Normal Mode Initialization for Shallow Water Flow Past a Mountain : Linear Aspects

Abstract

We have examined the shallow water flow initialized by the pseudo-secant method proposed by Rasch(1985). We develop his scheme for a regional model in the plane geometry, and investigate the solution to a mountain forcing in the shallow water equations. We find that this scheme gives the unphysical solution with fore-aft symmetry, which means the ingoing steady gravity wave from upwind to the mountain, in the super-critical flow, if the diffusion term is too small. In case of low mountain, comparing numerical solutions with the analytical one, we conclude that the above mentioned solution was given improperly by the wrong radiation condition for the gravity waves from the mountain. A new scheme is proposed so that the flow fields past mountain are retained. In the new scheme, to specify the radiation condition we insert a small imaginary, the value of which is determined by the resolution in the model wave number space, into the effective angular frequency. Moreover, we take into account the large contribution from the modes with small effective angular frequency.