having their lower part displaced southwards relative to their upper parts. Bottom waters containing nearly 20 percent of pure Antarctic Bottom Water are observed at 50°N in the eastern basin, in contrast with the western basin where proportions greater than 10 percent were found only south of 36°N along our section. This water mass analysis also gives indications that stron...

Gulf Stream Simulations and the Dynamics of Ring and Meander Processes

Abstract: We present here a regional, eddy resolving, numerical study of the dynamics of Gulf Stream Meander and Ring (GSMR) interaction processes. We initialize the Harvard quasi-geostrophic open-boundary model with realistic meander and ring locations as indicated by remotely sensed sea surface temperature (SST) data and predict the flow evolution for the period 23 November to 19 December 1984. The methodology of Feature-Model initialization is introduced to extend the surface information to the thermocline and deep levels in terms of climatological structures, which are then dynamically adjusted by the model. Six numerical simulators are carried out to explore the influence of initial and boundary conditions on the flow evolution. All of the major events observed in the SST data are simulated, including the birth of new warm and cold core rings. The results show the relevance of quasi-geostrophic dynamics for the GSMR region on these time scales in the thermocline. A set of parameter and sensitivity exp...

A Numerical Model Investigation of Tides and Diurnal-Period Continental Shelf Waves along Vancouver Island

Abstract: A numerical model study of the tidal regime west of Vancouver Island is presented. Ale model employed is a nonlinear barotropic two-dimensional tidal model incorporating realistic bathymetry. The M2 and K1 constituents are examined and comprehensive comparisons between computed and observed elevations and currents are given. For M2, the model reproduces observed motion very accurately. However, K1 is of greater interest since it contains a substantial contribution in the form of a continental shelf wave (CSW). The model correctly predicts the existence of the CSW but, consistent with the neglect of stratification and the influence of mean flows, underestimates its wavelength. It is shown that the CSW component of K1 is generated by the tidal flow in Juan de Fuca Strait. The influence of mean currents on the tidal regime is investigated by including them in a further model solution. Consistent with theory, the wavelength of the CSW component of K1 is increased, giving improved agreement with obser...

Currents through Torres Strait

Abstract: A five-month field study of the circulation in the Torres Strait was carried out. Baroclinic effects were negligible. The Arafura Sea and the Coral Sea forced a different tide on either side of Torres Strait, resulting in fluctuations of sea level difference of up to 6 m on either side of the Strait. The tidal dynamics in the Strait were controlled by a local balance between the acceleration, the sea level slope, and the bottom friction. Only 30% of the semidiurnal tidal wave was transmitted through Torres Strait. There were also fluctuations of the high-frequency sea level residuals (up to 0.8 m peak to trough) which appeared to be related to complex flows both through the Strait and across the Strait. Low-frequency sea level fluctuations were incoherent on either side of the Strait, and resulted in fluctuations of the low-frequency sea level differences on either side of the Strait of typically 0.3 m. These sea level gradients and the local wind forcing generated low-frequency current fluctuati...

Deep Currents in the Central Subarctic Pacific Ocean

Abstract: Sections of closely spaced CTD stations along Longs. 165°W, 175°W and 175°E, in combination with 14-month current records from the central longitude, define two deep, nearly zonal currants, with speed increasing upward, in the subarctic Pacific. One flows eastward above the Aleutian Rise and Aleutian Trench, and appears to be a concentration of geostrophic flow forced by the bottom topography. The other flows westward along the Aleutian Island Arc, and is the northern-boundary current predicted by deep-circulation theory. Both currents reach to the sea surface, the boundary current being simply the deep part of the Alaskan Stream. The current records were too few to permit better than rough estimates of volume transports but to the extent that they could be combined with thermal-wind calculations they suggest, at 175°W, (1) a transport of 28 × 106 m3 s−1 for the Alaskan Stream, of whch 5 × 106 m3 s−1 was found below 1500 m, and (2) a transport of around 20 × 1O6 m3 s−1 for the eastward jet, of wh...

Eddies at the Subtropical Convergence South of Africa

Abstract: A descriptive analysis of the occurrence and kinematics of mesoscale eddies at the subtropical convergence south of Africa is presented. Data used in this study include thermal infrared imagery from satellites since 1978 and a number of expendable hathythermogaph sections in the geographic area, supported by drift tracks of free-drifting buoys since 1975. The distribution of intense cold eddies to the north and warm eddies to the south of the subtropical convergence shows distinct geographic patterns. The morphology of these eddies is such as to allow them to be categorized into four distinct classes, each with a specific origin and kinematic behavior. This implies consistent underlying dynamics which is shown to include the influence of bottom topography as well as meridional current shear.

A Modified Inertial Dissipation Method for Estimating Seabed Stresses at Low Reynolds Numbers, with Application to Wave/Current Boundary Layer Measurements

Abstract: The inertial dissipation method for estimating seabed friction velocities from near-bed turbulence spectra requires few measurements; it is relatively insensitive to errors in sensor orientation and measurement of mean flows. However, the method is only valid if turbulence spectra are measured at a height above the seabed that is small enough to be within the constant stress layer but large enough to produce an inertial subrange. It is shown that such a height exists only if the friction velocity exceeds a critical value (typically 0.8 cm s−1 for a midlatitude ocean). Recent measurements from combined wave and mean flow conditions on the continental shelf do not satisfy this requirement. However, an empirical modification to the inertial dissipation method is suggested to allow estimation of the friction velocity even when a true inertial subrange does not exist. The modified method is applied to the combined wave and mean flow field data; it virtually removes an increase in estimated friction ve...

Wind-Forced Transport Fluctuations of the Florida Current

Abstract: Volume transport fluctuations of the Florida Current (Gulf Stream), generated within the Straits of Florida by local meridional wind stress, are investigated. A simple coastal response model was applied to the Straits of Florida and forced by along-channel winds only. The predicted volume transports were in good agreement with transport estimates derived from moored current meters and cable voltages for synoptic scale winter winds in the period band from 4 to 10 days. Good agreement was also found for the annual transport cycle for the two years of available data, suggesting that the seasonal change in along-channel wind forcing provides a significant contribution to the annual transport cycle of the Florida Current.

A Numerical Study on the Influence of the Mid-Atlantic Ridge on Nonlinear First-Mode Baroclinic Rossby Waves Generated by Seasonal Winds

Abstract: A numerical model simulation investigates the influence of the mid-Atlantic ridge on nonlinear first-mode baroclinic Rossby waves generated by seasonal wind fluctuations. The North Atlantic is simulated by a square-box, two-layer quasi-geostrophic (QG) model. The bottom topography is ridge-like and compromises the QG approximation and the actual shape of the ridge. Sponge layers protect all boundaries except the eastern one from wave reflection and eliminate the build-up of the western boundary current. The model is forced by a purely fluctuating wind stress curl derived from the most significant EOFs of the FGGE winds. A flat bottom and a ridge experiment are compared. In both experiments the eastern boundary is an important source of annual-period baroclinic Rossby waves. Wave trains having a wavelength of about 1060 km and a westward phase speed around 3.4 cm s−1 propagate energy westward at 3 cm s−1. In the flat bottom experiment a source of directly wind-forced baroclinic waves of annual per...

Seabed Stresses in Combined Wave and Steady Flow Conditions on the Nova Scotia Continental Shelf: Field Measurements and Predictions

Abstract: A tripod holding electromagnetic flowmeters at two heights within 1 m above the seabed has been deployed at two shallow sites (25 and 45 m depths) on the continental shelf off Nova Scotia, Canada. Wave flows are comparable with the small mean flows at both sites. Friction velocities have been estimated from the observed spectra of vertical turbulent velocities, using a modification of the dissipation method appropriate to low Reynolds number conditions. The results from each site show no significant change of friction velocity with height, as expected for measurements from within the constant stress layer. However, in each case the observed friction velocities are considerably larger than would be predicted on the basis of the observed bottom roughness and the mean flows alone, indicating that the wave flows were important in enhancing the friction velocity. The theory of Grant and Madsen (1979) has been used to predict the friction velocities, based on the observed mean and wave velocities and o...