Non-linear hydrodynamic stability of oceanic flows |
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| Authors: | R Purini E Salusti |
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| Institution: | 1. IFA-CNR , Roma, Italy;2. INFN, Istituto di Fisica, Università , Roma, Italy |
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| Abstract: | Abstract In this paper an analytical method to study the hydrodynamic stability of simple barotropic, non-divergent flows is discussed. The method is based on the variational approach introduced by Arnold and derived from the Lyapunov stability criteria. In this context, the sufficient condition for the stability of a steady barotropic flow ψ(x,y) is obtained when dP(ψ)/dPψ = ψ, the derivative of the absolute vorticity P(ψ), is positive definite. In this case, we discuss the effect of higher derivatives dnP(ψ)/dψnψψ = ψ on the non-linear stability. Then we show that some classical examples of oceanic non-divergent flows (i.e. lee waves downstream an Island, steady flows through a Strait, the Fofonoff gyre) are stable to finite-amplitude perturbations. |
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| Keywords: | Barotropic flows stability topographic effects |
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