Analytical investigations of horizontal meso-scale momentum equations with Newtonian nudging

This study presents an analytical investigation of the local behaviour of the solution to a mesoscale model with Newtonian nudging when observed winds are time varying. The analysis examines each Fourier component of the time series of observed winds. Unlike the case with a constant observed wind, the nudged wind vector does not asymptotically approach the observed wind. In response to sinusoidal oscillation of the observed wind, the nudged wind vector is always on a half circle connecting the vector ends of the observed and un-nudged modelled winds. When nudging parameter alpha --> 0, the nudged wind vector approaches the un-nudged wind; when alpha --> infinity, the nudged wind vector approaches the observed wind. For commonly used values of nudging parameter alpha, the modelled wind field always carries errors. A target nudging scheme is devised in this study in order to ensure the model result is identical to observed winds with sinusoidal oscillation. Investigation shows that such a target wind exists for a finite value of alpha, and the magnitude of the target-nudging term is about the same as that of a normal nudging term if alpha similar to f similar to omega where f is the Coriolis parameter and omega is the frequency of the wind oscillation.