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Fluid mechanics has emerged as a basic concept for nearly every field of technology. Despite a well-developed mathematical theory and available commercial software codes, the computation of solutions of the governing equations of motion is still challenging, especially due to the nonlinearity involved, and there are still open questions regarding the underlying physics of fluid flow, especially with respect to the continuum hypothesis and thermodynamic local equilibrium. The aim of this book is to reference recent advances in the field of fluid mechanics, both in terms of developing sophisticated mathematical methods for finding solutions to the equations of motion, on the one hand, and presenting novel approaches to the physical modeling, on the other hand. A wide range of topics is addressed, including general topics like formulations of the equations of motion in terms of conventional and potential fields; variational formulations, both deterministic and statistic, and their application to channel flows; vortex dynamics; flows through porous media; and also acoustic waves through porous media

image processing --- streaky structures --- hairpin vortex --- attached-eddy vortex --- streamwise vortex --- wetting shock fronts --- shear flow --- viscosity --- capillarity --- kinematic waves --- log-law --- flow partitioning theory --- characteristic point location --- velocity --- discharge --- groundwater inrush --- the Luotuoshan coalmine --- damage mechanism --- karst collapse column --- poroacoustics --- Rubin–Rosenau–Gottlieb theory --- solitary waves and kinks --- Navier–Stokes equation --- stochastic Lagrangian flows --- stochastic variational principles --- stochastic geometric mechanics --- potential fields --- Clebsch variables --- Airy’s stress function --- Goursat functions --- Galilean invariance --- variational principles --- boundary conditions --- film flows --- analytical and numerical methods --- variational calculus --- deterministic and stochastic approaches --- incompressible and compressible flow --- continuum hypothesis --- advanced mathematical methods