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Abstract
A modelling system is described that generates and runs models of short waves of any form (periodic or irregular), with any desired physically realistic current field over any given bathymetry. As this system constitutes the eighth version of the general System 21, “Jupiter”, described in an earlier contribution, it is called the “Mark 8”. The system-generated models are based upon Boussinesq equations, in which the vertical velocity is supposed to increase linearly from zero at the bed to a maximum magnitude at the surface, in two independent (horizontal) space variables and time. The Boussinesq equations are formulated as mass and momentum conservation laws while, by virtue of the high order of accuracy of the difference approximations, there is very little numerical energy falsification. This formulation also appears to provide genuine weak solutions, for correctly simulating breaking waves, and thus assures the correct simulation of wave thrusts, or radiation stresses, and associated longshore currents.
The System has been tested against analytical results in one and two dimensions and also against physical model tests, for all its main capabilities. In all cases, the agreement of the System model results with the analytical and physical results are satisfactory. The System is already being applied in engineering practice. A discussion is presented of future applications of the System to ship motion simulations, to sediment transport computations and also to more efficient nearly-horizontal flow computations.
