In this thesis we will investigate the role of diapycnal mixing on the ocean general circulation. This thesis is divided into three main parts. In the first part we show that there exists an almost infinite number of pathways to turbulence in oceanic energetic shear zones at high Reynolds number. Such a large number of accessible routes to truly chaotic motion is not typical of most of the existing body of laboratory and numerical experiments of shear-induced diapycnal mixing, but is shown to be of relevance to diapycnal mixing in geophysical flows. A key finding is that the use of generally accepted empirical relations based on laboratory experiments for the quantification of diapycnal mixing leads to large inaccuracies. In the second part we perform high resolution numerical experiments of diapycnal mixing in the oceanographically relevant high Reynolds number parameter range. Through detailed analysis of the flow energetics and mixing properties of these flows, we show that the net buoyancy flux facilitated by turbulence, the efficiency of diapycnal mixing, and the resultant effective diffusivity, all depend in non-trivial ways on the specific route to turbulence for each individual mixing event. This has important implications for practical methods of estimating an effective diapycnal mixing diffusivity from observations as well as for parametrization of mixing in ocean general circulation models. We show quantitatively that such methods can be inaccurate to the extent that they will need to be completely revised or replaced. In the third and final part of the thesis we investigate the sensitivity of the meridional overturning circulation of the abyssal ocean to the intensity and spatial variations of diapycnal mixing. We show that changes in intensity of mixing by factors well within the errors associated with practical estimates (as discussed above) lead to significant changes in ocean circulation. We show that enhanced abyssal mixing, surface winds, and meso-scale eddies play leading roles in driving the abyssal ocean circulation and in setting the stratification. As an example of the application of our analysis we show that proper parametrization of enhanced abyssal mixing leads to realization of the important role of the (often neglected) geothermal heat flux in driving the Antarctic Bottom Water circulation.

In this thesis we will investigate the role of diapycnal mixing on the ocean general circulation. This thesis is divided into three main parts. In the first part we show that there exists an almost infinite number of pathways to turbulence in oceanic energetic shear zones at high Reynolds number. Such a large number of accessible routes to truly chaotic motion is not typical of most of the existing body of laboratory and numerical experiments of shear-induced diapycnal mixing, but is shown to be of relevance to diapycnal mixing in geophysical flows. A key finding is that the use of generally accepted empirical relations based on laboratory experiments for the quantification of diapycnal mixing leads to large inaccuracies. In the second part we perform high resolution numerical experiments of diapycnal mixing in the oceanographically relevant high Reynolds number parameter range. Through detailed analysis of the flow energetics and mixing properties of these flows, we show that the net buoyancy flux facilitated by turbulence, the efficiency of diapycnal mixing, and the resultant effective diffusivity, all depend in non-trivial ways on the specific route to turbulence for each individual mixing event. This has important implications for practical methods of estimating an effective diapycnal mixing diffusivity from observations as well as for parametrization of mixing in ocean general circulation models. We show quantitatively that such methods can be inaccurate to the extent that they will need to be completely revised or replaced. In the third and final part of the thesis we investigate the sensitivity of the meridional overturning circulation of the abyssal ocean to the intensity and spatial variations of diapycnal mixing. We show that changes in intensity of mixing by factors well within the errors associated with practical estimates (as discussed above) lead to significant changes in ocean circulation. We show that enhanced abyssal mixing, surface winds, and meso-scale eddies play leading roles in driving the abyssal ocean circulation and in setting the stratification. As an example of the application of our analysis we show that proper parametrization of enhanced abyssal mixing leads to realization of the important role of the (often neglected) geothermal heat flux in driving the Antarctic Bottom Water circulation.

The speed and efficiency of stratified turbulent mixing in homogenising temperatures, chemical composition and flow speeds makes it one of farthest reaching fluid mechanical phenomenon for life on earth. It is an aesthetically beautiful phenomenon, rich in complex physical behaviours and extremely challenging to model mathematically. Laboratory experiments have a valuable role to play to guide theoretical and numerical work towards a better understanding of this phenomenon by providing insight into real flows under controlled conditions. This dissertation addresses some aspects of the laboratory buoyancy-driven exchange flows through an inclined duct connecting two reservoirs containing fluids of different densities. We employ a novel experimental technique to perform near-instantaneous, volumetric measurements of the three-component velocity field and density field simultaneously, providing an unprecedented quantitative picture of these sustained stratified shear flows. We start by characterising the variety of observed behaviours, or flow regimes, as we vary the density difference between the two reservoirs, the angle of inclination of the duct with respect to the horizontal, the way the density difference is achieved (solutions of salt/fresh water or cold/warm water) and the geometry of the duct. These empirical observations allow us to formulate a number of specific research questions, guiding the work of the next chapters. We then focus on the regime in which Holmboe waves are observed, and demonstrate that these well-known interfacial travelling disturbances have a distinct structure when confined by solid boundaries. We characterise this structure and identify the physical mechanisms at its origin by means of linear stability theory. Since Holmboe waves are found in the intermediate, transitional regime between laminar and turbulent flows, we conjecture that their structure may be relevant to more turbulent flows, where resembling structures are indeed observed. Next, we tackle the quantitative analysis of universal transition curves separating the observed flow regimes (laminar, waves, intermittently turbulent or fully turbulent) as well and the net mass flow rate exchanged by the reservoirs. We show that these long-lasting questions in the study of exchange flows can be addressed in the framework of frictional hydraulic theory, and we derive detailed scaling laws involving only a few nondimensional parameters. Finally, we overcome some of the limitations of hydraulic theory by performing a more detailed, time-resolved, three-dimensional analysis of the energetics of the wave, intermittent and turbulent regimes. We identify and quantify the sources and sinks of energy in each regime, and identify some of the structures responsible for viscous energy dissipation and mixing. We also suggest possible future directions for the present work given recent progress in the literature.

Density stratification is one of the essential underlying physical mechanisms for atmospheric and oceanic flow. As a first step to investigating the mechanisms of stratified turbulence, linear stability plays a critical role in determining under what conditions a flow remains stable or unstable. In the study of transition to stratified turbulence, a common vortex model, known as the Lamb-Chaplygin dipole, is used to investigate the conditions under which stratified flow transitions to turbulence. Numerous investigations have determined that a critical length scale, known as the buoyancy length, plays a key role in the breakdown and transition to stratified turbulence. At this buoyancy length scale, an instability unique to stratified flow, the zigzag instability, emerges. However investigations into sub-buoyancy length scales have remained unexplored. In this thesis we discover and investigate a new instability of the Lamb-Chaplyin dipole that exists at the sub-buoyancy scale. Through numerical linear stability analysis we show that this short-wave instability exhibits growth rates similar to that of the zigzag instability. We conclude with nonlinear studies of this short-wave instability and demonstrate this new instability saturates at a level proportional to the cube of the aspect ratio.

It is often desirable to study simulated turbulent flows at steady state even if the flow has no inherent source of turbulence kinetic energy. Doing so requires a numerical forcing scheme and various methods have been studied extensively for turbulence that is isotropic and homogeneous in three dimensions. A review of these existing schemes is used to form a framework for more general forcing methods. In this framework, the problem of developing a forcing scheme in Fourier space is abstracted into the two problems of (1) prescribing the spectrum of the input power and (2) specifying a force that has the desired characteristics and that adds energy to the flow with the correct spectrum. The framework is used to construct three forcing schemes for horizontally homogeneous and isotropic, vertically stratified turbulence. These schemes are implemented in large-eddy simulations and their characteristics analyzed. Which method is “best” depends on the purpose of the simulations, but the framework for specifying forcing schemes enables a systematic approach for identifying a method appropriate for a particular application.

Le climat de la Terre dépend en grande partie des échanges énergétiques entre les masses d’eau chaudes et froides de nos océans. Afin de prédire et de comprendre les variations de notre climat, les modèles numériques globaux de l’océan doivent pouvoir déterminer quelle fraction d'énergie est convertie en mélange irréversible dans un écoulement turbulent et stablement stratifié. Il apparaît que cette fraction est sensible aux paramètres de l’écoulement, ce qui a récemment conduit les océanographes à remettre en question la paramétrisation d'Osborn pour le coefficient de diffusion turbulente kz, qui utilise une efficacité de mélange constante et fixée à ŋ=0,17. Ceci nous a poussé à réaliser au laboratoire de Mécanique des Fluides et d'Acoustique (LMFA) des mesures conjointes de ŋ et kz, afin de mieux comprendre leur inter-dépendance. Cette étude est avant tout expérimentale et se base sur plusieurs dispositifs permettant de quantifier le mélange dans différents types d'écoulement. Trois de ses expériences ont été réalisées au LMFA : une expérience de lock-exchange dans laquelle le mélange est issu du cisaillement à l'interface de deux courants de gravité se déplaçant en sens opposés, une expérience de grille tractée dans un fluide stratifié et une expérience d’injection de stratification dans la grille d’un canal hydraulique. Ce travail a été complété, d'une part par une collaboration sur la plateforme Coriolis du LEGI à Grenoble, permettant d’atteindre de plus grands nombres de Reynolds ; et d'autre part par une campagne de mesure in situ dans le fjord du Saguenay au Canada en collaboration avec l'ISMER, visant à estimer le mélange turbulent conduisant au renouvellement des eaux profondes du fjord, à partir de l'analyse de transects successifs de densité. Dans ces différentes configurations, l'évolution temporelle des profils verticaux de densité ont permis d'analyser la dépendance du coefficient de diffusion turbulente et de l'efficacité de mélange avec les nombres de Reynolds et de Froude. Nos résultats ont permis de quantifier la décroissance de l'efficacité de mélange avec l'augmentation du nombre de Froude dans un écoulement turbulent, ainsi que la sensibilité du coefficient de diffusion turbulente aux nombres de Froude et de Reynolds de flottabilité. L'utilisation de trois dispositifs expérimentaux différents permet de montrer qu'au-delà de ces lois dites universelles, la variabilité propre à chaque géométrie influence fortement les valeurs de l'efficacité de mélange. Ceci est particulièrement mis en lumière dans la configuration de lock-exchange, pour laquelle la valeur limite de ŋ=0.25 prédite par la physique statistique n'est atteinte que dans une configuration fortement tri-dimensionnelle, jusqu'alors peu utilisée dans la littérature. Enfin, toutes les méthodes d'analyse développées pour les expériences de laboratoire ont pu être utilisées pour l'analyse des données in situ, permettant de clore ce travail de thèse sur une étude environnementale. / Our climate partly depends on energy exchange between warm and cold water masses in the ocean's interior. In order to understand and forecast the climate variations, numerical models of the ocean must estimate the amount of energy converted into irreversible mixing in turbulent stably stratified flows. It seems that this quantity depends on the flow parameters. This assertion challenges the famous Osborn model for turbulent diffusivity kz which uses a fixed mixing efficiency of ŋ=0.17. This motivated us to measure separately kz and ŋ in order to obtain a better understanding of their inter-dependencies. The present work is an experimental study based on set-ups which enable to quantify the mixing in different types of flow. Three of those experiments are held in our lab (LMFA) and consist respectively in a lock-exchange experiment where mixing is generated by the shear at the interface of two opposite gravity currents, a stratified towed grid experiment, and a hydraulic channel experiment where the stratification is injected directly by the grid. This study has been complemented with two international collaborations. The first one, on the Coriolis platform (LEGI) consisted in a stratified towed grid experiment in a rotating tank allowing to broaden our parameter spectrum. The second one is a series of in situ measurements led in collaboration with ISMER in the Saguenay fjord (Canada) aiming at measuring density transects over time in order to quantify the turbulent mixing that participates in the renewal of the fjord's deep water. In all of those configurations, dependencies of mixing efficiency and turbulent diffusivity along with the Froude and the Reynolds numbers are extracted from the time evolution of density profiles. In our results, we were able to quantify the decay of the mixing efficiency with the increase of the Froude number. We also highlighted the sensitivity of turbulent diffusivity on the buoyancy Reynolds number. We used three different experimental setups to show that beyond the so called universal turbulence laws, the flow geometry has a huge impact on the mixing efficiency values. This is especially true in the lock-exchange configuration where the asymptotic value of ŋ=0.25, predicted by statistical physics, can only be reached in a set-up which allows 3D flows. Such investigations are still scarce in the literature. Finally, all the data analysis methods developed for the lab experiments were of great help for the analysis of in situ data and thereby enabled us to consider a real-life environnemental flow.

Une étude numérique de la dynamique d'ondes internes de gravité en fluide stablement stratifié est menée. On décrit un algorithme pseudo-spectral<br />parallèle permettant d'intégrer les équations de Navier-Stokes sur une machine paralèele. En deux dimensions d'espace, on analyse la dynamique d'un<br />champ d'ondes internes propagatives, d'amplitude modérée et initialement plan et monochromatique. Le champ d'ondes est instable et déferle. Le déferlement produit une turbulence de petites échelles spatiales influencées par la stratification. L'étude<br />est étendue au cas tridimensionnel, plus réaliste. En trois dimensions, on étudie le même champ d'ondes internes, que l'on perturbe par un bruit infinitésimal ondulatoire tridimensionnel, mais on considère des ondes statiquement stables et<br />instables (grandes amplitudes). On montre que le déferlement d'une onde interne est un processus intrinsèquement tridimensionnel, y compris pour les ondes de faible amplitude. La tridimensionalisation du champ d'ondes s'opère dans les zones de l'espace où le champ de densité devient statiquement instable. L'effondrement gravitationnel d'une zone est de structure transverse au plan de propagation de l'onde. Les effets de la turbulence des petites échelles sur la production de la composante non propagatrice de l'écoulement, le mode de vorticité potentielle et la production d'un écoulement moyen, permet de conclure que seule une petite proportion de l'énergie mécanique initiale est convertie sous ses deux formes, la majeure partie étant dissipée par la dissipation visqueuse et conduction thermique. On reconsidère le mode de vorticiée potentielle par une approche Hamiltonienne non-canonique du fluide parfait stratifié. La dérivation d'un système de dynamique modifiée permet d'étudier la relaxation d'un écoulement stratifié, conservant sa vorticité potentielle et sa densité, vers un état stationnaire d'énergie minimale, correspondant au mode de vorticité potentielle.