This thesis concerns the numerical investigation of suddenly expanded flows featuring separation, instabilities and transition, in the context of Implicit Large Eddy Simulation (ILES). The study of separated flows through suddenly expanded geometries is a classic yet complex area of research. These types of flows feature instabilities which may lead to bifurcation. Non-linear bifurcation is of great importance when considering hydrodynamic stability and the mechanism of laminar to turbulent flow transition. A detailed numerical investigation of various high-resolution methods and their ability to correctly predict the flow through a suddenly expanded and contracted geometry demonstrates that the choice of the particular numerical method employed can lead to an incorrect solution of the flow. The key di erence between the various highresolution methods employed is in the calculation of the nonlinear wave-speed dependent term. It is shown that the nonlinearity of this term provides an asymmetric dissipation to the flow which triggers symmetry-breaking bifurcation in a fully symmetric computational set-up. High-resolution simulations of three-dimensional flow through a plane suddenly expanded channel at low Reynolds numbers show that this type of flow is characterised by a symmetric separation of the fluid which is nominally two-dimensional in the spanwise direction. Increasing the Reynolds number reveals a symmetry-breaking bifurcation of the fluid flow which becomes three-dimensional as Reynolds number is further increased. Simulations confirm that it is this threedimensional disturbance which leads to the onset of time-dependent flow characterised by the periodic shedding of vortices from the upstream recirculation zones. Preconditioning techniques which aim to alleviate sti ness in the calculation of the advective fluxes for low Reynolds number flows are shown to be unsuitable for flows featuring instabilities. The added dissipation to the flow causes the predictio.

Instabilities of fluid flows and the associated transitions between different possible flow states provide a fascinating set of problems that have attracted researchers for over a hundred years. This book addresses state-of-the-art developments in numerical techniques for computational modelling of fluid instabilities and related bifurcation structures, as well as providing comprehensive reviews of recently solved challenging problems in the field.

The reshocked single-mode Richtmyer-Meshkov instability is simulated in two spatial dimensions using the fifth- and ninth-order weighted essentially non-oscillatory shock-capturing method with uniform spatial resolution of 256 points per initial perturbation wavelength. The initial conditions and computational domain are modeled after the single-mode, Mach 1.21 air(acetone)/SF6 shock tube experiment of Collins and Jacobs [J. Fluid Mech. 464, 113 (2002)]. The simulation densities are shown to be in very good agreement with the corrected experimental planar laser-induced fluorescence images at selected times before reshock of the evolving interface. Analytical, semianalytical and phenomenological linear and nonlinear, impulsive, perturbation and potential flow models for single-mode Richtmyer-Meshkov unstable perturbation growth are summarized. The simulation amplitudes are shown to be in very good agreement with the experimental data and with the predictions of linear amplitude growth models for small times and with those of nonlinear amplitude growth models at later times up to the time at which the driver-based expansion in the experiment (but not present in the simulations or models) expands the layer before reshock. The qualitative and quantitative differences between the fifth- and ninth-order simulation results are discussed. Using a local and global quantitative metric, the prediction of the Zhang and Sohn [Phys. Fluids 9, 1106 (1997)] nonlinear Pade model is shown to be in best overall agreement with the simulation amplitudes before reshock. The sensitivity of the amplitude growth model predictions to the initial growth rate from linear instability theory, the post-shock Atwood number and amplitude, and the velocity jump due to the passage of the shock through the interface is also investigated numerically. In Part II [Phys. Fluids (2006)], a comprehensive investigation of mixing induced by the reshocked single-mode Richtmyer-Meshkov instability is performed using the present simulation data to assess and quantify the effects of reshock and other waves on the mixing dynamics, including the post-reshock growth, circulation deposition, mixing profiles and fractions, baroclinic circulation deposition, energy spectra and statistics.

Modeling Atmospheric and Oceanic Flows: Insights from Laboratory Experiments and Numerical Simulations provides a broad overview of recent progress in using laboratory experiments and numerical simulations to model atmospheric and oceanic fluid motions. This volume not only surveys novel research topics in laboratory experimentation, but also highlights recent developments in the corresponding computational simulations. As computing power grows exponentially and better numerical codes are developed, the interplay between numerical simulations and laboratory experiments is gaining paramount importance within the scientific community. The lessons learnt from the laboratory–model comparisons in this volume will act as a source of inspiration for the next generation of experiments and simulations. Volume highlights include: Topics pertaining to atmospheric science, climate physics, physical oceanography, marine geology and geophysics Overview of the most advanced experimental and computational research in geophysics Recent developments in numerical simulations of atmospheric and oceanic fluid motion Unique comparative analysis of the experimental and numerical approaches to modeling fluid flow Modeling Atmospheric and Oceanic Flows will be a valuable resource for graduate students, researchers, and professionals in the fields of geophysics, atmospheric sciences, oceanography, climate science, hydrology, and experimental geosciences.

"The role of high performance computing in current research on transitional and turbulent flows is undoubtedly very important. This review volume provides a good platform for leading experts and researchers in various fields of fluid mechanics dealing with transitional and turbulent flows to synergistically exchange ideas and present the state of the art in the fields. Contributed by eminent researchers, the book chapters feature keynote lectures, panel discussions and the best invited contributed papers."--