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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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David A. Siegel and Albert J. Plueddemann

Abstract

Several popular techniques employed to remotely sense oceanic velocity fields utilize the Doppler shifts of backscattered radiation (such as sound or light) from suspended particles to estimate fluid velocities. Implicit in this use is the assumption that the motion of the particles and the fluid parcels about them is identical. Here, a simple dynamical model of a solid sphere in a unidirectional oscillating flow is used to evaluate the effects of differential particle motion on remotely sensed Doppler velocity estimates. The analysis indicates that typical oceanic particles will move with the fluid if their density is equal to the fluid's density or if the oscillation frequency (ω) is less than a critical frequency (ωc≡0.1νa −2; where ν is the kinematic viscosity of the fluid and a is the particle radius). For oscillation frequencies greater than ωc, the particle and flow velocities diverge significantly from each other. Particle motion will be amplified for particles less dense than the fluid and reduced for relatively heavy particles. The motions of particles and the fluid may have significant phase differences as well. Critical frequencies are estimated for some common oceanic particles enabling the performance of several Doppler velocity measurement techniques to be evaluated. The present results indicate that for some oceanographic applications the Doppler sensing of fluid velocities using particulate backscatter may be limited by the inability of the particles to follow the fluid motion. The model results suggest that it is possible to correct for the velocity differences between the particle and its fluid parcel if the size and relative density of the backscattering material is known. This strongly indicates that a greater emphasis must be placed on the characterization of the materials that are producing the backscattered signals.

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J. Carter Ohlmann, David A. Siegel, and Catherine Gautier

Abstract

A hybrid parameterization for the determination of in-water solar fluxes is developed and applied to compute the flux of solar radiation that penetrates beyond the upper-ocean mixed layer into permanent pycnocline waters on global space and climatological timescales. The net flux of solar radiation at depth is modeled using values of the solar flux incident at the sea surface, derived from the International Satellite Cloud Climatology Project dataset, and in-water attenuation coefficients, determined using upper ocean chlorophyll concentration supplied by Coastal Zone Color Scanner imagery. Solar radiation penetration can be a significant term (20 W m−2) in the mixed layer heat budget for tropical regions. In mid- and high-latitude regions, the annual solar flux entering permanent pycnocline waters is small (<5 W m−2). However, solar penetration in these regions is important on seasonal timescales since annual cycles in incident solar flux, upper-ocean chlorophyll concentration, and mixed layer depth cause trapping of penetrating solar energy of O(10 W m−2) within the seasonal pyonocline. This trapped thermal energy is unavailable for atmospheric exchange until winter—a period as long as nine months. A nondimensional parameter is introduced that quantifies the fraction of incident solar radiation contributing to mixed layer radiant heating. This parameter can be used to characterize the relative importance of solar penetration to ocean mixed layer thermal climate.

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David A. Siegel, Toby K. Westberry, and J. Carter Ohlmann

Abstract

It is well recognized that clouds regulate the flux of solar radiation reaching the sea surface. Clouds also affect the spectral distribution of incident irradiance. Observations of spectral and total incident solar irradiance made from the western equatorial Pacific Ocean are used to investigate the “color” of clouds and to evaluate its role in upper-ocean radiant heating. Under a cloudy sky, values of the near-ultraviolet to green spectral irradiance are a significantly larger fraction of their clear-sky flux than are corresponding clear-sky fractions calculated for the total solar flux. For example, when the total solar flux is reduced by clouds to one-half of that for a clear sky, the near-ultraviolet spectral flux is only reduced ∼35% from its clear-sky value. An empirical parameterization of the spectral cloud index is developed from field observations and is verified using a plane-parallel, cloudy-sky radiative transfer model. The implications of cloud color on the determination of ocean radiant heating rates and solar radiation transmission are assessed using both model results and field determinations. The radiant heating rate of the upper 10 cm of the ocean (normalized to the climatological incident solar flux) may be reduced by a factor of 2 in the presence of clouds. This occurs because the near-infrared wavelengths of solar radiation, which are preferentially attenuated by clouds, are absorbed within the upper 10 cm or so of the ocean while the near-ultraviolet and blue spectral bands propagate farther within the water column. The transmission of the solar radiative flux to depth is found to increase under a cloudy sky. The results of this study strongly indicate that clouds must be included in the specification of ocean radiant heating rates for air–sea interaction studies.

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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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Molly Baringer, Mariana B. Bif, Tim Boyer, Seth M. Bushinsky, Brendan R. Carter, Ivona Cetinić, Don P. Chambers, Lijing Cheng, Sanai Chiba, Minhan Dai, Catia M. Domingues, Shenfu Dong, Andrea J. Fassbender, Richard A. Feely, Eleanor Frajka-Williams, Bryan A. Franz, John Gilson, Gustavo Goni, Benjamin D. Hamlington, Zeng-Zhen Hu, Boyin Huang, Masayoshi Ishii, Svetlana Jevrejeva, William E. Johns, Gregory C. Johnson, Kenneth S. Johnson, John Kennedy, Marion Kersalé, Rachel E. Killick, Peter Landschützer, Matthias Lankhorst, Tong Lee, Eric Leuliette, Feili Li, Eric Lindstrom, Ricardo Locarnini, Susan Lozier, John M. Lyman, John J. Marra, Christopher S. Meinen, Mark A. Merrifield, Gary T. Mitchum, Ben Moat, Didier Monselesan, R. Steven Nerem, Renellys C. Perez, Sarah G. Purkey, Darren Rayner, James Reagan, Nicholas Rome, Alejandra Sanchez-Franks, Claudia Schmid, Joel P. Scott, Uwe Send, David A. Siegel, David A. Smeed, Sabrina Speich, Paul W. Stackhouse Jr., William Sweet, Yuichiro Takeshita, Philip R. Thompson, Joaquin A. Triñanes, Martin Visbeck, Denis L. Volkov, Rik Wanninkhof, Robert A. Weller, Toby K. Westberry, Matthew J. Widlansky, Susan E. Wijffels, Anne C. Wilber, Lisan Yu, Weidong Yu, and Huai-Min Zhang
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