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"Radko, Timour"
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Thermohaline layering in dynamically and diffusively stable shear flows
In this study we examine two-component shear flows that are stable with respect to Kelvin–Helmholtz and to double-diffusive instabilities individually. Our focus is on diffusively stratified ocean regions, where relatively warm and salty water masses are located below cool fresh ones. It is shown that such systems may be destabilized by the interplay between shear and thermohaline effects, caused by unequal molecular diffusivities of density components. Linear stability analysis suggests that parallel two-component flows can be unstable for Richardson numbers exceeding the critical value for non-dissipative systems
$(Ri=1/4)$
by up to four orders of magnitude. Direct numerical simulations indicate that these instabilities transform the initially linear density stratification into a series of well-defined horizontal layers. It is hypothesized that the combined thermohaline–shear instabilities could be ultimately responsible for the widespread occurrence of thermohaline staircases in diffusively stable regions of the World Ocean.
Journal Article
Initiation of diffusive layering by time-dependent shear
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.
Journal Article
A generalized theory of flow forcing by rough topography
An analytical model is developed which explores the impact of irregular sea-floor roughness on large-scale oceanic flows. The previously reported asymptotic ‘sandpaper’ theory of flow-topography interaction represents relatively swift currents and exhibits singular behaviour in the weak flow limit. The present investigation systematically spans a wider parameter space and identifies the principal dissimilarities in the topographic regulation of slow and fast currents. The fast flows are controlled by the Reynolds stresses produced by topographically generated eddies. In contrast, relatively weak flows are more affected by the eddy-induced bottom form drag. The asymptotic models for fast and slow currents are then combined to arrive at a concise description of flow forcing by small-scale topography in homogeneous and multilayer models. The proposed closure is validated by comparing corresponding topography-resolving and parametric simulations.
Journal Article
A mechanism for layer formation in a double-diffusive fluid
The dynamics of layer formation by salt fingers from the uniform temperature and salinity gradients is studied by direct numerical simulations of the two-dimensional Navier–Stokes equations. It is shown that formation of steps in the model is caused by the parametric variation of the flux ratio ($\\gamma\\,{=}\\,{\\overline{wT}}/{\\overline{wS}}$) as a function of the density ratio ($R$), which leads to an instability of equilibrium with uniform stratification. These unstable large-scale perturbations continuously grow in time until well-defined layers are formed. Subsequent evolution of the numerical staircases is explained by considering the secondary instabilities of a series of salt finger interfaces.
Journal Article
Spin-down of a baroclinic vortex by irregular small-scale topography
This study explores the impact of small-scale variability in the bottom relief on the dynamics and evolution of broad baroclinic flows in the ocean. The analytical model presented here generalizes the previously reported barotropic ‘sandpaper’ theory of flow–topography interaction to density-stratified systems. The multiscale asymptotic analysis leads to an explicit representation of the large-scale effects of irregular bottom roughness. The utility of the multiscale model is demonstrated by applying it to the problem of topography-induced spin-down of an axisymmetric vortex. We find that bathymetry affects vortices by suppressing circulation in their deep regions. As a result, vortices located above rough topography tend to be more stable than their flat-bottom counterparts. The multiscale theory is validated by comparing corresponding topography-resolving and parametric simulations.
Journal Article
The sandpaper theory of flow–topography interaction for multilayer shallow-water systems
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.
Journal Article
The sandpaper theory of flow–topography interaction for homogeneous shallow-water systems
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 interaction a priori assumes 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.
Journal Article
Double-Diffusive Convection
Double-diffusive convection is a mixing process driven by the interaction of two fluid components which diffuse at different rates. Leading expert Timour Radko presents the first systematic overview of the classical theory of double-diffusive convection in a coherent narrative, bringing together the disparate literature in this developing field. The book begins by exploring idealized dynamical models and illustrating key principles by examples of oceanic phenomena. Building on the theory, it then explains the dynamics of structures resulting from double-diffusive instabilities, such as the little-understood phenomenon of thermohaline staircases. The book also surveys non-oceanographic applications, such as industrial, astrophysical and geological manifestations, and discusses the climatic and biological consequences of double-diffusive convection. Providing a balanced blend of fundamental theory and real-world examples, this is an indispensable resource for academic researchers, professionals and graduate students in physical oceanography, fluid dynamics, applied mathematics, astrophysics, geophysics and climatology.
eBook
The instability of non-monotonic drag laws
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.
Journal Article