Kwasu Function: A Closed-Form Analytical Solution to the Complete Three-Dimensional Unsteady Compressible Navier-Stokes Equation

Abstract

An attempt is made to re ne the classical potential theory of the flow over a circular cylinder by introducing a viscous sink-source-vortex sheet on the surface of the cylinder. These singularities introduced into the flow are modeled as concentric at every location. The vortices are modeled as variations of Lamb-Oseen, Batchelor and Burgers vortices and analytic expressions for their strengths and those of the sinks/sources are obtained from the classical theory. These are employed to obtain a viscous potential function named the Kwasu function which provides a closed form analytic solution to the complete three dimensional unsteady compressible Navier-Stokes equation. Preliminary results of the work show that the theory presented captures important features of a bluff body flow includin flow separation, wake formation, vortex shedding as well as compressibilty effects. The condition at a viscous wall is shown to be transient from slip towards a complete no-slip for a steady freestream flow. It is the hope that the present theory will shed more light on the important phenomenon of turbulence in planned future work in which quantitative analysis of the theory will be carried out.