The nature of viscous and wall effects: options for modelling

The turbulence models considered in earlier chapters were based on the assumption that the turbulent Reynolds numbers were high enough everywhere to permit the neglect of viscous effects. Thus, they are not applicable to flows with a low bulk Reynolds number (where the effects of viscosity may permeate the whole flow) or to the viscosity-affected regions adjacent to solid walls (commonly referred to as the viscous sublayer and buffer regions but which we shall normally collectively refer to as the viscous region) which always exist on a smooth wall irrespective of how high the bulk Reynolds number may be. In other words, while at high Reynolds number, viscous effects on the energy-containing turbulent motions are indeed negligible throughout most of the flow, the condition of no-slip at solid interfaces always ensures that, in the immediate vicinity of a wall, viscous contributions will be influential, perhaps dominant. Figure 6.1 shows the typical ‘layered’ composition for a near-wall turbulent flow (though with an expanded scale for the near-wall region) as found in a constant-pressure boundary layer, channel or pipe flow. Although the thickness of this viscosity-affected zone is usually two or more orders of magnitude less than the overall width of the flow (and decreases as the Reynolds number increases), its effects extend over the whole flow field since, typically, half of the velocity change from the wall to the free stream occurs in this region.

Because viscosity dampens velocity fluctuations equally in all directions, one may argue that viscosity has a ‘scalar’ effect. However, turbulence in the proximity of a solid wall or a phase interface is also subjected to non-viscous damping arising from the impermeability of the wall and the consequent reflection of pressure fluctuations. This ‘wall-blocking’ effect, which is also felt outside the viscous layer well into the fully turbulent wall region, directly dampens the velocity fluctuations in the wall-normal direction and thus it has a ‘vector’ character. A good illustration of this effect is the reduction of the surface-normal velocity fluctuations that has been observed in flow regions close to a phase interface, where there are no viscous effects, for example the DNS of Perot and Moin (1995).