Asymptotic analysis of turbulent channel and boundary-layer flow

Abstract

Asymptotic expansion techniques are used, in the limit of large Reynolds number, to study the structure of fully turbulent shear layers. The relevant Reynolds number characterizes the ratio of the local turbulent stress to the local laminar stress, so that a relatively thick outer defect layer, in which, to lowest order, there is a balance between turbulent stress and convection of momentum, may be distinguished from a relatively thin wall layer, in which, to lowest order, there is a balance between turbulent and laminar stresses. The two cases examined are channel (or pipe) flow and two-dimensional boundary-layer flow with an applied pressure gradient, upstream of any separation. Attention, for these two cases, is confined to the flow of incompressible constant property fluids. Closure is effected through the introduction of an eddy-viscosity model formulated with sufficient generality for most existing models to be special cases. Results are carried to higher orders of approximation to indicate what properties for the friction velocity, integral thicknesses, and velocity profiles, and what conditions for similarity are implied by current eddy-viscosity closures.

Turbulent flow on a planar moving belt and a rotating disk: modelling and comparisons

“…Next a structure for the turbulent boundary layer is proposed which leads to the boundary layer being split into two coupled regions. A structure similar to that used by Mellor (1972), Bush & Fendell (1972) and Neish & Smith (1988) for the flow past a fixed flat plate in an outer stream is found to lead to a contradiction. The resolution of this problem requires an enhanced boundary layer where the thickness must be taken to be significantly larger than for flows driven by an outer stream.…”

The turbulent boundary layer and wake of an aligned flat plate

“…The classical boundary layer for 0 < x < 1 has the structure indicated by Mellor [5] and Bush and Fendell [6], at large Reynolds numbers. It takes on a two-tiered form I, II (see Fig.…”

“…Notably, Mellor [5], Bush and Fendell [6] and Fendell [7] developed an asymptotic approach for the attached turbulent boundary-layer description assuming a rather general form for the turbulence closure consistent with a two-tiered boundary layer. This has been followed through, and extended significantly, by Melnik and his co-workers [8][9][10][11] for the examination of trailing-edge motions, interactive effects (see also Sykes [12]) and transonic conditions, while proposals for the structure of turbulent separation have been put forward by Sychev and Sychev [13] and Sychev [14] as discussed later in this section.…”

Feasible domain of Walker's unsteady wall-layer model for the velocity profile in turbulent flows

“…The time-mean structure of the flow in Walker et al (1989) is based on the classical two-layered asymptotic analyses (Yajnik (1970), Bush andFendell (1972), Mellor (1972)) of large Reynolds number turbulent boundary layer flow. Solutions are then developed in terms of two small parameters, R -1 and u * , where R denotes the Reynolds number based on representative external flow scales and…”