Etude numérique de couches limites sur paroi courbe : rôle de l’instabilité de Görtler et transition à la turbulence

Field: Engineering (Physical Sciences)

Gravity currents are relevant to many geophysical and environmental flows such as salt intrusions into lakes, reservoirs and estuaries, glacial runoff into the ocean, or cold downhill airflows in mountain areas. On a larger scale they play an important role for the transport of water masses in the oceans and the understanding of their dynamics is therefore important for ocean circulation models and climate models. These currents are generated due to a density stratification which is induced by salinity differences, as in oceanic overflows, or by temperature differences, as it is more the case in the atmosphere. In the ocean, the dense currents descend the continental slope for long distances before encountering the ocean bottom or interleaving at their level of neutral buoyancy. During the descent, gravity currents have been observed to entrain the surrounding ambient water. The final properties of their water masses are dictated by the amount and properties of entrained fluid. The correct parametrization of sub-grid turbulent processes related to gravity flows over complex topography (sudden slope changes and curved slopes) are a problem of growing concern since predictions are often unreliable when the overflows themselves and the turbulent and mixing processes are not correctly included in atmospheric, coastal and oceanic circulation models.In this context, a numerical and theoretical study of the dynamics of boundary layer flows on a curved walls is carried out.First, we characterize the centrifugal hydrodynamic instability, called the Görtler instability, by a theoretical approach which consists in solving the linearized equations of motion called linear stability analysis (LSA). We show the influence of the wave number as well as of the Görtler number G on the flow dynamics.In a second step, a series of unsteady numerical simulations is carried out for moderate Reynolds numbers (moderate turbulence level) using large-eddy simulations (LES). These simulations allow a description of the non-linear region of the flow, as well as the transition to turbulence (unlike LSA). We study the influence of a wavelength forcing method on the flow dynamics, as well as the behavior of the flow when the instability is triggered naturally. A comparison with the results of the linear stability analysis is presented.Thirdly, a numerical simulation of a turbulent boundary layer on a curved wall is performed. We show the influence of the curvature on the flow topology as well as on the turbulence which develops. It is also shown that spatial heterogeneities persist in the turbulent region, which constitutes a major result of this thesis.Finally, we present a series of numerical simulations aiming to describe a physics similar to those of the geophysical flows in which we are interested. In this configuration, the buoyancy forces impact the dynamics of the flow. The impacts on the development of Görtler's instability, on the topology of the flow as well as on the turbulent properties of the flow are studied. An analogy between centrifugal forces and buoyancy forces is presented.