Survey of planetary‐scale traveling waves: The state of theory and observations

Abstract

There exists a considerable body of evidence relating the gravest‐scale transient components of planetary wave activity (periods shorter than a couple of weeks) to the eigenmodes of an unbounded isothermal atmosphere in uniform rotation. The latter, termed “Lamb modes,” have horizontal structures of Hough functions, with a 10‐km equivalent depth, and the external vertical structure of a Lamb wave. They asymptote, for large total wave number, to normal modes of the nondivergent barotropic vorticity equation. Phase speeds of the gravest modes, however, are significantly retarded by divergence. A historical account of the development of large‐scale traveling waves is presented, culminating with the emergence of global observations and the identification of several modes in atmospheric data. Theoretical ingredients of the simple normal mode problem are reviewed. The relationship between these features and extratropical transients is developed via the notion of a “planetary wave spectrum.” Influences of realistic distributions of dissipation and refractive properties are discussed for a prototypical mode. Calculations for several of the gravest modes are then presented for typical climatological configurations. For all of these the simple eigenstructures are largely preserved at tropospheric levels. Recent observational evidence is collected from global satellite and conventional meteorological analyses and compared with theoretical concepts. An overview of realistic considerations, requisite for an understanding of “particular realizations” of these features, is developed. Response to localized, transient forcing is shown to consist not of any single mode, but rather of a spectrum of normal modes. For sufficiently large amplitudes, Lamb modes can give rise to vacillations in eddy flux fields via modulation of the stationary waves. These, in turn, may be accompanied by vacillations in the basic stream.