Browsing by Author "Rakotoarisoa, Avotra Elie"

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    Incompressible flow with variations in density
    (Stellenbosch : Stellenbosch University, 2018-12) Rakotoarisoa, Avotra Elie; Diedericks, G. P. J.; Maritz, M. F.; Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences. Division Applied Mathematics.
    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 this ambiguity by investigating examples of incompressible flow with density that varies with pressure, temperature and salinity. In order to investigate incompressible flow with variations in density, the conditions of incompressibility that will simplify the continuity equation are determined by using scaling analysis. The Boussinesq approximation as well as the hydrostatic approximation is then applied to simplify the momentum equations of incompressible fluid flow with variations in density. Depth-averaging is also used to re-derive the shallow 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 and applied to solve some typical examples in order to illustrate the behaviour of the flow under the assumptions of incompressible flow with density that varies with temperature 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, and that the diffusion of heat and salt should be negligible. Next, the solution of the one-dimensional shallow water equations, using the stated numerical method, yields qualitatively expected results.