THREE-DIMENSIONAL STRATIFIED FLUIDS

THE PROPOSED RESEARCH HAS THE GENERAL OBJECTIVE OF CREATING INNOVATIVE NEW NUMERICAL ENGINEERING TOOLS FOR SOLVING THREE-DIMENSIONAL STRATIFIED FLOWS CONTAINING HYDRAULIC JUMPS. THE PROPOSED NUMERICAL TECHNIQUE IS BASED ON A MULTILAYER MODEL CONSISTING OF N HORIZONTAL, HOMOGENEOUS LAYERS WHICH IS USED TO APPROXIMATE STEADY, STRATIFIED, INCOMPRESSIBLE FLOWS UNDER THE ASSUMPTION OF HYDROSTATIC BALANCE. OUR TREATMENT OF FLOW DISCONTINUITIES IS BASED ON THE WELL-KNOWN ANALOGY BETWEEN CLASSICAL SHALLOW WATER HYDRAULICS AND STEADY, TWO-DIMENSIONAL, COMPRESSIBLE GAS DYNAMICS. A FINITE DIFFERENCE METHOD, ADAPTED FROM STANDARD GAS DYNAMICS NUMERICAL TECHNIQUES, EMPLOYING A SECOND ORDER PREDICTOR-CORRECTOR SCHEME FOR SPATIAL DERIVATIVES WHICH AUTOMATICALLY ADAPTS TO THE LOCAL PROPERTIES OF THE GOVERNING DIFFERENTIAL EQUATIONS WILL BE USED. TIME DERIVATIVES WILL BE APPROXIMATED USING CERTAIN CHARACTERISTIC FORMS OF THE GOVERNING EQUATIONS. FLOW DISCONTINUITIES WILL BE AUTOMATICALLY DETECTED AND TRACKED USING RIEMANN INVARIANTS FOR DETECTION AND THE RANKINE-HUGONIOT CONDITIONS FOR TRACKING. INTENDED APPLICATIONS INCLUDE SMALL-SCALE GEOPHYSICAL PHENOMENA SUCH AS WINDS IN THREE-DIMENSIONAL VALLEY-RIDGE SYSTEMS, OCEANIC CURRENTS AROUND ISOLATED ISLANDS OR SEA MOUNTS, ETC. EMPHASIS WILL BE PLACED ON APPLICABILITY AND EFFICIENCY, WITH A PRIMARY GOAL OF DEVELOPING SOUND NUMERICAL PREDICTIVE TOOLS APPLICABLE TO REALISTIC GEOPHYSICAL FLOW PROBLEMS.