Session H36: Geophysical: Oceanographic V

Relevancy of the buoyancy Reynolds number in stably stratified turbulence

The buoyancy Reynolds number, $Re_b = \epsilon/(\nu N^2)$, has become a widely popular parameter with which to describe turbulent mixing in the stratified environment of the open ocean. This popularity has arisen largely on the practical grounds that the constituent quantities are available through common measurement techniques: estimates of turbulent kinetic energy dissipation ($\epsilon$) are available from observations of fine-scale shear, and the buoyancy frequency ($N$) can be determined from profiles of density. Despite practical appeal, however, $Re_b$ is ambiguous in that it fails to distinguish between regimes of weak stratification and strong turbulence. This becomes obvious in the formulation $Re_b = Re_L(Fr_k)^2$, where $Re_L=k^2/(\epsilon\nu)$ is a turbulent Reynolds number, $Fr_k = \epsilon/(Nk)$ is a turbulent Froude number, and $k$ is the turbulent kinetic energy. In considering both $Re_L$ and $Fr_k$ independently, the time scale of the turbulence, $T_L=k/\epsilon$, is made explicit. We explore the duality of $Re_b$ in describing mixing efficiency using a $Re_L-Fr_k$ parameter space and argue the importance of $T_L$ in parameterization of flow behavior. Data from direct numerical simulations, laboratory experiments, and field observations are considered.   

Stability of Baroclinic Vortices in Rotating Stratified Flows

The stability of axisymmetric shielded vortices in rotating linearly stratified flows is examined using three-dimensional numerical simulations of the Boussinesq equations. Vortices are initially in cyclo-geostrophic/hydrostatic dissipationless equilibrium in accord with the constraint presented in Hassanzadeh et al. (2012 JFM) and Aubert et al. (2012 JFM). For a range of Rossby numbers, vortex aspect ratios, and Burger numbers relevant to the oceanic and atmospheric flows, both cyclones and anticyclones are studied, and the type and growth rate of instabilities are reported for the unstable cases. Significance of these results for the cyclone-anticyclone asymmetry observed in rotating stratified flows is discussed.   

From Balanced Barotropic and Baroclinic Shear to Turbulence in Rotating and Stratified Flow

In the oceanic submesoscale regime, rotation is important but does not control dynamics. Instabilities and nonlinear cascades are possible even for stably stratified flows. Previous work by the authors explored the rotating stratified barotropic shear layer. Here, the vertical wavenumber band associated with linear barotropic instability greatly increased when centerline absolute vorticity was approximately zero. Correspondingly, nonlinear simulations showed a marked transition event during the changing in sign of centerline absolute vorticity. Our study will include direct numerical simulations exploring the effect of a weak isolated front in combination with the previously explored barotropic shear layer. The primary aim of this study is to explore how the instabilities of the barotropic simulations are modified by weak baroclinicity. We will explore coherent structure evolution to qualitatively assess the importance of the numerous possible instability mechanisms, especially the zero absolute vorticity mechanism. Additionally, energy and enstrophy budgets will be analyzed comparing the various pathways from large-scale kinetic and potential energies to turbulence.   

Efficiency of mixing by heating or cooling in thermally stratified nonlinear spin-up

Spin-up (the transient flow of a fluid, either at rest or in solid body rotation, due to an increase in rotation rate), is particularly relevant to large-scale geophysical flows. Here we present numerical experiments of spin-up in a cylindrical container with shear-free upper boundary for four different thermal boundary conditions on the horizontal walls: (1) prescribed temperatures, (2) adiabatic conditions, (3) adiabatic on top and prescribed temperature on the bottom, and (4) prescribed temperature on top and adiabatic on the bottom. Studies on spin-up subjected to different boundary conditions and stratifications matter, as they may be helpful to understand the spin of water masses in basins for different physical scenarios. Most of the time, new water masses are formed at the surface by cooling, and their spin-up is clearly of utility in determining ensuing flow patterns. The focus here is on the efficiency of mixing due to spin-up when the horizontal boundaries are subjected to different thermal conditions.   

Turbulence Statistics in the Inner Part of the Coastal Ocean Bottom Boundary Layer

PIV measurements were performed in the inner part of the coastal bottom boundary layer under varying bottom roughness conditions, relative wave current orientation and ratio of mean current to amplitude of wave induced motion (WCR). Velocity distributions with resolution of 4.5 mm were obtained in two 28 x 28 cm$^{2}$ planes down to 5 mm off the seabed. Co-located ADV measurements were used to calculate Reynolds stresses by filtering out wave-induced motions from PIV data, and high-resolution sonar was used to map the bottom roughness. Mean velocity and Reynolds stress profiles varied with WCR and their relative alignment. An inflection in mean velocity profile developed below the log layer for WCR$\sim$1, but not for higher ratios. Reynolds stresses peaked in the lower portion of the log layer, decreasing with elevation above. The peak location, and the stress scaling trends depended on WCR. A second stress peak appeared just above the ripple crest. Wave-induced wall-normal momentum transport (``stress'') became substantial within the roughness sublayer, where the relative phase between streamwise and vertical velocity components were altered. The dissipation rate profiles showed a rapid increase with decreasing elevation, but the shear production varied with WCR and roughness orientation.   

Numerical Simulation of Bottom Boundary Layer Turbulence under an Internal Solitary Wave of Depression

The turbulent bottom boundary layer (BBL) under a mode-1 internal solitary wave (ISW) of depression is examined using spectral multidomain-based implicit large eddy simulations. The ISW propagates in a two-layer stratification in either quiescent waters or against an idealized barotropic current augmented with an idealized laminar Blasius boundary layer. Various non-trivial aspects of this highly expensive numerical process study are examined with the focus on the effectiveness of various strategies aimed towards establishing a self-sustained near-bed turbulent wake. Such a near-bed wake is considered to be the 3-D extension of the corresponding 2-D global instability observed in the ISW footprint by previous investigations. To this end, in analogy with recent aerodynamics studies, the incorporation of localized volumetric forcing aft the separated BBL under the ISW appears to be the optimal choice. Following a characterization of the structure and dynamics of the ISW-induced BBL, we discuss key differences with related laboratory experiments, assess the relevance of volumetric forcing to both the laboratory and field and speculate on whether numerically simulated self-sustained near-bed turbulence is indeed possible for a pure no-slip bottom.   

Two-dimensional irrotational nonlinear flow over arbitrary bottom topography in a Channel

The problem involving two-dimensional irrotational flow over arbitrary bottom topography in an infinite channel is investigated within the framework of fully nonlinear theory. This two-dimensional problem can be cast into a mixed boundary value problem. Using certain transformations, the mixed boundary value problem is formulated as a Dirichlet problem. The Dirichlet problem is solved by the aid of integral equation method, and the solution of the Dirichlet problem involves an unknown potential function that is to be determined. This unknown function can be determined completely, once a pair of singular integral equations appearing here are solved completely. By the help of Newton's method, the free surface profile is determined and shown graphically.