11th Conference on Mesoscale Processes


Non-modal growths of symmetric perturbations produced by paired normal modes

Qin Xu, NOAA/NSSL, Norman, OK

A complete set of normal modes is obtained for symmetric perturbations in a layer of vertically sheared basic flow. The modes exist in pairs and can be classified into three types: paired growing and decaying modes, paired slowly propagating modes, and paired fast propagating modes. For a growing (or decaying mode), the cross-band vertical circulation is tilted between the absolute-momentum surface (M-surface) and isentropic surface (B-surface) of the basic state, so the growth (or decay) of the mode is caused by the positive (negative) feedback of the inertial and buoyancy perturbation forces to the cross-band motions. For a slowly propagating mode, the cross-band circulation is tilted more slantwise than the M-surface and B-surface, so the mode propagation is driven by the inertial restoring force in the forward direction but retarded by the buoyancy restoring force in the backward direction. For a fast propagating mode, the cross-band circulation is tilted in the opposite direction with respect to the M-surface and B-surface, so the mode propagation is driven by the inertial and buoyancy restoring forces both in the forward direction. The cross-band velocity component modes are found to be orthogonal between different pairs, but the full-component modes are non-orthogonal (measured by the inner-product associated with the perturbation energy). Within each pair, the two modes have the same pattern in each component field but opposite polarization relationships between the cross-band velocity and the remaining component fields. Thus, large non-modal energy growths can be produced by paired normal modes. Four types of non-modal growths are identified based on their physical mechanisms. The detailed results will be presented at the conference.

extended abstract  Extended Abstract (1.1M)

wrf recording  Recorded presentation

Session 6M, Idealized Modeling Studies
Friday, 28 October 2005, 10:30 AM-12:45 PM, Alvarado GH

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