The hydrodynamic stability of boundary-layer flow over a class of anisotropic compliant walls

Abstract

This paper examines the linear stability of zero-pressure-gradient boundary-layer flow over a class of anisotropically responding compliant walls. The anisotropic wall behaviour is derived from a material anisotropy which is characterized by relatively high tensile and compressive strength along a certain direction, termed the fibre axis. When the material stiffness along the fibre axis is sufficiently high, the resulting correlation between the horizontal and the vertical components of wall displacement induces at the flow–wall interface a Reynolds shear stress of a sign that is predetermined by the angle with which the fibre axis makes with the direction of the flow. The notion that anisotropic surface response could be employed to produce turbulent Reynolds shear stresses of predetermined sign at a surface was first explored by Grosskreutz (1971) in an experimental study on turbulent drag reduction. The present paper examines the implications of this interesting idea in the context of two-dimensional flow stability over anisotropic compliant walls. The study covers single- and two-layer compliant walls using the methodology described in Yeo (1988). The effects of wall anisotropy, as determined by the orientation of the fibre axis and the material stiffness along the fibre axis, on flow stability are examined for a variety of walls. The potential of some anisotropic compliant walls for delaying laminar–turbulent transition is investigated, and the contribution of the anisotropy to transition delay is appraised.