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David A. Siegel
and
J. Andrzej Domaradzki

Abstract

A large-eddy simulation (LES) model is developed and employed to study the interactions among turbulent and internal gravity wave motions in a uniformly stratified fluid at oceanic space and time scales. The decay of a random initial energy spectrum is simulated in a triply periodic domain (L=10 m) by solving the full nonlinear, three-dimensional Navier-Stokes equations using pseudospectral techniques and a numerical resolution of 643 modes. The subgrid scale (SGS) fluxes are parameterized using the Smargorinsky SGS flux parameterization. Three experiments were performed with mean buoyancy frequencies (N) of 1, 3, and 10 cph for a period of 10 buoyancy times (Nt).

The temporal evolution of the domain-averaged statistics is used to examine the nature of decaying stratified turbulence. Initially (0≤Nt≤2), energy levels rapidly decay as the spectral energy distributions evolve toward more isotropic forms. During this time, the buoyancy flux (BF) remains negative indicating a conversion of kinetic to potential energy and downgradient scalar mixing. After an initial period of decay (Nt≳2), rapid oscillatory exchanges of vertical kinetic energy (VKE) and potential energy (PE) are observed. These energy exchanges are driven by a nearly reversible BF that is supporting internal gravity wave motions. Synchronous oscillations in horizontal kinetic energy are also found although their amplitudes are significantly smaller. Irreversible aspects of the BF can still be observed during this latter stage of decay, especially for the N=1 and 3 cph experiments. Estimates of the irreversible portion of BF are used to determine values of vertical eddy diffusivity, Kp , for this period. Resulting values for Kp are 2.4×10−5 and 7.2×10−5 m2 s−1, for the N=1 and 3 cph experiments, respectively, consistent with oceanographic estimates for the main thermocline.

The domain-averaged energetics indicate that, although an equipartition is not observed between PE and the total kinetic energy, a robust equipartition is observed between the “wave” kinetic energy and PE. However, this equipartition does not appear to hold spectrally. Spectral analyses also indicate that the larger spatial scales are dominated by “vortical” energy. Evaluation of SGS energetics, fluxes, and dissipation rates indicates that SGS motions control energy dissipation rates but make small contributions to the energetics and fluxes, consistent with the LES assumptions. Spectral analyses of the SGS eddy viscosity and energy transfer rates are used to suggest improvements for future LES experiments of stably stratified turbulence.

One of the most exciting observations made here is the rapid transition in the character of the buoyancy flux evolution as part of the “turbulent collapse.” The BF changes suddenly from a state of irreversible mixing to an oscillatory, nearly reversible BF when the Ozmidoy length scale is the same order as the vertical energy- containing length scale [ i.e., the Froude number becomes O(1)]. Vertical temperature cross sections also exhibit some evidence of the collapse (i.e., chaotic structures evolving into wavelike variations). However, these changes occur gradually compared with the rapid transition observed in BF. Unlike most previous laboratory observations, energy decay rates and characteristic length scales appear to be unaffected by this dynamic transition. It is speculated that differences between the present LES results and previous laboratory and numerical results may be attributed to extreme differences in the Reynolds numbers for these flows.

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J. Carter Ohlmann
and
David A. Siegel

Abstract

Accurate determination of sea surface temperature (SST) is critical to the success of coupled ocean–atmosphere models and the understanding of global climate. To accurately predict SST, both the quantity of solar radiation incident at the sea surface and its divergence, or transmission, within the water column must be known. Net irradiance profiles modeled with a radiative transfer model are used to develop an empirical solar transmission parameterization that depends on upper ocean chlorophyll concentration, cloud amount, and solar zenith angle. These factors explain nearly all of the variations in solar transmission. The parameterization is developed by expressing each of the modeled irradiance profiles as a sum of four exponential terms. The fit parameters are then written as linear combinations of chlorophyll concentration and cloud amount under cloudy skies, and chlorophyll concentration and solar zenith angle during clear-sky periods. Model validation gives a climatological rms error profile that is less than 4 W m−2 throughout the water column (when normalized to a surface irradiance of 200 W m−2). Compared with existing solar transmission parameterizations this is a significant improvement in model skill. The two-equation solar transmission parameterization is incorporated into the TOGA COARE bulk flux model to quantify its effects on SST and subsequent rates of air–sea heat exchange during a low wind, high insolation period. The improved solar transmission parameterization gives a mean 12 W m−2 reduction in the quantity of solar radiation attenuated within the top few meters of the ocean compared with the transmission parameterization originally used. This results in instantaneous differences in SST and the net air–sea heat flux that often reach 0.2°C and 5 W m−2, respectively.

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J. Carter Ohlmann
,
David A. Siegel
, and
Curtis D. Mobley

Abstract

Radiative transfer calculations are used to quantify the effects of physical and biological processes on variations in the transmission of solar radiation through the upper ocean. Results indicate that net irradiance at 10 cm and 5 m can vary by 23 and 34 W m−2, respectively, due to changes in the chlorophyll concentration, cloud amount, and solar zenith angle (when normalized to a climatological surface irradiance of 200 W m−2). Chlorophyll influences solar attenuation in the visible wavebands, and thus has little effect on transmission within the uppermost meter where the quantity of near-infrared energy is substantial. Beneath the top few meters, a chlorophyll increase from 0.03 to 0.3 mg m−3 can result in a solar flux decrease of more than 10 W m−2. Clouds alter the spectral composition of the incident irradiance by preferentially attenuating in the near-infrared region, and serve to increase solar transmission in the upper few meters as a greater portion of the irradiance exists in the deep-penetrating, visible wavebands. A 50% reduction in the incident irradiance by clouds causes a near 60% reduction in the radiant heating rate for the top 10 cm of the ocean. Solar zenith angle influences transmission during clear sky periods through changes in sea-surface albedo. This study provides necessary information for improved physically and biologically based solar transmission parameterizations that will enhance upper ocean modeling efforts and sea-surface temperature prediction.

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Leonel Romero
,
Yusuke Uchiyama
,
J. Carter Ohlmann
,
James C. McWilliams
, and
David A. Siegel

Abstract

Knowledge of horizontal relative dispersion in nearshore oceans is important for many applications including the transport and fate of pollutants and the dynamics of nearshore ecosystems. Two-particle dispersion statistics are calculated from millions of synthetic particle trajectories from high-resolution numerical simulations of the Southern California Bight. The model horizontal resolution of 250 m allows the investigation of the two-particle dispersion, with an initial pair separation of 500 m. The relative dispersion is characterized with respect to the coastal geometry, bathymetry, eddy kinetic energy, and the relative magnitudes of strain and vorticity. Dispersion is dominated by the submesoscale, not by tides. In general, headlands are more energetic and dispersive than bays. Relative diffusivity estimates are smaller and more anisotropic close to shore. Farther from shore, the relative diffusivity increases and becomes less anisotropic, approaching isotropy ~10 km from the coast. The degree of anisotropy of the relative diffusivity is qualitatively consistent with that for eddy kinetic energy. The total relative diffusivity as a function of pair separation distance R is on average proportional to R 5/4. Additional Lagrangian experiments at higher horizontal numerical resolution confirmed the robustness of these results. Structures of large vorticity are preferably elongated and aligned with the coastline nearshore, which may limit cross-shelf dispersion. The results provide useful information for the design of subgrid-scale mixing parameterizations as well as quantifying the transport and dispersal of dissolved pollutants and biological propagules.

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