Interactions of Tollmien-Schlichting waves and Dean vortices. Comparison of direct numerical simulation and a weakly nonlinear theory

Direct numerical simulation is used to evaluate a weakly nonlinear theory describing the interaction of Tollmien-Schlichting waves with Dean vortices in curved channel flow. The theory and the simulation agree for certain combinations of parameters, but the two approaches give conflicting results for other combinations. Some possibilities for these discrepancies are discussed

Numerical experiments on the stability of controlled boundary layers

Nonlinear simulations are presented for instability and transition in parallel water boundary layers subjected to pressure gradient, suction, or heating control. In the nonlinear regime, finite amplitude, 2-D Tollmein-Schlichting waves grow faster than is predicted by linear theory. Moreover, this discrepancy is greatest in the case of heating control. Likewise, heating control is found to be the least effective in delaying secondary instabilities of both the fundamental and subharmonic type. Flow field details (including temperature profiles) are presented for both the uncontrolled boundary layer and the heated boundary layer

Multiple paths to subharmonic laminar breakdown in a boundary layer

Numerical simulations demonstrate that laminar breakdown in a boundary layer induced by the secondary instability of two-dimensional Tollmien-Schlichting waves to three-dimensional subharmonic disturbances need not take the conventional lambda vortex/high-shear layer path

Algorithm implementation on the Navier-Stokes computer

The Navier-Stokes Computer is a multi-purpose parallel-processing supercomputer which is currently under development at Princeton University. It consists of multiple local memory parallel processors, called Nodes, which are interconnected in a hypercube network. Details of the procedures involved in implementing an algorithm on the Navier-Stokes computer are presented. The particular finite difference algorithm considered in this analysis was developed for simulation of laminar-turbulent transition in wall bounded shear flows. Projected timing results for implementing this algorithm indicate that operation rates in excess of 42 GFLOPS are feasible on a 128 Node machine

Numerical simulation of channel flow transition, resolution requirements and structure of the hairpin vortex

Three-dimensional, nonlinear numerical simulations are presented for the K-type and H-type transitions for channel flow. There are two objectives. The first is to establish firmly the resolution requirements for the various stages in the transition process. Comparisons between calculations on various grids suggest a set of guidelines for maintaining a physically meaningful calculation. The second objective is to map out the structure of the hairpin vortices which arise in K-type and H-type transitions in channel flow, to the latest stage currently feasible. Flow field details are presented for both a subcritical Reynolds number of 1500 and a supercritical Reynolds number of 8000. The diagnostics include illustrations of the vertical shear, streamwise and spanwise vorticity, helicity, vortex stretching, and vortex diffusion fields

A weakly nonlinear theory for wave-vortex interactions in curved channel flow

A weakly nonlinear theory is developed to study the interaction of Tollmien-Schlichting (TS) waves and Dean vortices in curved channel flow. The predictions obtained from the theory agree well with results obtained from direct numerical simulations of curved channel flow, especially for low amplitude disturbances. Some discrepancies in the results of a previous theory with direct numerical simulations are resolved

TS - Dean interactions in curved channel flow

A weakly nonlinear theory is developed to study the interaction of TS waves and Dean vortices in curved channel flow. The prediction obtained from the theory agree well with results obtained from direct numerical simulations of curved channel flow, especially for low amplitude disturbances. At low Reynolds numbers the wave interaction is generally stabilizing to both disturbances, though as the Reynolds number increases, many linearly unstable TS waves are further destabilized by the presence of Dean vortices

On the nonlinear interaction of Gortler vortices and Tollmien-Schlichting waves in curved channel flows at finite Reynolds numbers

The flow in a two-dimensional curved channel driven by an azimuthal pressure gradient can become linearly unstable due to axisymmetric perturbations and/or nonaxisymmetric perturbations depending on the curvature of the channel and the Reynolds number. For a particular small value of curvature, the critical neighborhood of this curvature value and critical Reynolds number, nonlinear interactions occur between these perturbations. The Stuart-Watson approach is used to derive two coupled Landau equations for the amplitudes of these perturbations. The stability of the various possible states of these perturbations is shown through bifurcation diagrams. Emphasis is given to those cases which have relevance to external flows

Discussion of the potential and limitations of direct and large-eddy simulations

The full text of the discussion paper presented at the Whither Turbulence Workshop on the potential and limitations of direct and large-eddy simulations is provided. Particular emphasis is placed on discussing the role of numerics and mathematical theory in direct simulations of both compressible and incompressible flows. A variety of unresolved issues with large-eddy simulations such as their implementation in high-order finite difference codes, problems with defiltering, and modifications to accommodate integrations to solid boundaries are elaborated on. These as well as other points are discussed in detail along with the authors' views concerning the prospects for future research

Spectral methods for CFD

One of the objectives of these notes is to provide a basic introduction to spectral methods with a particular emphasis on applications to computational fluid dynamics. Another objective is to summarize some of the most important developments in spectral methods in the last two years. The fundamentals of spectral methods for simple problems will be covered in depth, and the essential elements of several fluid dynamical applications will be sketched