Viscous stratified flow past an object

Diffusion-driven flow occurs when an object with a sloping surface is immersed in a stratified fluid, both of which are stationary in a stable configuration. The influence of this flow is examined on slow vertical fluid motion moving past an object, particularly for a cylinder and a sphere. Analytical solutions for streamfunction and density fields are presented, for which the governing equations are derived using perturbation theory. It is found that the solutions violate far-field flow conditions in a region surrounding the object. This difficulty is similar to that encountered for the Stokes’ streamfunction in a homogeneous viscous flow. An analogous approach to the Oseen’s method is followed here by introducing an "outer region", in which the dynamical balances are slightly different. In this thesis, the "outer solutions" (Oseen-type solutions) for viscous stratified fluid motion around the cylinder are successfully derived using the Fourier transform method. On the other hand, the "inner solutions" (Stokes-type solutions) are derived using a standard approach to solving differential equations. Results show that the outer solutions not only satisfy the conditions at a large radius but also match with the inner solutions at a small radius, based on the matched asymptotic expansions principle. In the case of the sphere, the exact outer solutions based on the same approach appear to be unavailable, but the fundamentals of the outer flow are presented; for instance, the governing equations and the relevant boundary conditions. Despite the unavailability of the exact outer solutions for the sphere, a numerical approach indicates that suitable outer solutions appear to exist. Previous studies have ignored the effect of the diffusion-driven flow on the viscous stratified flow past an object, but here the solutions reveal their relative importance in this parameter regime.