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A series of recent studies has indicated that the component of the bottom drag caused by irregular small-scale topography in the ocean varies non-monotonically with the flow speed. The roughness-induced forcing increases with the speed of relatively slow abyssal currents but, somewhat counterintuitively, starts to decrease when flows are sufficiently swift. This reduction in drag at high speeds leads to the instability of laterally uniform currents, and the resulting evolutionary patterns are explored using numerical and analytical methods. The drag-law instability manifests in the spontaneous emergence of parallel jets, aligned in the direction of the basic flow and separated by relatively quiescent regions. We hypothesize that the mechanisms identified in this investigation could play a role in the dynamics of zonal striations commonly observed in the ocean. 

Seafloor roughness profoundly influences the pattern and dynamics of large-scale oceanic flows. However, these kilometre-scale topographic patterns are unresolved by global numerical Earth system models and will remain subgrid for the foreseeable future. To properly represent the effects of small-scale bathymetry in analytical and coarse-resolution numerical models, we develop the stratified ‘sandpaper’ theory of flow–topography interaction. This model, which is based on the multilayer shallow-water framework, extends its barotropic antecedent to stratified flows. The proposed theory is successfully tested on the configuration representing the interaction of a zonal current with a corrugated cross-flow ridge. 

Recent studies reveal the dramatic impact of seafloor roughness on the dynamics and stability of broad oceanic flows. These findings motivate the development of parameterizations that concisely represent the effects of small-scale bathymetric patterns in theoretical and coarse-resolution numerical circulation models. The previously reported quasi-geostrophic ‘sandpaper’ theory of flow–topography interactiona prioriassumes gentle topographic slopes and weak flows with low Rossby numbers. Since such conditions are often violated in the ocean, we now proceed to formulate a more general model based on shallow-water equations. The new version of the sandpaper model is validated by comparing roughness-resolving and parametric simulations of the flow over a corrugated seamount. 

Abstract Arctic staircases mediate the heat transport from the warm water of Atlantic origin to the cooler waters of the Arctic mixed layer. For this reason, staircases have received much due attention from the community, and their heat transport has been well characterized for systems in the absence of external forcing. However, the ocean is a dynamic environment with large-scale currents and internal waves being omnipresent, even in regions shielded by sea-ice. Thus, we have attempted to address the effects of background shear on fully developed staircases using numerical simulations. The code, which is pseudo-spectral, evolves the governing equations for a Boussinesq fluid with temperature and salinity in a shearing coordinate system. We find that—– unlike many other double-diffusive systems—the sheared staircase requires three-dimensional simulations to properly capture the dynamics. Our simulations predict shear patterns that are consistent with observations and show that staircases in the presence of external shear should be expected to transport heat and salt at least twice as efficiently as in the corresponding non-sheared systems. These findings may lead to critical improvements in the representation of micro-scale mixing in global climate models. 

This study attempts to quantify and explain the systematic weakening of internal gravity waves in fingering and diffusive thermohaline staircases. The interaction between waves and staircases is explored using a combination of direct numerical simulations (DNS) and an asymptotic multiscale model. The multiscale theory makes it possible to express the wave decay rate $$({\lambda _d})$$ as a function of its wavenumbers and staircase parameters. We find that the decay rates in fully developed staircases greatly exceed values that can be directly attributed to molecular dissipation. They rapidly increase with increasing wavenumbers, both vertical and horizontal. At the same time, $${\lambda _d}$$ is only weakly dependent on the thickness of layers in the staircase, the overall density ratio and the diffusivity ratio. The proposed physical mechanism of attenuation emphasizes the significance of eddy diffusion of temperature and salinity, whereas eddy viscosity plays a secondary role in damping internal waves. The asymptotic model is successfully validated by the DNS performed in numerically accessible regimes. We also discuss potential implications of staircase-induced suppression for diapycnal mixing by overturning internal waves in the ocean. 

Abstract We introduce a pseudo‐spectral algorithm that includes full compressible dynamics with the intent of simulating near‐incompressible fluids, CaTSM (Compressible and Thermodynamically consistent Spectral Model). A semi‐implicit scheme is used to model acoustic waves in order to evolve the system efficiently for such fluids. We demonstrate the convergence properties of this numerical code for the case of a shock tube and for Rayleigh‐Taylor instability. A linear equation of state is also presented, which relates the specific volume of the fluid linearly to the potential temperature, salinity, and pressure. This permits the results to be easily compared to a Boussinesq framework in order to assess whether the Boussinesq approximation adequately represents the relevant exchange of energy to the problem of interest. One such application is included, that of the development of a single salt finger, and it is shown that the energetic behavior of the system is comparable to the typical canonical development of the problem for oceanographic parameters. However, for more compressible systems, the results change substantially even for low‐Mach number flows. 

A theoretical model is developed which illustrates the dynamics of layering instability, frequently realized in ocean regions with active fingering convection. Thermohaline layering is driven by the interplay between large-scale stratification and primary double-diffusive instabilities operating at the microscale – temporal and spatial scales set by molecular dissipation. This interaction is described by a combination of direct numerical simulations and an asymptotic multiscale model. The multiscale theory is used to formulate explicit and dynamically consistent flux laws, which can be readily implemented in large-scale analytical and numerical models. Most previous theoretical investigations of thermohaline layering were based on the flux-gradient model, which assumes that the vertical transport of density components is uniquely determined by their local background gradients. The key deficiency of this approach is that layering instabilities predicted by the flux-gradient model have unbounded growth rates at high wavenumbers. The resulting ultraviolet catastrophe precludes the analysis of such basic properties of layering instability as its preferred wavelength or the maximal growth rate. The multiscale model, on the other hand, incorporates hyperdiffusion terms that stabilize short layering modes. Overall, the presented theory carries the triple advantage of (i) offering an explicit description of the interaction between microstructure and layering modes, (ii) taking into account the influence of non-uniform stratification on microstructure-driven mixing, and (iii) avoiding unphysical behaviour of the flux-gradient laws at small scales. While the multiscale approach to the parametrization of time-dependent small-scale processes is illustrated here on the example of fingering convection, we expect the proposed technique to be readily adaptable to a wide range of applications. 

The Arctic halocline is generally stable to the development of double-diffusive and dynamic instabilities – the two major sources of small-scale mixing in the mid-latitude oceans. Despite this, observations show the abundance of double-diffusive staircases in the Arctic Ocean, which suggests the presence of some destabilizing process facilitating the transition from smooth-gradient to layered stratification. Recent studies have shown that an instability can develop in such circumstances if weak static shear is present even when the flow is dynamically and diffusively stable. However, the impact of oscillating shear, associated with the presence of internal gravity waves, has not yet been addressed for the diffusive case. Through two-dimensional simulations of diffusive convection, we have investigated the impact of the magnitude and frequency of externally forced oscillatory shear on the thermohaline-shear instability. Simulations with stochastic shear – characterized by a continuous spectrum of frequencies from inertial to buoyancy – indicate that thermohaline layering does occur due to the presence of destabilizing modes (oscillations of near the buoyancy frequency). These simulations show that such layers appear as well-defined steps in the temperature and salinity profiles. Thus, the thermohaline-shear instability is a plausible mechanism for staircase formation in the Arctic and merits substantial future study. 

Abstract This study presents the linear theory of thermohaline‐shear instability, which is realized in oceanic flows that are dynamically and diffusively stable. The framework is based on the unbounded Couette model, which makes it possible to decouple the destabilizing effects of spatially uniform shear from instabilities caused by the presence of inflection points in velocity profiles. The basic state is assumed to be time dependent, which reflects the role of internal waves in controlling fine‐scale shear. Linear stability analysis suggests that conditions for thermohaline‐shear instability are met in most ocean regions where temperature and salinity concurrently increase downward. We conclude that thermohaline‐shear instability represents a plausible mechanism for the initiation of active diffusive convection, which, in turn, is essential for the formation of thermohaline staircases and maintenance of double‐diffusive interleaving.