Incompressible flow with variations in density

[摘要] ENGLISH ABSTRACT : This study involves the investigation of incompressible flow with variable density.The fact that variable density does not necessarily imply that the flow is compressible, may require some clarification. An attempt is made in this thesis to clarify thisambiguity by investigating examples of incompressible flow with density that varieswith pressure, temperature and salinity.In order to investigate incompressible flow with variations in density, the conditionsof incompressibility that will simplify the continuity equation are determined byusing scaling analysis. The Boussinesq approximation as well as the hydrostatic approximation is then applied to simplify the momentum equations of incompressiblefluid flow with variations in density. Depth-averaging is also used to re-derive theshallow water equations, also with variable density.A numerical method for solving the one-dimensional shallow water equations (suggested by Benkaldoun and Saiëd) is then reviewed. It is also implemented andapplied to solve some typical examples in order to illustrate the behaviour of theflow under the assumptions of incompressible flow with density that varies withtemperature and salinity.The main results of this study can be summarized as follows: The scaling analysis serves to explain in a systematic way some conditions of incompressible flow,such as that the speed of sound must be large compared to the flow velocity, andthat the diffusion of heat and salt should be negligible. Next, the solution of theone-dimensional shallow water equations, using the stated numerical method, yieldsqualitatively expected results.

[发布机构] Stellenbosch University