Simple atmospheric model produces hurricanelike vortices
Simple atmospheric model produces hurricanelike vortices lead image
Fifty years ago, Robert Kraichnan showed that small whirling eddies in a 2-D model can sometimes feed larger ones, suggesting to us the idea that, for example, small eddies can produce hurricane-sized disturbances. Since that time, much debate has ensued about whether this can also occur in 3-D. In a special issue of the Physics of Fluids, commemorating the Kraichnan paper, Swedish investigators show that a simple 2-D model that behaves more like a 3-D one can explain motions in a range corresponding to atmospheric wavelengths between 2 and 500 kilometers.
The model, constructed to mimic geophysical turbulence, contains a scalar playing the role of potential temperature, and consists of kinetic (KE) and available potential energy (APE) terms. The KE term is quadratic in the velocity, while APE is quadratic in the scalar. The equations of motion contain an exchange term that allows a velocity field to develop when the scalar is forced.
Numerical simulations with this model reveal an inverse energy cascade, in which small eddies are amplified to produce larger ones. Their results also show that the motions observed by aircraft in the Kolmogorov-like k−5/3 wave number spectrum range, where turbulence dominates, occur by a forward energy cascade, more like that expected in 3-D systems.
The assumptions made in constructing this model are consistent with atmospheric dynamics, where the velocity field is dominated by large scale rotational motions. Significantly, in contrast to other 2-D geophysical turbulence models, this model does not produce any shocks, or strong discontinuities in the wave field. The authors did observe the formation of vortices, strong centers of high wave activity that follow the organization of vortex filaments. Future work will further explore the model and make comparisons to atmospheric data collected from commercial aircraft.
Source: “A two-dimensional toy model for geophysical turbulence,” by Erik Lindborg and Ashwin Vishnu Mohanan, Physics of Fluids (2017). The article can be accessed at https://doi.org/10.1063/1.4985990 .
