Lyapunov, Floquet, and singular vectors for baroclinic waves

Lyapunov, Floquet, and singular vectors for baroclinic waves

The dynamics of the growth of linear disturbances to a chaotic basic state is analyzed in an asymptotic model of weakly nonlinear, baroclinic wave-mean interaction. In this model, an ordinary differential equation for the wave amplitude is coupled to a partial differential equation for the zonal flow correction. The leading Lyapunov vector is nearly parallel to the leading Floquet vector φ1 of ...

On the Singular Vectors of the Generalized Lyapunov Operator

In this paper, we study the largest and the smallest singular vectors of the generalized Lyapunov operator. For real matrices A,B with order n , we prove that max‖X‖F =1 ‖AXBT + BXA‖F is achieved by a symmetric matrix for n 3 and give a counterexample for order n = 4 . We also prove that min‖X‖F =1 ‖AXBT +BXA‖F is achieved by a symmetric matrix for n 2 and give a counterexample for order n = 3 ...

Physical Simulation of Baroclinic Waves and Vortices in the Atmosphere

Nonlinear Generalization of Singular Vectors: Behavior in a Baroclinic Unstable Flow

Singular vector (SV) analysis has proved to be helpful in understanding the linear instability properties of various types of flows. SVs are the perturbations with the largest amplification rate over a given time interval when linearizing the equations of a model along a particular solution. However, the linear approximation necessary to derive SVs has strong limitations and does not take into ...

Singular Continuous Floquet Operator for Systems with Increasing Gaps

Consider the Floquet operator of a time independent quantum system, periodically perturbed by a rank one kick, acting on a separable Hilbert space: e0 e |φ〉〈φ| where T and κ are the period and the coupling constant respectively. Assume the spectrum of the self adjoint operator H0 is pure point, simple, bounded from below and the gaps between the eigenvalues (λn) grow like: λn+1 − λn ∼ Cn with d...