Session Q35: Geophysical Fluid Dynamics: Oceanographic II

Large eddy simulations of turbulent oceanic flows

SOMAR-LES is a numerical tool combining adaptive mesh refinement and large eddy simulation developed to study high-resolution large-scale oceanic flows. In this study, we consider two different test cases: (1)stratified shear layer, (2)baroclinic front. In the first test case, a simple vertical shear layer is set up in a linearly stratified medium. Adaptive refinement is used to refine the mesh along the braids such that secondary instabilities are well captured. Results from this simulation are compared with DNS. Quantitative analysis of turbulent kinetic energy budget shows that the turbulent production, buoyancy flux, and the dissipation rate agree well with DNS results. In the second test case, the flow is initialized with a balanced geostrophic current and a lateral density gradient. The geostrophic current becomes unstable due to baroclinic instability and forms turbulent eddies which mix up the fluid in both vertical and lateral directions. Again, using the adaptive refinement, a fine resolution is achieved along the regions of high buoyancy gradients. It will be demonstrated that SOMAR-LES is both computationally efficient and accurate in computing turbulence and mixing parameters.   

Comparison of Ocean Models for Tsunami Formation and Propagation with Nearfield Sources

Given the destructive capability of a tsunami and the resulting inundation, tsunami hazard assessment is crucial for mitigating risk to coastal communities.  To assess the hazard from a tsunami generated by a distant seismic source, the shallow water equations (SWE) provide an accurate and efficient model.  This is largely due to the valid assumption that the ocean is in a vertically hydrostatic state after the seismic event has ceased.  For a nearfield seismic source, however, this assumption may no longer be valid.  To investigate this, a compressible ocean model is derived by adding a hydroacoustic component to the hydrostatic pressure.  This model is then coupled to a seismic model to capture the interaction between elastic seismic waves in the ground, acoustics waves in the ocean, and the sea surface deformation that creates the tsunami as a gravity wave.  The applicability of the hydrostatic assumption for a nearfield seismic source is discussed by comparing tsunami waveforms from the derived ocean model to those of the SWE model for a variety of seismic rupture patterns.   

Stratified turbulent mixing from the small-scale oceanic internal wave field

In the pycnocline, where internal waves produce transient stratification and shear, the dominant mechanisms producing mixing are unknown. Identifying these mechanisms is key for determining the contribution of the wave field to diapycnal mixing in the ocean and improving parametrizations of mixing efficiency. We use direct numerical simulations (DNS) to investigate the properties of stratified turbulence representative of such small-scale ocean dynamics. Initializing the large-scale flow with an internal wave spectrum inspired by Garrett & Munk, we perform DNS of a Boussinesq fluid in a triply-periodic domain subject to a linear stratification. Forcing is applied to low-wavenumber internal waves throughout the simulation to represent energy transfer from larger scales. We then identify how key quantities such as mixing efficiency, diapycnal diffusivity and vertical buoyancy flux vary both locally within each simulation, and with different background stratifications. The local and temporal variation in these quantities also allows us to investigate the mechanisms by which turbulence is generated and sustained in the flow.   

Direct numerical simulation of deep-ocean convection in a rotating stratified fluid.

Deep-ocean convection is observed at high latitudes and occurs under the influence of intense surface cooling. DNS are performed to understand the small-scale turbulent processes in a scaled-down configuration while keeping the Rossby number relevant to the realistic ocean convection. The effect of the Earth's rotation on the convection process is studied by varying the Rossby number Ro=B₀^1/2/(Hf)^3/2, where H is the depth, f is the Coriolis parameter, and B₀ is the magnitude of surface buoyancy flux. The initial evolution of the flow is governed solely by the B₀ and thermal diffusivity κ_t. At a later time t>100(κ_t/B₀)^1/2, the flow becomes turbulent and the plumes lose their coherence. When time t>2π/f, rotational effects become prominent thereby stabilizing the flow due to the diminished conversion of potential to kinetic energy. At moderate to low rotation rates(Ro>0.1), the turbulent fluid spreads as gravity current along the bottom surface. However, at high rotation rates(Ro<0.1), the flow reaches a quasi-steady state. Due to the complex nature of the flow physics and multiple controlling parameters, it has been found that a simple parametric scaling for length and velocity scales cannot be proposed, in contrast to the findings from some of the previous studies.    

Numerical study on the heterogeneous bottom bed stress map due to coastal Langmuir circulations

Langmuir cells generally extend until the mixing layer depth and remain unaffected by bathymetry. However, coastal Langmuir cells are different as they extend to the seafloor and interact with the bottom boundary layer. In this large-eddy simulation study, we further probe into the components of such strong, coherent, full-depth, counter-rotating cells i.e. downwelling and upwelling limbs, and examine their individual roles in shaping the characteristics of the whole flow as well as the heterogeneous bottom bed stress map. As such, analysis of turbulent flow quantities of respective limbs, extracted separately through conditional averages, is performed. We show that the downwelling limbs impinging upon the bottom elevates the bed stress in the zone below and can act as a precursor to sediment erosion and resuspension. Furthermore, apart from the helical motions by Langmuir circulations, elevated bed stress is linked with the passage of inclined, large-scale motions composed of high-momentum fluid consequential to the presence of bottom boundary layer. However, coherent Langmuir cells suppress the structural inclination angle of those large-scale motions.   

Can limited observations recover irreversible turbulent fluxes? A test case using DNS

Turbulent mixing plays a key role in setting the distribution of heat and other tracers in the ocean. However, quantifying irreversible turbulent mixing in a stratified flow is complicated by reversible motions associated, for example, with internal waves. Given limited space and time coverage, can observations meaningfully recover the irreversible mixing associated with a turbulent event?

Winters & D'Asaro (J. Fluid Mech.(317), 1996) established a framework in which the irreversible heat flux is computed by first globally sorting the buoyancy field and then interpreting turbulent dissipation quantities in that sorted space. This approach has been successfully applied to numerical simulations in which the full flow field is known. Here we apply such an approach to moored turbulence observations by subsampling the output of direct numerical simulations of shear instability in a manner that mimics real instruments. We compare the heat flux inferred from the subsampled data to the true heat flux computed using the full three-dimensional sorted buoyancy field. This comparison lets us evaluate our ability to infer, and refine our estimates of, irreversible heat fluxes in a turbulent flow using limited observational measurements.   

A Numerical Study of the Sea Surface Microlayer

The sea surface microlayer (SML), defined as the top 1-1000 micrometers of the sea surface, is instrumental to the transport of momentum between the ocean and atmosphere. Researchers have attempted to record specific characteristics such as concentration profiles of various chemicals and biological matter variation in the layer but a comprehensive picture of the SML is lacking. Prediction of changes in the SML as a result of changing temperature / atmospheric also prepare for the large-scale effect of the air-sea interactions in coastal areas. On a shorter time scale, the near surface layer (NSL) dictates upper ocean dynamics and the progression of extreme events such as hurricanes and storms. The objective of this study is to carry out high resolution numerical simulations of the SML to isolate specific instability mechanisms responsible for air-sea interactions. While the NSL has been analyzed via field and numerical data, it is notoriously difficult to study the SML owing to large property gradients in the layer and optical issues in resolving the air-sea interface. This study therefore focuses on two phase, transient Large Eddy Simulations of an ocean-air domain  to closely resolve the SML and demonstrate corresponding mixing mechanisms.   

Non-hydrostatic effects in supercritical oceanic lee waves

Lee waves occur wherever a steady current with stable stratification interacts with topography. Their generation causes drag on the current. In the ocean, lee waves exist on length scales smaller than the resolution of global ocean circulation models. Their drag thus requires parameterization.

Lee waves are characterized by the dimensionless numbers J=Nh/U and ε=Uk/N, where U and N are the background velocity and buoyancy frequency, and h and k are height and width scales of the bathymetry. For periodic bathymetry of supercritical height (J>O(1)), the lowest layers of the flow become blocked, and the wave drag saturates, allowing for simple parameterization. However, saturation based parameterization considers only one of the two dimensionless numbers.

To diagnose the role of ε in supercritical lee waves, we use idealized numerical simulations of oceanic scale lee waves and study the evolution of the lowest over-topping streamline. We find that after the onset of blocking, the lowest streamline exhibits bounces with horizontal scales of the internal gravity wavelength. To the background flow, these undulations represent ε=1 width bathymetry, which does not cause drag. Blocking thus has an additional non-hydrostatic effect which further reduces lee wave drag.   

New Parametrization for Heat Transport Through Diffusive Convection Interface

A laboratory experiment of two-layer diffusive convection (DC) within a rectangular cell is reported. Heat flux across the interface is respectively evaluated in terms of the heat energy conservation and the assumption of conductive interface. Both of them give the consistent heat flux values. When the 4/3 scaling between heat flux F and ΔT holds (F ~C(R_ρ) ΔT^4/3, where C(Rρ) is function of density ratio Rρ), previous heat flux parameterizations are found to have low coefficient of determination (r²<0.5) with our heat flux data within 1.6<Rρ<13.0. Heat flux is proposed to be a power-law function of Rρ, and the best fitting is C(Rρ)= 0.081(Rρ- 1)^-1.28, resulting in r² as high as 0.74. By using all available heat flux data over a wide Rρ range (1.2 ~27.6), including those collected in previous literatures, C(Rρ) is revised as C(Rρ)= 0.065(Rρ- 1)^-1.20 accompanied by r²=0.70 and reduced chi-square χ² = 0.91. Alternatively, C(Rρ) can be derived from previous DC layer thickness parameterization, which is expressed as C(Rρ)= 0.076(Rρ- 1)^-4/3. This formula is also superior to previous parameterizations in the evaluation of heat flux, indicated by higher r² and lower χ² .   

Investigation of the effect of wave age on the wind turbulence over breaking waves

Wind turbulence over breaking waves is investigated using direct numerical simulation (DNS) of two-fluids flows.  We focus on analyzing the effect of wave age on the statistics of wind turbulence over breaking waves.  It is found that before wave breaking, the vertical gradient of mean streamwise velocity is positive at small and intermediate wave ages, but it becomes negative near the wave surface at large wave ages. The turbulence kinetic energy (TKE) is enhanced during wave plunging at small and large wave ages, but at intermediate wave ages, the transient enhancement of TKE is absent.  The analyses of TKE production shows that at small wave ages, the TKE enhancement is caused by the magnitude increase of turbulence momentum flux. At large wave ages, the TKE enhancement is correlated to the sign change in the wave-coherent momentum flux. At intermediate wave ages, both of these two processes are absent, such that the TKE enhancement does not occur.