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Johanna H. Rosman and Gregory P. Gerbi

Abstract

Assigning a physical interpretation to turbulent fluctuations beneath waves is complex because eddies are advected by unsteady wave orbital motion. Here, the kinematic effects of wave orbital motion on turbulent fluctuations at a fixed location were investigated using model turbulence spatial spectra (κ spectra) together with a general form of the frozen turbulence approximation. Model autospectra and cospectra included an inertial subrange, a rolloff at energy-containing scales (L = 2π/κ 0), and a dissipation range. Turbulence was advected by a background flow composed of waves (rms orbital velocity σ w, peak frequency ω w, and spectral width Δω w) propagating parallel to a current u c. Expressions were derived for turbulence frequency spectra (ω spectra), and parameters were varied across ranges typical in the coastal ocean. Except close to the wave band, the ω-spectrum shape collapses with two dimensionless parameters, a velocity ratio σ w/u c, and a time-scale ratio u c κ 0/ω w, which can be used to diagnose the effects of wave advection on turbulence spectra. As σ w/u c increases, less variance and covariance appear at low frequencies (ω < u c κ 0) and more appear at high frequencies (ω > u c κ 0). If σ w/u c > 2, wave advection must be taken into account when estimating turbulence length scales and integral quantities (e.g., Reynolds stress) from the low-frequency portion of spectra. The offset of the −5/3 region due to waves is unaffected by the rolloff or dissipation range; therefore, previously proposed methods for estimating dissipation rate from wave-affected −5/3 spectra are robust. Although idealized, the results inform the interpretation of turbulence ω spectra beneath waves and guide the estimation of turbulence properties from those spectra.

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Gregory P. Gerbi, Samuel E. Kastner, and Genevieve Brett

Abstract

The effects of wind-driven whitecapping on the evolution of the ocean surface boundary layer are examined using an idealized one-dimensional Reynolds-averaged Navier–Stokes numerical model. Whitecapping is parameterized as a flux of turbulent kinetic energy through the sea surface and through an adjustment of the turbulent length scale. Simulations begin with a two-layer configuration and use a wind that ramps to a steady stress. This study finds that the boundary layer begins to thicken sooner in simulations with whitecapping than without because whitecapping introduces energy to the base of the boundary layer sooner than shear production does. Even in the presence of whitecapping, shear production becomes important for several hours, but then inertial oscillations cause shear production and whitecapping to alternate as the dominant energy sources for mixing. Details of these results are sensitive to initial and forcing conditions, particularly to the turbulent length scale imposed by breaking waves and the transfer velocity of energy from waves to turbulence. After 1–2 days of steady wind, the boundary layer in whitecapping simulations has thickened more than the boundary layer in simulations without whitecapping by about 10%–50%, depending on the forcing and initial conditions.

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Gregory P. Gerbi, Robert J. Chant, and John L. Wilkin

Abstract

This study examines the dynamics of a buoyant river plume in upwelling-favorable winds, concentrating on the time after separation from the coast. A set of idealized numerical simulations is used to examine the effects of breaking surface gravity waves on plume structure and cross-shore dynamics. Inclusion of a wave-breaking parameterization in the two-equation turbulence submodel causes the plume to be thicker and narrower, and to propagate offshore more slowly, than a plume in a simulation with no wave breaking. In simulations that include wave breaking, the plume has much smaller vertical gradients of salinity and velocity than in the simulation without breaking. This leads to decreased importance of shear dispersion in the plumes with wave breaking. Much of the widening rate of the plume is explained by divergent Ekman velocities at the off- and onshore edges. Some aspects of plume evolution in all cases are predicted well by a simple theory based on a critical Richardson number and an infinitely deep ocean. However, because the initial plume in these simulations is in contact with the sea floor in the inner shelf, some details are poorly predicted, especially around the time that the plume separates from the coast.

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Anthony R. Kirincich, Steven J. Lentz, and Gregory P. Gerbi

Abstract

Recently, the velocity observations of acoustic Doppler current profilers (ADCPs) have been successfully used to estimate turbulent Reynolds stresses in estuaries and tidal channels. However, the presence of surface gravity waves can significantly bias stress estimates, limiting application of the technique in the coastal ocean. This work describes a new approach to estimate Reynolds stresses from ADCP velocities obtained in the presence of waves. The method fits an established semiempirical model of boundary layer turbulence to the measured turbulent cospectra at frequencies below those of surface gravity waves to estimate the stress. Applied to ADCP observations made in weakly stratified waters and variable significant wave heights, estimated near-bottom and near-surface stresses using this method compared well with independent estimates of the boundary stresses in contrast to previous methods. Additionally, the vertical structure of tidal stress estimated using the new approach matched that inferred from a linear momentum balance at stress levels below the estimated stress uncertainties. Because the method makes an estimate of the horizontal turbulent length scales present as part of the model fit, these results can also enable a direct correction for the mean bias errors resulting from instrument tilt, if these scales are long relative to the beam separation.

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Gregory P. Gerbi, John H. Trowbridge, Eugene A. Terray, Albert J. Plueddemann, and Tobias Kukulka

Abstract

Observations of turbulent kinetic energy (TKE) dynamics in the ocean surface boundary layer are presented here and compared with results from previous observational, numerical, and analytic studies. As in previous studies, the dissipation rate of TKE is found to be higher in the wavy ocean surface boundary layer than it would be in a flow past a rigid boundary with similar stress and buoyancy forcing. Estimates of the terms in the turbulent kinetic energy equation indicate that, unlike in a flow past a rigid boundary, the dissipation rates cannot be balanced by local production terms, suggesting that the transport of TKE is important in the ocean surface boundary layer. A simple analytic model containing parameterizations of production, dissipation, and transport reproduces key features of the vertical profile of TKE, including enhancement near the surface. The effective turbulent diffusion coefficient for heat is larger than would be expected in a rigid-boundary boundary layer. This diffusion coefficient is predicted reasonably well by a model that contains the effects of shear production, buoyancy forcing, and transport of TKE (thought to be related to wave breaking). Neglect of buoyancy forcing or wave breaking in the parameterization results in poor predictions of turbulent diffusivity. Langmuir turbulence was detected concurrently with a fraction of the turbulence quantities reported here, but these times did not stand out as having significant differences from observations when Langmuir turbulence was not detected.

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Gregory P. Gerbi, John H. Trowbridge, James B. Edson, Albert J. Plueddemann, Eugene A. Terray, and Janet J. Fredericks

Abstract

This study makes direct measurements of turbulent fluxes in the mixed layer in order to close heat and momentum budgets across the air–sea interface and to assess the ability of rigid-boundary turbulence models to predict mean vertical gradients beneath the ocean’s wavy surface. Observations were made at 20 Hz at nominal depths of 2.2 and 1.7 m in ∼16 m of water. A new method is developed to estimate the fluxes and the length scales of dominant flux-carrying eddies from cospectra at frequencies below the wave band. The results are compared to independent estimates of those quantities, with good agreement between the two sets of estimates. The observed temperature gradients were smaller than predicted by standard rigid-boundary closure models, consistent with the suggestion that wave breaking and Langmuir circulation increase turbulent diffusivity in the upper ocean. Similarly, the Monin–Obukhov stability function ϕh was smaller in the authors’ measurements than the stability functions used in rigid-boundary applications of the Monin–Obukhov similarity theory. The dominant horizontal length scales of flux-carrying turbulent eddies were found to be consistent with observations in the bottom boundary layer of the atmosphere and from laboratory experiments in three ways: 1) in statically unstable conditions, the eddy sizes scaled linearly with distance to the boundary; 2) in statically stable conditions, length scales decreased with increasing downward buoyancy flux; and 3) downwind length scales were larger than crosswind length scales.

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Gregory P. Gerbi, Emmanuel Boss, P. Jeremy Werdell, Christopher W. Proctor, Nils Haëntjens, Marlon R. Lewis, Keith Brown, Diego Sorrentino, J. Ronald V. Zaneveld, Andrew H. Barnard, John Koegler, Hugh Fargher, Matthew DeDonato, and William Wallace

Abstract

The use of autonomous profiling floats for observational estimates of radiometric quantities in the ocean is explored, and the use of this platform for validation of satellite-based estimates of remote sensing reflectance in the ocean is examined. This effort includes comparing quantities estimated from float and satellite data at nominal wavelengths of 412, 443, 488, and 555 nm, and examining sources and magnitudes of uncertainty in the float estimates. This study had 65 occurrences of coincident high-quality observations from floats and MODIS Aqua and 15 occurrences of coincident high-quality observations floats and Visible Infrared Imaging Radiometer Suite (VIIRS). The float estimates of remote sensing reflectance are similar to the satellite estimates, with disagreement of a few percent in most wavelengths. The variability of the float–satellite comparisons is similar to the variability of in situ–satellite comparisons using a validation dataset from the Marine Optical Buoy (MOBY). This, combined with the agreement of float-based and satellite-based quantities, suggests that floats are likely a good platform for validation of satellite-based estimates of remote sensing reflectance.

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