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Local energy generation in barotropic flows

TitleLocal energy generation in barotropic flows
Publication TypeArticolo su Rivista peer-reviewed
Year of Publication2002
AuthorsIacono, Roberto
JournalJournal of the Atmospheric Sciences
Volume59
Pagination2153-2163
ISSN00224928
Keywordsatmospheric dynamics, barotropic instability, Energy generation, Shear flow, Shear vectors, Vectors, Wave effects, Wave equations, zonal flow
Abstract

The local growth of disturbances to a steady, nondivergent shear flow is investigated in the context of the barotropic vorticity equation (BVE). A new expression for the instantaneous energy generation rate is derived by using a local coordinate frame defined by the directions parallel and perpendicular to the basic flow. The equilibrium information enters this expression through two scalar coefficients, which can be interpreted as local components of an "effective shear" vector S (S coincides with the shear vector for irrotational flows). A simple picture of local instability results: the magnitude of S gives the maximum possible energy growth rate for localized unstable disturbances, while its orientation determines the direction of maximum energy growth, which is given by the perpendicular to the bisector of the angle between S and the equilibrium velocity. This allows extension of the familiar "leaning against the shear" instability picture, developed for zonal currents, to generic, two-dimensional (2D), steady-state solutions of the BVE. Applications of the new approach to some simple basic flows of interest for atmospheric dynamics are discussed.

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URLhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-0036647006&partnerID=40&md5=537ec16a9aa4ebb86592d43f50f5cb62
Citation KeyIacono20022153