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Three-dimensional mathematical models are necessary to simulate wind driven circulations anddensity currents that occur in coastal waters, which are stratified by salinity and temperaturelayers resulting in significant vertical and lateral density gradients. The developed threedimensionalmathematical model is capable of computing the water levels and water particlevelocity distributions in three principal directions by solving the Navier–Stokes equations.Only two simplifying approximations are used in the model. First, it is assumed that the weightof the fluid balances the pressure, i.e. the hydrostatic pressure distribution assumption; andsecond, the density differences are neglected unless the differences are multiplied by thegravity, i.e. the Boussinesq approximation. Since the horizontal extent of the coastal sea ismuch larger than the vertical extent, the vertical component of the motion is much weakerthan the horizontal velocity [12]. If the flow is predominantly horizontal, and the verticalacceleration is small compared with the gravity acceleration, the equation of motion can bereduced to the simple hydrostatic law. Although the vertical acceleration is assumed to benegligible, the vertical velocity can be calculated from the equation of continuity.
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