David J. Muraki

Assistant Professor, Mathematics Department

Department of Mathematics
Courant Institute of Mathematical Sciences
New York University

Mail Address
      251 Mercer St.
      New York, NY 10012, U.S.A.

Phones
      212.998.3307 (voice)   212.995.4121 (fax)

Email
      muraki@cims.nyu.edu

Applied Math II (spring 00)   
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An Interfacial Wave Treatment of Tropopause Dynamics

atmospheric cross-sections: tropopause waves

Revisiting Queney's Flow over Mesoscale Topography

The foundations for our understanding of wave generation by topography were established in studies of Queney (1947, 1948) for steady flow past a two-dimensional ridge. In this seminal work, the downstream radiation pattern was inferred from the dispersion characteristics of linear gravity waves. Queney's streamline figures, obtained by approximating a Fourier integral, are frequently reproduced as the canonical illustration of downstream topographic waves. For the case of constant stratification with f-plane rotation, we find there are significant differences in the near-ridge flow pattern upon comparing the original approximation (Queney 1948, Figure 3) with direct computation of the Fourier integral. Flow corrections in the near-field aloft and downslope regions will be presented in updated figures. These new figures are computed using a high-order numerical integration scheme which is especially designed to resolve the near-inertial singular waves. The implementation of these ideas to computing three-dimensional topographic wave flows will be discussed. Finally, a new analytical approximation suggests that an additional by-product of the topographic wave generation is a weak, near-inertial wave that is produced by backscattering from the downslope surface.

The figure below shows the displacement streamlines for steady flow over a mesoscale ridge as studied by Queney 1948. The Fourier integral solution has been computed using a high-accuracy quadrature and reveals subtle yet significant differences from Queney's original figure (see Gill's Atmosphere-Ocean Dynamics, p278). The incident flow is uniform in altitude and from the left.

Direct quadrature: isentropes

Steepest descent approximation: displacement streamlines , isentropes

Associated fields: buoyancy anomaly , vertical motion , across-ridge wind , along-ridge wind

Equivalent topography: surface plots

An sQG Travelling Dipole

The figure below shows the surface streamlines (streamfunction in colour) for a steady travelling dipole within a surface QG model. The potential temperature is zero outside the circular streamline, so that this exact surface QG solution is derived in a manner typical of "modon" constructions.