Table of contents

Discussed are asymptotic aspects of the three characteristic functions in the nonstationary theory of a flat-plate aerofoil, i.e. the Wagner function for impulsive start, the Theodorsen function for oscillatory motion, and the Küssner function for an aerofoil entering a sharp-edged gust.

The effect of temperature-dependent viscosity on thermohaline convection in a Bousinesq fluid saturating an anisotropic porous medium is investigated, taking into account the effect of the process of thermal diffusion which is a cross-diffusion phenomenon (Soret effect). The variation in viscosity has mixed results in the setting up of convection currents, either by delaying or advancing it. This depends on various significant factors, namely, (i) the mode by which convection is encouraged to set in, whether stationary or oscillatory, (ii) the magnitude of the Soret parameter and (iii) the anisotropy parameter of the Soret effect.

All numerical, and some experimental studies of merging of two-dimensional vortex patches point at the existence of a critical initial distance of separation below which merging occurs and above which it does not. Some other laboratory experiments, however, report no such marked sensitivity of merging behaviour on the initial distance of separation. We study the effects of noise, which is one of the possible causes of the above mentioned difference, on vortex merging. We find that noise accelerates merging, and the time needed for merging decreases nearly linearly with increasing noise for high noise levels. However, the level of noise required for merging within the advection time scale is higher than what is usually found in "clean" wind tunnels or water tanks, and thus the presence of noise in laboratories is not the sole cause of the above difference.

The classical Dean problem is modified by letting the radius of curvature of the channel and the channel thickness be functions of a slow variable S = δx. By taking Taylor-Dean disturbance theory to O(δ^1/2), modifications to the spatial growth rate of the local problem are obtained. These are studied for three examples and it is found that divergence of the channel is destabilizing and convergence is stabilizing.

The unsteady axisymmetric case of a three-dimensional stagnation flow is investigated. The incompressible potential flow far away from the stagnation point oscillates about a constant mean value. Using perturbation methods, an analytical solution of the problem is obtained for the extreme cases of low and high oscillation frequencies.