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The Boussinesq Approximation simplifies the Navier-Stokes Equations for Fluid Flow by assuming that Density Variations are negligible except where they appear in Buoyancy terms, making it useful for modeling Incompressible flows with Small temperature differences. This approximation is particularly valuable in geophysical and Environmental fluid dynamics, such as oceanography and Atmospheric Science, where it helps to model the effects of Buoyancy-driven flows without solving the full Compressible equations.
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