Effect of viscosity on the conditions for the formation of centrifugal solitons in the translational-rotational flow of a liquid☆

Abstract The viscosity of the medium is taken into consideration in deriving an evolution equation describing the propagation of non-linear centrifugal waves along the free surface of a translational-rotational liquid flow. The result is the Burgers-Korteweg-de Vries (BKdV) equation, for which a steady solution is described in the form of a shock wave with soliton oscillators near the front. Estimates are presented for the effect of viscosity on the wave-front structure and the conditions of formation previously predicted by the author /1/ for centrifugal solitons, which play an important role in various atmosphere processes ∗∗ .