Wavenumber transition and wavenumber vacillation in Eady‐type baroclinic flows

Abstract

AbstractWavenumber transition and wavenumber vacillation are studied numerically in a ‘maximum simplification’ model of the Eady type with uneven Ekman dissipation. The spectral wave solution contains three waves having adjacent zonal wavenumbers and the gravest meridional mode. The model only allows for wave‐mean‐flow interaction.As the stratification parameter decreases away from the upper symmetric flow, we observe that baroclinic forcing increases faster than dissipation, implying the prevalence of a higher wave energy state. This state is realized by an increase in wave amplitude, number of temporal and/or spatial degrees of freedom, or dominant wavenumber. The first two occur first, but for small enough stratification, the flow transits to a higher wavenumber in order to realize the increased energy.Wavenumber vacillation is a flow regime observed at some parameter settings when the flow has at least two spatial and three temporal degrees of freedom. This regime is usually found in the region of parameter space where wavenumber transitions occur as parameters change.The balance between baroclinic forcing and damping adjusted by wave‐mean‐flow interaction seems to be a basic mechanism for wavenumber transition and wavenumber vacillation. Wave‐wave interaction is not necessary for such phenomena to exist.