Researchers in Michigan and Massachusetts conducted a broad parameter sweep of a simple model for large-scale oceanic and atmospheric dynamics, investigating wavenumber-frequency spectra for a variety of flow regimes. They present their findings in Physics of Fluids.

The researchers numerically simulated the single-layer shallow-water quasi-geostrophic equation on the beta-plane. They varied three parameters: the deformation radius (Ld), the narrow-band forcing wavenumber (kf), and the meridional gradient of the Coriolis parameter (β).

Notably, they discovered that a nondispersive line (NDL) forms in zonal wavenumber-frequency spectra for a wide range of parameters. The NDL not only appears in simulations with westward propagating vortices, as expected, but also in all simulations with meandering jets. The implication is that the meandering jets also propagate westward roughly uniformly.

The authors systematically investigated wavenumber-frequency spectra for three flow regimes determined by a single nondimensional parameter γβ. Moderately low values of γβ correspond to westward propagating vortices and an NDL in zonal wavenumber-frequency spectra. Moderately high and very high values of γβ correspond to westward propagating meandering jets with or without background vortices and an NDL in zonal wavenumber-frequency spectra. Two other dispersion relations corresponding to linear waves on a zonal background flow appear at moderately high and very high γβ.

In their paper, the authors state that their model and parameter choices are relevant to the Earth’s oceans and atmosphere as well as the atmospheres of the gas giants and add that “it would be interesting to know whether the NDL also persists when γβ is increased beyond its threshold for jet formation in a two-layer or more realistic ocean model.”

Source: “Wavenumber-frequency analysis of single-layer shallow-water beta-plane quasi-geostrophic turbulence,” by A. J. Morten, B. K. Arbic, and G. R. Flierl, Physics of Fluids (2017). The article can be accessed at