A theory for the viscous sublayer of a turbulent flow

Abstract

The laminar sublayer and ‘transition zone’ are shown to be the region where the turbulent velocity fluctuations are directly dissipated by viscosity. A simplified linearized from of the equations of motion for the turbulent fluctuations is used to describe the turbulent field between the wall and the fully turbulent part of the flow. The mean flow in the viscous sublayer and the turbulent field outside the sublayer are assumed to be known from experiment. The thickness of the sublayer arises naturally in the theory and is directly analogous to the inner viscous region for the fluctuations in a laminar flow. It is shown that the large-scale fluctuations containing most of the turbulent energy are convected downstream with a velocity characteristic of the middle of the boundary layer. Thus Taylor's hypothesis does not apply to these large-scale fluctuations near the wall. The convective velocity found in the measurements of pressure fluctuations at the boundaries of turbulent flows is in accord with the theory. Calculations are given for the energy spectra and u′ fluctuation level in the sublayer and other aspects of the fluctuation field are discussed. The linear pressure fluctuation field at the edge of the sublayer is calculated and found to be much larger than the nonlinear field. Examining the effect of strong free-stream turbulence on laminar boundary-layer transition, it appears that the physical model underlying Taylor's parameter is incorrect.