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Singular Vectors and Time-Dependent Normal Modes of a Baroclinic Wave-Mean Oscillation

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  • Linear disturbance growth is studied in a quasigeostrophic baroclinic channel model with several thousand degrees of freedom. Disturbances to an unstable, nonlinear wave-mean oscillation are analyzed, allowing the comparison of singular vectors and time-dependent normal modes (Floquet vectors). Singular vectors characterize the transient growth of linear disturbances in a specified inner product over a specified time interval and, as such, they complement and are related to Lyapunov vectors, which characterize the asymptotic growth of linear disturbances. The relationship between singular vectors and Floquet vectors (the analog of Lyapunov vectors for time-periodic systems) is analyzed in the context of a nonlinear baroclinic wave-mean oscillation. It is found that the singular vectors divide into two dynamical classes that are related to those of the Floquet vectors. Singular vectors in the “wave dynamical” class are found to asymptotically approach constant linear combinations of Floquet vectors. The most rapidly decaying singular vectors project strongly onto the most rapidly decaying Floquet vectors. In contrast, the leading singular vectors project strongly onto the leading adjoint Floquet vectors. Examination of trajectories that are near the basic cycle show that the leading Floquet vectors are geometrically tangent to the local attractor while the leading initial singular vectors point off the local attractor. A method for recovering the leading Floquet vectors from a small number of singular vectors is additionally demonstrated.
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  • Wolfe, Christopher L., Roger M. Samelson, 2008: Singular Vectors and Time-Dependent Normal Modes of a Baroclinic Wave-Mean Oscillation. Journal of Atmospheric Sciences, 65(3), 875–894.
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  • 65
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  • 3
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  • The authors gratefully acknowledge the Office Naval Research, Grants N00014-98-1- 0813 and N00014-06-1-0369, Code 322 OM, for support of this work.
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