Turbulent Boundary Layer

Abstract

The three-dimensional unsteady Navier-Stokes equations given in Appendix I also apply to turbulent flow if the values of dependent variables are understood as instantaneous values. A direct approach to solving the equations for turbulent flows is to solve them for specific boundary conditions and initial values that include time-dependent quantities. Mean values are needed in most practical cases, so an ensemble of solutions of time-dependent equations is required. Even for the most restricted cases, this approach, referred to as direct numerical simulation, becomes a difficult and extremely expensive computing problem because the unsteady eddy motions of turbulence appear over a wide range. The usual procedure is to average the equations rather than their solutions [77]. The averaged Navier-Stokes equations are also called Reynolds equations. This procedure is used here to study the turbulent boundary layer.