GPU Parallelization of a Hybrid Pseudospectral Geophysical Turbulence Framework Using CUDA

An existing hybrid MPI-OpenMP scheme is augmented with a CUDA-based fine grain parallelization approach for multidimensional distributed Fourier transforms, in a well-characterized pseudospectral fluid turbulence code. Basics of the hybrid scheme are reviewed, and heuristics provided to show a potential benefit of the CUDA implementation. The method draws heavily on the CUDA runtime library to handle memory management and on the cuFFT library for computing local FFTs. The manner in which the interfaces to these libraries are constructed, and ISO bindings utilized to facilitate platform portability, are discussed. CUDA streams are implemented to overlap data transfer with cuFFT computation. Testing with a baseline solver demonstrated significant aggregate speed-up over the hybrid MPI-OpenMP solver by offloading to GPUs on an NVLink-based test system. While the batch streamed approach provided little benefit with NVLink, we saw a performance gain of 30 % when tuned for the optimal number of streams on a PCIe-based system. It was found that strong GPU scaling is nearly ideal, in all cases. Profiling of the CUDA kernels shows that the transform computation achieves 15% of the attainable peak FlOp-rate based on a roofline model for the system. In addition to speed-up measurements for the fiducial solver, we also considered several other solvers with different numbers of transform operations and found that aggregate speed-ups are nearly constant for all solvers.

Role of Surface-Layer Coherent Eddies in Potential Vorticity Transport in Quasigeostrophic Turbulence Driven by Eastward Shear

The transport by materially coherent surface-layer eddies was studied in a two-layer quasigeostrophic model driven by eastward mean shear. The coherent eddies were identified by closed contours of the Lagrangian-averaged vorticity deviation obtained from Lagrangian particles advected by the flow. Attention was restricted to eastward mean flows, but a wide range of flow regimes with different bottom friction strengths, layer thickness ratios, and background potential vorticity (PV) gradients were otherwise considered. It was found that coherent eddies become more prevalent and longer-lasting as the strength of bottom drag increases and the stratification becomes more surface-intensified. The number of coherent eddies is minimal when the shear-induced PV gradient is 10–20 times the planetary PV gradient and increases for both larger and smaller values of the planetary PV gradient. These coherent eddies, with an average core radius close to the deformation radius, propagate meridionally with a preference for cyclones to propagate poleward and anticyclones to propagate equatorward. The meridional propagation preference of the coherent eddies gives rise to a systematic upgradient PV transport, which is in the opposite direction as the background PV transport and not captured by standard Lagrangian diffusivity estimates. The upgradient PV transport by coherent eddy cores is less than 15% of the total PV transport, but the PV transport by the periphery flow induced by the PV inside coherent eddies is significant and downgradient. These results clarify the distinct roles of the trapping and stirring effect of coherent eddies in PV transport in geophysical turbulence.

Geophysical turbulence dominated by inertia–gravity waves

Recent evidence from both oceanic observations and global-scale ocean model simulations indicate the existence of regions where low-mode internal tidal energy dominates over that of the geostrophic balanced flow. Inspired by these findings, we examine the effect of the first vertical mode inertia–gravity waves on the dynamics of balanced flow using an idealized model obtained by truncating the hydrostatic Boussinesq equations on to the barotropic and the first baroclinic mode. On investigating the wave–balance turbulence phenomenology using freely evolving numerical simulations, we find that the waves continuously transfer energy to the balanced flow in regimes where the balanced-to-wave energy ratio is small, thereby generating small-scale features in the balanced fields. We examine the detailed energy transfer pathways in wave-dominated flows and thereby develop a generalized small Rossby number geophysical turbulence phenomenology, with the two-mode (barotropic and one baroclinic mode) quasi-geostrophic turbulence phenomenology being a subset of it. The present work therefore shows that inertia–gravity waves would form an integral part of the geophysical turbulence phenomenology in regions where balanced flow is weaker than gravity waves.

A Unified Model Spectrum for Anisotropic Stratified and Isotropic Turbulence in the Ocean and Atmosphere

In the decade or so below the Ozmidov wavenumber (N3/ε)1/2, that is, on scales between those attributed to internal gravity waves and isotropic turbulence, ocean and atmosphere measurements consistently find k1/3 horizontal wavenumber spectra for horizontal shear uh and horizontal temperature gradient Th and m−1 vertical wavenumber spectra for vertical shear uz and strain ξz. Dimensional scaling is used to construct model spectra below as well as above the Ozmidov wavenumber that reproduces observed spectral slopes and levels in these two bands in both vertical and horizontal wavenumber. Aspect ratios become increasingly anisotropic below the Ozmidov wavenumber until reaching ~O(f/N), where horizontal shear uh ~ f. The forward energy cascade below the Ozmidov wavenumber found in observations and numerical simulations suggests that anisotropic and isotropic turbulence are manifestations of the same nonlinear downscale energy cascade to dissipation, and that this turbulent cascade originates from anisotropic instability of finescale internal waves at horizontal wavenumbers far below the Ozmidov wavenumber. Isotropic turbulence emerges as the cascade proceeds through the Ozmidov wavenumber where shears become strong enough to overcome stratification. This contrasts with the present paradigm that geophysical isotropic turbulence arises directly from breaking internal waves. This new interpretation of the observations calls for new approaches to understand anisotropic generation of geophysical turbulence patches.

Is spontaneous generation of coherent baroclinic flows possible?

Geophysical turbulence is observed to self-organize into large-scale flows such as zonal jets and coherent vortices. Previous studies of barotropic $\unicode[STIX]{x1D6FD}$-plane turbulence have shown that coherent flows emerge from a background of homogeneous turbulence as a bifurcation when the turbulence intensity increases. The emergence of large-scale flows has been attributed to a new type of collective, symmetry-breaking instability of the statistical state dynamics of the turbulent flow. In this work, we extend the analysis to stratified flows and investigate turbulent self-organization in a two-layer fluid without any imposed mean north–south thermal gradient and with turbulence supported by an external random stirring. We use a second-order closure of the statistical state dynamics, that is termed S3T, with an appropriate averaging ansatz that allows the identification of statistical turbulent equilibria and their structural stability. The bifurcation of the statistically homogeneous equilibrium state to inhomogeneous equilibrium states comprising zonal jets and/or large-scale waves when the energy input rate of the excitation passes a critical threshold is analytically studied. Our theory predicts that there is a large bias towards the emergence of barotropic flows. If the scale of excitation is of the order of (or larger than) the deformation radius, the large-scale structures are barotropic. Mixed barotropic–baroclinic states with jets and/or waves arise when the excitation is at scales shorter than the deformation radius with the baroclinic component of the flow being subdominant for low energy input rates and insignificant for higher energy input rates. The predictions of the S3T theory are compared with nonlinear simulations. The theory is found to accurately predict both the critical transition parameters and the scales of the emergent structures but underestimates their amplitude.