Revisiting the slow manifold of the Lorenz-Krishnamurthy quintet

Abstract

The slow-manifold for the Lorenz-Krishnamurthy model has been studied. By minimizing the evolution rate we ¯nd that the analytical functions for the fast variables are devoid of high frequency oscillations. However upon solving this model with initial values of the fast variables obtained from the analytical functions, the LK model exhibits high frequency oscillations. Upon using the time derivatives of the analytic functions for computing the evolution of fast variables, we ¯nd a slow-manifold in the neighbourhood of the LK model. Minimization of evolution rate does not guarantee the invariance of the manifold. Using a locally linear approximate reduction scheme, the invariance can be maintained. However, the solutions so obtained do develop high frequency oscillations. The onset of these high frequency oscillations is delayed vis-a-vis other previous studies. These methods have potential to be used in improving the predictions of weather systems.