An efficient compressible nonhydrostatic ocean model. Part I: eigenvalue analysis

Abstract A single parameter α >>1 is introduced to the Modified Continuity Equation (MCE). The eigenvalues derived from the linearized equations show this modification significantly slows and damps acoustic waves, while neither altering the equation of state nor affecting the amplification or propagation speed of internal gravity waves. The MCE preserves the realistic property of gravity waves while relaxes time-step constraints imposed by acoustic waves, where the speed reduced to 1/ $$\sqrt \alpha$$ of that in the unmodified acoustic waves.