Stratified turbulence and ocean mixing

In this thesis, I explore the complexities of stratified turbulence and its fundamental role in controlling the rate of planetary-scale ocean circulation. The thesis focuses upon two major cornerstones. The first part contributes to extend the fluid dynamical understanding associated with two archetypical instabilities in inhomogeneously stratified and sheared flows, namely (i) the Kelvin-Helmholtz instability (KHI) and (ii) the Holmboe wave instability (HWI). Direct Numerical Simulation (DNS) is employed to thoroughly analyze the growth and collapse of these instabilities in the computationally challenging, but oceanographically relevant, regime of high Reynolds and high Prandtl number. Through careful analysis of the mixing engendered by these instabilities, the intricate variations of mixing efficiency and diapycnal diffusivity with respect to various important non-dimensional parameters is investigated. Furthermore, I will introduce generalized theoretical formulations that are required for an accurate representation of the diapycnal diffusivities of mass and momentum that are required to distinguish carefully between reversible stirring and irreversible mixing. One of my key findings concerning the characterization of mixing associated with KHI is that mixing may become less efficient if turbulence is too vigorous, corroborating previous results of homogeneously stratified sheared flows and further suggesting a degree of universality in mixing properties of fully turbulent flows. Insofar as HWI is concerned, I demonstrate, for the first time, that this instability mechanism may truly become turbulent under sufficiently high Reynolds number conditions with its inertial subrange revealing a â 5/3 power-law spectral behavior that is characteristic of stratified turbulent flows. The categorical distinctions between KHI and HWI will also be discussed. Most importantly, unlike the rapid burst that characterizes the transition of KHI into turbulence, HWI will be shown to be much more long-lived due to a distinct localisation of mixing and the emergence of self-organized criticality as a characterization of the turbulence itself. The second part of this thesis applies the understanding of the stratified shear-induced turbulence developed in the first part of the thesis in the oceanographic context. I will use detailed modern measurements of ocean turbulence to establish that the â KH-ansatzâ may serve as a useful basis for the study of ocean turbulence and proceed to consolidate the results of the ensemble of KHI simulations in such a way as to propose a multi-dimensional parameterization for mixing efficiency (and thus the turbulent diapycnal diffusivities of mass and momentum). Using this proposed parameterization together with inferred dissipation rates from the Argo floats, I will present spatial maps of diapycnal mixing determined on this basis for the upper 2 km of the global oceans and will argue that current estimates of diapycnal diffusivity warrant further consideration. Furthermore, I will demonstrate that a variable and non-monotonic representation of mixing efficiency produces vastly different rates of abyssal circulation, thus exerting a leading order control on the ocean meridional overturning circulation.

Keywords: geophysical fluid dynamics
mixing and dispersion
ocean circulation
stratified turbulence
wave breaking
Advisor: Peltier, W. R.