Shallow-Water Modelling of the Atmospheric Circulation Regimes of Brown Dwarfs and their Observable Features

Observations of time-varying thermal emission from brown dwarfs suggest that they have large-scale atmospheric circulation. The magnitude of this variability ranges from a few percent to tens of percent, implying a range of sizes of atmospheric perturbations. Periodograms of phase curves of the thermal emission reveal a range of peaks with different periods and widths, suggesting different atmospheric flow speeds and directions. This implies a variety of atmospheric circulations in the different brown dwarfs observed to date, but there is no general theoretical understanding of the circulation regimes these objects can support, and the resulting sizes and velocities of their atmospheric features. We therefore use an idealised two-dimensional shallow-water model of a brown dwarf atmosphere to understand their potential large-scale circulation regimes. We non-dimensionalise the model to reduce the number of input parameters to two non-dimensional numbers: the thermal Rossby number and the non-dimensional radiative timescale. This allows us to define a parameter space that bounds the entire range of brown dwarf behaviour possible in our model. We analyse the resulting height, velocity, and potential vorticity fields in this parameter space, and simulate observed phase curve and periodograms for comparison with real observations. We use our results to qualitatively define four circulation regimes, which we hope will be useful for interpreting observations and for guiding simulations with more detailed physical models.