Numerical modeling of simple laboratory experiments of rotating flows

Resumen

Despite the large amount of research which has been conducted on turbulent flows, a full understanding of their dynamics as well as the mechanisms involved in the onset of turbulence is still missing. Experimental studies of transition to turbulence are generally carried out in setups with simple geometries which allow isolating the physical mechanisms underlying the dynamics. However, in spite of the simplicity of the models, the problem is extremely complex and it is difficult to reach definitive conclusions on many of the observed dynamical features. Since a few decades ago numerical simulations complement laboratory experiments, significantly accelerating the scientific progress and improving the quality of investigations. In order to compare experimental and numerical results, it is essential to carry out a calibration process in which the possible discrepancies are identified and adjustments (typically modifications in the numerical formulation of the problem) are made in order to minimize them as far as possible. The results of this thesis are primarily intended as an aid in the calibration process of rotating flows in presence of a temperature gradient, which are of great interest in multiple industrial, geophysical and astrophysical applications. Numerical simulations of the flow enclosed in rotating cylindrical and annular cavities subjected to either a vertical or horizontal temperature gradient (rotating Rayleigh--Bénard convection and laterally heated Taylor--Couette flows) have been performed. Several techniques of numerical analysis such as direct simulation of the governing equations, linear stability analysis, continuation methods or time--series analysis have been used for the completion of the thesis. Three sources of discrepancies between experimental and numerical results have been investigated. First,we show a detailed study of how symmetry-breaking due to experimental imperfections may modify the dynamics of the idealized systems used in numerical simulations. An example in rotating Rayleigh-Bénard convection is illustrated in which simulations only capture the experimental behavior when this symmetry-breaking is introduced in the formulation of the problem, i.e. through the boundary conditions. Second, we consider the influence of centrifugal effects which are often neglected in theoretical and numerical studies of rotating flows. This may result in substantial differences with experimental results in those ranges of parameters in which centrifugal buoyancy plays a significant dynamical role. To this extent, we provide a straightforward Boussinesq-type approximation which allows for considering centrifugal effects in an inertial reference frame, including secondary effects stemming from differential rotation or strong internal vorticity, which had not been previously considered in any other formulation. Third, the influence of axial end walls in the dynamics of simple models for the study of baroclinic flows is discussed. The objective of this study is to identify the degree to which simulations in axially periodic systems, with a lower computational cost, can be used to reproduce experimental results. A strong stabilizing effect, which increases significantly at high temperature differences between the cylinders, results from the boundary layers and cause large discrepancies with the onset of instability in the case of axially periodic boundary conditions. Finally, a numerical study of a recently reported experimental bifurcation scenario in isothermal Taylor-Couette flow is also presented. We focus on the dynamics of flow patterns characterized by large amplitude oscillations that are localized only in some vortex-pairs. In this case, experimental and numerical results are in full agreement.