| The aim of the dissertation is to obtain a general understanding of the process of transition to turbulence for a boundary-layer with no pressure gradient. As a first step, a highly accurate algorithm has been developed to study the process of spatial transition to turbulence. The equations are in the vertical velocity-vertical vorticity formulation. The linear viscous terms are discretized using an implicit Crank-Nicholson scheme, and a low-storage Runge-Kutta method is used for the nonlinear terms. For the spatial discretization, fourth-order compact finite differences have been used, as these have been found to have better resolution compared to explicit differencing schemes of comparable order. The number of grid points that are needed per wavelength is close to the theoretical optimum for any numerical scheme. The resulting time-discretized fourth-order equations are split up into two second-order equations, resulting in Helmholtz- and Poisson-type equations. The boundary conditions for the Laplacian of the vertical velocity are determined technique. The parallel computing performance characteristics, speedup and scaled efficiency have been determined. Both the algorithmic and implementation scalability features have resulted in efficient parallelization. Message-passing-interface (MPI) has been used for the communication between the various nodes. For the outflow boundary, a buffer domain method, which smoothly reduces the disturbances to zero, in conjunction with parabolization of the Navier-Stokes equations has been used. The validation of the results for the DNS solver is done both for linear and weakly nonlinear cases. Analysis has been performed for the case of forced transition, a single frequency disturbance has been introduced, and fundamental breakdown and the characteristic events of a transitional boundary layer have been observed. The focus is on the structures and events in the transitional boundary layer and the role they play in the process of breakdown to turbulence. The typical events observed are—the presence of a high-shear layer, formation of the Λ-vortices, formation and amplification of streamwise vortices, a peak-valley structure in the spanwise direction and the occurrence of spikes. The presence of ω 1 is an indication of the secondary instability and the formation of secondary instability has been explained by a scenario similar to that observed in Langmuir cells in the ocean layer. Further, the analysis of the harmonics in time have also been performed. |
