Author : Narsimha Reddy Rapaka
Publisher :
ISBN 13 : 9781339091792
Total Pages : 92 pages
Book Rating : 4.0/5 (917 download)
Book Synopsis Simulation of Stratified Turbulent Flows in Complex Geometry by : Narsimha Reddy Rapaka
Download or read book Simulation of Stratified Turbulent Flows in Complex Geometry written by Narsimha Reddy Rapaka and published by . This book was released on 2015 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt: Direct and Large Eddy Simulation approaches are used to study internal tide generation and turbulence at a model topography. A three dimensional finite difference code using an immersed boundary method is developed to simulate stratified turbulent flows over complex geometry on a Cartesian grid. The thesis is comprised of two phases. In the first phase, a mixed spectral/finite difference code is used to solve the governing equations in generalized coordinates. Direct and large eddy simulations are performed using a body fitted grid (BFG) to study the internal waves generated by the oscillation of a barotropic tide over a model ridge of triangular shape. The objective is to assess the role of nonlinear interactions including turbulence in situations with low tidal excursion number. The criticality parameter, defined as the ratio of the topographic slope to the characteristic slope of the tidal rays, is varied from subcritical to supercritical values. The barotropic tidal forcing is also systematically increased. In laminar flow at low forcing, numerical results of the energy conversion agree well compared to linear theory in subcritical and supercritical cases but not at critical slope angle. In critical and supercritical cases with higher forcing, there are convective overturns, turbulence and significant reduction (as much as 25%) of the radiated wave flux with respect to laminar flow results. The phase dependence of turbulence within a tidal cycle is examined and found to differ substantially between the ridge slope and the ridge top where the beams from the two sides cross. In the second phase, a sharp-interface Immersed Boundary Method (IBM) is developed to simulate high Reynolds number density-stratified turbulent flows in complex geometry. The basic numerical scheme corresponds to a central second-order finite difference method, third-order Runge-Kutta integration for the advective terms and an alternating direction implicit (ADI) scheme for the viscous and diffusive terms. Both direct numerical simulation (DNS) and large eddy simulation (LES) approaches are considered. The focus is on accurate computation of the internal gravity wave field and turbulence near an underwater obstacle in a model problem where a tide oscillates over the obstacle. Methods to enhance the mass conservation and numerical stability of the solver to simulate high Reynolds number flows are discussed. The solver is validated using Direct Numerical Simulations (DNS) of channel flow with and without stratification, and tidal flow over a laboratory-scale (order of few meters) smoothed triangular ridge. The results including baroclinic energy flux, mean flow properties and turbulent kinetic energy agree reasonably well with our previous results obtained using a body-fitted grid (BFG). The deviation of IBM results from BFG results is found to increase with increasing steepness of the topography relative to the internal wave propagation angle. LES is performed on a large scale ridge, of the order of few kilometers in length, at significantly larger Reynolds number. A non-linear drag law is utilized to parameterize turbulent losses due to bottom friction. The large scale problem exhibits qualitatively similar behavior to the laboratory scale problem with some differences: slightly larger intensification of the boundary flow and somewhat higher nondimensional values for conversion, baroclinic wave flux and turbulent kinetic energy. The phasing of wave breaking and turbulence exhibits little difference between small and large scale obstacles. We conclude that IBM is a viable approach to the simulation of internal waves and turbulence in high Reynolds number stratified flows over topography.