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Frontal Instability

Fronts in the atmosphere or in the oceans are unstable, and distubances develop there. What shape of disturbances develop under what condition?

The basic state of the most simple frontal model is expressed by sole non-dimensional parameter (Ri). The wavenumber of the given disturbance is non-dimensionalized to Ro, and the problem is described by these two non-dimensional parameters.

The imaginary part of phase speed Ci of the fastest-growing (and partly the second fastest) mode for each combination of Ri and Ro.

Bird view

The dispersion relation (the relation between wavenumber and phase speed C) is as following figure (black lines indicate neutral modes and red lines unstable modes) :

There is also an animation wherein the parameter is swept from Ri=0.0 to 3.0.

Expressed by growth rate.