The growth and saturation of submesoscale instabilities in the presence of a barotropic jet

AbstractMotivated by recent observations of submesoscales in the Southern Ocean, we use nonlinear numerical simulations and a linear stability analysis to examine the influence of a barotropic jet on submesoscale instabilities at an isolated front. Simulations of the nonhydrostatic Boussinesq equations with a strong barotropic jet (approximately matching the observed conditions) show that submesoscale disturbances and strong vertical velocities are confined to a small region near the initial frontal location. In contrast, without a barotropic jet, submesoscale eddies propagate to the edges of the computational domain and smear the mean frontal structure. Several intermediate jet strengths are also considered. A linear stability analysis reveals that the barotropic jet has a modest influence on the growth rate of linear disturbances to the initial conditions, with at most a ~20% reduction in the growth rate of the most unstable mode. On the other hand, a basic state formed by averaging the flow at the end of the simulation with a strong barotropic jet is linearly stable, suggesting that nonlinear processes modify the mean flow and stabilize the front.</jats:p

Numerical modelling in a multiscale ocean

Systematic improvement in ocean modelling and prediction systems over the past several decades has resulted from several concurrent factors. The first of these has been a sustained increase in computational power, as summarized in Moore\u27s Law, without which much of this recent progress would not have been possible. Despite the limits imposed by existing computer hardware, however, significant accruals in system performance over the years have been achieved through novel innovations in system software, specifically the equations used to represent the temporal evolution of the oceanic state as well as the numerical solution procedures employed to solve them. Here, we review several recent approaches to system design that extend our capability to deal accurately with the multiple time and space scales characteristic of oceanic motion. The first two are methods designed to allow flexible and affordable enhancement in spatial resolution within targeted regions, relying on either a set of nested structured grids or, alternatively, a single unstructured grid. Finally, spatial discretization of the continuous equations necessarily omits finer, subgrid-scale processes whose effects on the resolved scales of motion cannot be neglected. We conclude with a discussion of the possibility of introducing subgrid-scale parameterizations to reflect the influences of unresolved processes

Generalized Quasilinear Approximation: Application to Zonal Jets

Quasilinear theory is often utilized to approximate the dynamics of fluids exhibiting significant interactions between mean flows and eddies. We present a generalization of quasilinear theory to include dynamic mode interactions on the large scales. This generalized quasilinear (GQL) approximation is achieved by separating the state variables into large and small zonal scales via a spectral filter rather than by a decomposition into a formal mean and fluctuations. Nonlinear interactions involving only small zonal scales are then removed. The approximation is conservative and allows for scattering of energy between small-scale modes via the large scale (through nonlocal spectral interactions). We evaluate GQL for the paradigmatic problems of the driving of large-scale jets on a spherical surface and on the beta plane and show that it is accurate even for a small number of large-scale modes. As GQL is formally linear in the small zonal scales, it allows for the closure of the system and can be utilized in direct statistical simulation schemes that have proved an attractive alternative to direct numerical simulation for many geophysical and astrophysical problems

Topological Signature of Stratospheric Poincare -- Gravity Waves

The rotation of the earth breaks time-reversal and reflection symmetries in an opposite sense north and south of the equator, leading to a topological origin for certain atmospheric and oceanic equatorial waves. Away from the equator the rotating shallow water and stably stratified primitive equations exhibit Poincare-gravity waves that have nontrivial topology as evidenced by their strict superinertial timescale and a phase singularity in frequency-wavevector space. This non-trivial topology then predicts, via the principle of bulk-interface correspondence, the existence of two equatorial waves along the equatorial interface, the Kelvin and Yanai waves. To directly test the nontrivial topology of Poincare-gravity waves in observations, we examine ERA5 reanalysis data and study cross-correlations between the wind velocity and geopotential height of the mid-latitude stratosphere at the 50 hPa height, and find the predicted vortex and anti-vortex in the phase of the correlations at the high frequencies of the waves. By contrast, lower-frequency planetary waves are found to have trivial topology. These results demonstrate a new way to understand stratospheric waves, and provide a new qualitative tool for the investigation of waves in other components of the climate system.Comment: 24 pages, 6 figure

Parameterization of mixed layer eddies. III: Implementation and impact in global ocean climate simulations

A parameterization for the restratification by finite-amplitude, submesoscale, mixed layer eddies, formulated as an overturning streamfunction, has been recently proposed to approximate eddy fluxes of density and other tracers. Here, the technicalities of implementing the parameterization in the coarse-resolution ocean component of global climate models are made explicit, and the primary impacts on model solutions of implementing the parameterization are discussed. Three global ocean general circulation models including this parameterization are contrasted with control simulations lacking the parameterization. The MLE parameterization behaves as expected and fairly consistently in models differing in discretization, boundary layer mixing, resolution, and other parameterizations. The primary impact of the parameterization is a shoaling of the mixed layer, with the largest effect in polar winter regions. Secondary impacts include strengthening the Atlantic meridional overturning while reducing its variability, reducing CFC and tracer ventilation, modest changes to sea surface temperature and air–sea fluxes, and an apparent reduction of sea ice basal melting.National Science Foundation (U.S.) (Grant OCE-0612143)National Science Foundation (U.S.) (Grant OCE-0612059)National Science Foundation (U.S.) (Grant OCE-0825376)National Science Foundation (U.S.) (Grant DMS-0855010)National Science Foundation (U.S.) (Grant OCE-0934737

Estimating the sea ice floe size distribution using satellite altimetry: Theory, climatology, and model comparison

In sea-ice-covered areas, the sea ice floe size distribution (FSD) plays an important role in many processes affecting the coupled sea-ice-ocean-atmosphere system. Observations of the FSD are sparse - traditionally taken via a painstaking analysis of ice surface photography - and the seasonal and inter-annual evolution of floe size regionally and globally is largely unknown. Frequently, measured FSDs are assessed using a single number, the scaling exponent of the closest power-law fit to the observed floe size data, although in the absence of adequate datasets there have been limited tests of this "power-law hypothesis". Here we derive and explain a mathematical technique for deriving statistics of the sea ice FSD from polar-orbiting altimeters, satellites with sub-daily return times to polar regions with high along-track resolutions. Applied to the CryoSat-2 radar altimetric record, covering the period from 2010 to 2018, and incorporating 11 million individual floe samples, we produce the first pan-Arctic climatology and seasonal cycle of sea ice floe size statistics. We then perform the first pan-Arctic test of the power-law hypothesis, finding limited support in the range of floe sizes typically analyzed in photographic observational studies. We compare the seasonal variability in observed floe size to fully coupled climate model simulations including a prognostic floe size and thickness distribution and coupled wave model, finding good agreement in regions where modeled ocean surface waves cause sea ice fracture