UNSTEADY VISCOUS-FLOW OVER IRREGULAR BOUNDARIES

Unsteady viscous flow over irregular and fractal walls is discussed, and flow generated by the longitudinal and transverse vibrations of an infinite period two-dimensional wall with cylindrical grooves is considered in detail. The behaviour of the Stokes layer and the functional dependence between the drag force and the frequency are illustrated in a broad band of frequencies for walls with sinusoidal corrugations and a family of walls with triangular asperities leading to fractal shapes. It is shown that, in the case of longitudinal oscillations, the drag force on a fractal wall with self-similar structure exhibits a power-law dependence on the frequency with an exponent that is related to the fractal dimension of the microstructure expressing the gain in surface area with increasing spatial resolution. Numerical evidence suggests that, in the case of transverse oscillations, the dissipative component of the drag force may show a power-law dependence on the frequency, but the exponent is not directly related to the geometry of the microstructure. The significance of these results on the behaviour of the drag force on walls with three-dimensional irregularities is discussed.