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November  2006, 6(6): 1403-1416. doi: 10.3934/dcdsb.2006.6.1403

Revisiting the slow manifold of the Lorenz-Krishnamurthy quintet

M. Phani Sudheer 1, , Ravi S. Nanjundiah 2, and  A. S. Vasudeva Murthy 3,

1. 

Department of Mechanical Engineering, National Institute of Technology Karnataka, Surathkal, India
2. 

Center for Atmospheric and Oceanic Sciences, Indian Institute of Science, Bangalore 560 012, India
3. 

TIFR Centre, Indian Institute of Science, Bangalore 560 012, India

Received  August 2005 Revised  March 2006 Published  August 2006

The slow-manifold for the Lorenz-Krishnamurthy model has been studied. By minimizing the evolution rate we find 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 find 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.
Keywords: predictability., minimization of evolution rate, invariant slow-manifold.
Mathematics Subject Classification: Primary: 37D10; Secondary: 35B4.
Citation: M. Phani Sudheer, Ravi S. Nanjundiah, A. S. Vasudeva Murthy. Revisiting the slow manifold of the Lorenz-Krishnamurthy quintet. Discrete & Continuous Dynamical Systems - B, 2006, 6 (6) : 1403-1416. doi: 10.3934/dcdsb.2006.6.1403
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