On the convergence of non-linear normal mode initialization methods

Abstract

Non-linear, normal mode initialization schemes are studied in a low order β-plane, shallow water model. In this model, Machenhauer's initialization scheme may diverge both due to linear advective terms and non-linear effects. Using more general methods to find non-linearily balanced states, convergence may be obtained and several possible balanced states can be found for a given meteorological field. Also, the effect of linearizing the model around a non-zero mean state and applying Machenhauer's method is investigated. Convergence is then more rapid and time integrations show an increased smoothness of the time evolution.