Eady Edge Waves and Rapid Development

H. C. Davies Institute for Atmospheric Physics, ETH Zurich, Switzerland

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C. H. Bishop Department of Meteorology, University of Reading, Reading, England

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Abstract

Perturbations of the classical Eady model are treated in terms of the system's two intrinsic baroclinic edge waves. This provides a simple quantitative example of the wave coupling interpretation of quasigeostrophic instability and a compact framework for examining the rudiments of upper level–lower level dynamical interaction.

The reformulation consolidates and extends a series of earlier theoretical results: the existence of transient growth at wavenumbers beyond the Eady cutoff scale, the disparity between different measures of the maximum instantaneous growth rate with the highest values being associated with thermal (pressure) development at large (small) wavelengths, the existence of maximum instantaneous thermal growth rates substantially exceeding that of the Eady normal modes, and the vertical alignment of the couplet most favorable for initial rapid development–quadrature phase of the thermal (pressure) components for optimum thermal (pressure) growth.

There is also diversity in the finite time evolution of couplets. Short wavelength couplets undergo a periodic temporal development with comparatively mild amplitude changes. Longer-scale couplets asymptote toward the counterpart Eady normal mode. The latter achieve maximum thermal growth in a stipulated time if the relative phase of the couplet transits symmetrically through the quadrature configuration, and the fastest growing couplet can typically sustain a thermal amplitude doubling in ∼6 hours and a fivefold increase in ∼24 hours. During such development the eastward thermal slope of the very long (intermediate) scale couplets become less (more) inclined to the vertical.

It is further shown that a coherent packet of edge wave couplets can evolve rapidly (∼1 day) from a suitably shaped initial disturbance composed predominantly of either ultralong or intermediate-scale waves. The vertical structure of the emerging intermediate-scale packet is akin to that of observed atmospheric developments.

The edge wave formulation is also used to explore the effect of interior PV perturbations. Consideration of the influence of an idealized, but elemental, potential vorticity distribution upon a surface edge wave leads to inferences regarding the cyclogenetic potential of certain atmospheric flow structures.

Abstract

Perturbations of the classical Eady model are treated in terms of the system's two intrinsic baroclinic edge waves. This provides a simple quantitative example of the wave coupling interpretation of quasigeostrophic instability and a compact framework for examining the rudiments of upper level–lower level dynamical interaction.

The reformulation consolidates and extends a series of earlier theoretical results: the existence of transient growth at wavenumbers beyond the Eady cutoff scale, the disparity between different measures of the maximum instantaneous growth rate with the highest values being associated with thermal (pressure) development at large (small) wavelengths, the existence of maximum instantaneous thermal growth rates substantially exceeding that of the Eady normal modes, and the vertical alignment of the couplet most favorable for initial rapid development–quadrature phase of the thermal (pressure) components for optimum thermal (pressure) growth.

There is also diversity in the finite time evolution of couplets. Short wavelength couplets undergo a periodic temporal development with comparatively mild amplitude changes. Longer-scale couplets asymptote toward the counterpart Eady normal mode. The latter achieve maximum thermal growth in a stipulated time if the relative phase of the couplet transits symmetrically through the quadrature configuration, and the fastest growing couplet can typically sustain a thermal amplitude doubling in ∼6 hours and a fivefold increase in ∼24 hours. During such development the eastward thermal slope of the very long (intermediate) scale couplets become less (more) inclined to the vertical.

It is further shown that a coherent packet of edge wave couplets can evolve rapidly (∼1 day) from a suitably shaped initial disturbance composed predominantly of either ultralong or intermediate-scale waves. The vertical structure of the emerging intermediate-scale packet is akin to that of observed atmospheric developments.

The edge wave formulation is also used to explore the effect of interior PV perturbations. Consideration of the influence of an idealized, but elemental, potential vorticity distribution upon a surface edge wave leads to inferences regarding the cyclogenetic potential of certain atmospheric flow structures.

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