Dynamics of thin jets generated by temperature fronts

The path equations are derived to describe the nonlinear evolution of thin jets generated by temperature fronts. An approximate approach is based on the thermal rotating shallow-water model that accounts for the effect of the temperature gradient and uses the variational principle of least action. The dynamics of jets is shown to be effectively described by a nonlinear system of two $(1+1)$-dimensional partial differential equations. Particular solutions are found in the form of a steady-state meandering jet, a cusped jet, and a two-armed spiral.

Figure 1

Periodic steady-state solutions. Both solutions oscillate with the same amplitude $a=3$. The solid line corresponds to $m=1$, while the dotted line corresponds to $m=0.5$.

Figure 2

The cusped steady-state solution.

Figure 3

Two-armed spiral solution for $\nu =-4$ and ${\phi }_0=\pi$. A satellite image of an occluded front wrapping-up in a spiral is used as the background for comparison.