Residual-mean theory is applied to the streamwise-averaged Antarctic Circumpolar Current to arrive at a concise description of the processes that set up its stratification and meridional overturning circulation on an f plane. Simple solutions are found in which transfer by geostrophic eddies colludes with applied winds and buoyancy fluxes to determine the depth and stratification of the thermocline and the pattern of associated (residual) meridional overturning circulation.

Double-diffusive convection is a mixing process driven by the interaction of two fluid components that diffuse at different rates. This phenomenon has important ramifications in oceanography and in numerous other fields, from crystal growth to magma chambers and stellar interiors. Nevertheless, several aspects of doublediffusive convection still remain unclear and controversial. Leading expert Timour Radko presents the first systematic overview of the classical theory of double-diffusive convection, in a coherent narrative which brings together the disparate literature in this developing field. The book begins by exploring idealized dynamical models and illustrating key principles through 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. Timour Radko teaches courses in ocean dynamics, circulation analysis and wave motion at the Oceanography Department of the Naval Postgraduate School. Previously, he worked as a research scientist at the Department of Earth, Atmospheric and Planetary Sciences (EAPS) at the Massachusetts Institute of Technology. He has been active in the area of double-diffusive convection for over fifteen years and was closely involved in developing the theory surrounding this topic. Dr. Radko has authored numerous papers on physical oceanography and fluid mechanics, and has received the prestigious NSF CAREER award in 2006, the NPS Merit Award for Research in 2008, and the Schieffelin (2010) and Griffin (2011) Awards for Excellence in Teaching.

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.

Regions of the ocean's thermocline unstable to salt fingering are often observed to host thermohaline staircases, stacks of deep well-mixed convective layers separated by thin stably-stratified interfaces. Decades after their discovery, however, their origin remains controversial. In this paper we use 3D direct numerical simulations to shed light on the problem. We study the evolution of an analogous double-diffusive system, starting from an initial statistically homogeneous fingering state and find that it spontaneously transforms into a layered state. By analysing our results in the light of the mean-field theory developed in Paper I, a clear picture of the sequence of events resulting in the staircase formation emerges. A collective instability of homogeneous fingering convection first excites a field of gravity waves, with a well-defined vertical wavelength. However, the waves saturate early through regular but localized breaking events, and are not directly responsible for the formation of the staircase. Meanwhile, slower-growing, horizontally invariant but vertically quasi-periodic γ-modes are also excited and grow according to the γ−instability mechanism. Our results suggest that the nonlinear interaction between these various mean-field modes of instability leads to the selection of one particular γ−mode as the staircase progenitor. Upon reaching a critical amplitude, this progenitor overturns into a fully-formed staircase. We conclude by extending the results of our simulations to real oceanic parameter values, and find that the progenitor γ−mode is expected to grow on a timescale of a few hours, and leads to the formation of a thermohaline staircase in about one day with an initial spacing of the order of one to two metres.

Double-diffusive instabilities are often invoked to explain enhanced transport in stably stratified fluids. The most-studied natural manifestation of this process, fingering convection, commonly occurs in the ocean's thermocline and typically increases diapycnal mixing by 2 orders of magnitude over molecular diffusion. Fingering convection is also often associated with structures on much larger scales, such as thermohaline intrusions, gravity waves and thermohaline staircases. In this paper, we present an exhaustive study of the phenomenon from small to large scales. We perform the first three-dimensional simulations of the process at realistic values of the heat and salt diffusivities and provide accurate estimates of the induced turbulent transport. Our results are consistent with oceanic field measurements of diapycnal mixing in fingering regions. We then develop a generalized mean-field theory to study the stability of fingering systems to large-scale perturbations using our calculated turbulent fluxes to parameterize small-scale transport. The theory recovers the intrusive instability, the collective instability and the γ -instability as limiting cases. We find that the fastest growing large-scale mode depends sensitively on the ratio of the background gradients of temperature and salinity (the density ratio). While only intrusive modes exist at high density ratios, the collective and γ instabilities dominate the system at the low density ratios where staircases are typically observed. We conclude by discussing our findings in the context of staircase-formation theory.