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Waves and turbulence in sustained stratified shear flows



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Lefauve, Adrien Sébastien Paul  ORCID logo


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.





Linden, Paul


stratified turbulence, exchange flows, stratified flows, shear instabilities, Holmboe waves


Doctor of Philosophy (PhD)

Awarding Institution

University of Cambridge
EPSRC (1480426)
Engineering and Physical Sciences Research Council (EPSRC) Cambridge Trust Department of Applied Mathematics and Theoretical Physics