Generation of turbulence through frontogenesis in sheared stratified flows

Abstract

The large-scale structures in the ocean and the atmosphere are in geostrophic balance, and a conduit must be found to channel the energy to the small scales where it can be dissipated. In turbulence this takes the form of an energy cascade, whereas one possible mechanism in a balanced flow at large scales is through the formation of fronts, a common occurrence in geophysical dynamics. We show in this paper that an iconic configuration in laboratory and numerical experiments for the study of turbulence, that of the Taylor-Green or von Kármán swirling flow, can be suitably adapted to the case of fluids with large aspect ratios, leading to the creation of an imposed large-scale vertical shear. To this effect we use direct numerical simulations of the Boussinesq equations without net rotation and with no small-scale modeling, and with this idealized Taylor-Green set-up. Various grid spacings are used, up to 2048 2 × 256 spatial points. The grids are always isotropic, with box aspect ratios of either 1 : 4 or 1 : 8. We find that when shear and stratification are comparable, the imposed shear layer resulting from the forcing leads to the formation of multiple fronts and filaments which destabilize and further evolve into a turbulent flow in the bulk, with a sizable amount of dissipation and mixing, and with a cycle of front creation, instability, and development of turbulence. The results depend on the vertical length scales for shear and for stratification, with stronger large-scale gradients being generated when the two length scales are comparable.

Vertical dispersion of Lagrangian tracers in fully developed stably stratified turbulence

“…Integration of particles' trajectories was done using a second-order Runge-Kutta method in time, and a three-dimensional cubic spline interpolation to estimate Lagrangian velocities at the particles positions x i from the velocity u in the regular Eulerian grid [37]. All simulations were done using the GHOST code (Geophysical High-Order Suite for Turbulence), recently extended to work with non-cubic boxes [38].…”

“…In each domain, simulations were done using two different forcing functions. Some simulations were forced with Taylor-Green (TG) forcing (see, e.g., [10,38,40]), which only excites directly the two horizontal components of the velocity field, and has vertical shear. The geometry of the large-scale flow generated by this forcing is that of pairs of counter-rotating horizontal vortices at large scales, and the expression of the forcing is…”

GPU Parallelization of a Hybrid Pseudospectral Geophysical Turbulence Framework Using CUDA

“…Note that both the physical box size, L i , and the number of physical space points, N i , may be specified independently in each direction in our implementation enabling non-isotropic expansions in the (L x , L y , L z ) domain. This is a major difference between the current algorithm and the version discussed in M11 (Sojovolosky et al, 2018). Taking the continuous Fourier transform and utilizing the discrete expansion given by Eq.…”

Correlation between Buoyancy Flux, Dissipation and Potential Vorticity in Rotating Stratified Turbulence

“…For example, we already know that, in the presence of a strong shear, dissipation is much more efficient, in particular through the formation of localized fronts and filaments [61]. In fact, one commanding question regarding turbulent flows is whether they are best described through a state of maximal energy dissipation, or of maximum entropy production (see, e.g., [62] and references therein).…”