Cross-hatching: A consequence of differential deformation of a viscous solid

Abstract

The hypothesis, proposed by Probstein and Gold, that cross‐hatching results from the differential deformation of an inelastic material at its surface, has been used in this analysis. Wall pressure and wall shear stress perturbations leading to the deformation were calculated with the linearized small perturbation theory. The supersonic boundary layer was composed of an inviscid outer layer and a viscous sublayer. Both laminar and turbulent mean velocity and Mach number profiles were used in the calculation. In contrast to the work of Probstein and Gold the viscous sublayer was included and wall pressure perturbations were also considered. The essential result is the prediction of the pattern cant angle, which was not possible with the inviscid analysis. The theory qualitatively confirms the experimentally observed features of cross‐hatching, similarly seen by Probstein and Gold. For instance, for cross‐hatching to occur, the boundary layer must be supersonic and turbulent, whilst the inelastic body material must be of the Maxwell type. Theory and experiment also show that the pattern is charcterized by a cant angle equal to the local Mach angle, by a wavelength inversely proportional to the static pressure and directly proportional to the viscosity of the material.