Large-Eddy Simulation of Decaying Stably Stratified Turbulence

View More View Less
  • 1 Department of Geography and Center for Remote Sensing and Environmental Optics, University of California, at Santa Barbara, Santa Barbara, California
  • | 2 Department of Aerospace Engineering, University of Southern California, Los Angeles, California
© Get Permissions
Restricted access

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.

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.

Save