Solitary Rossby Waves Research Articles

On Solitary Rossby Waves

Abstract A variational principle and an associated integral invariant are constructed for two-dimensional (non-divergent) waves of permanent form in a Rossby β-plane. A solitary-wave solution is obtained, and it is shown that the effects of cubic nonlinearity may be comparable with those of quadratic nonlinearity and may limit the amplitude of the wave.

Solitary Rossby waves in a two-layer system

Solitary Rossby waves in a two-layer system

Solitary Rossby waves in a two-layer system

The solutions for solitary Rossby waves with no critical level in a two-layer system which contains a zonal, baroclinic, mean shear flow are presented. When the mean shear flow has a barotropic structure, these solutions agree with those of Redekopp (1977) in the sense that the barotropic mode obeys the Korteweg-deVries equation, whereas the baroclinic mode obeys the modified Korteweg-deVries equation. It is found that the presence of vertical shear in the mean flow generally tends to steepen the solitary Rossby waves, but the tendency depends strongly on the particular wave mode and the magnitude of the internal rotational Froude number characterizing the wave field. DOI: 10.1111/j.2153-3490.1979.tb00893.x

Solitary Rossby waves in a two-layer system : Hukuda, Hisashi, 1979. Tellus, 31(2): 161–169

Solitary Rossby waves in a two-layer system : Hukuda, Hisashi, 1979. Tellus, 31(2): 161–169

Solitary Rossby Waves in Zonal Shear Flows and Their Interactions

Interactions of long-wave solitons propagating in shear flows are described by a coupled pair of Korteweg-de Vries equations. The basic equation of motion for the analysis is the quasi-geostrophic forecast equation, and the interaction of two wave modes is studied. The solution for mode 1-mode 2 interaction of solitary waves in an asymmetric shear flow of a barotropic atmosphere with divergence is constructed. Streamline patterns for certain flows are obtained. An unsteady solitary wave solution for a modified Korteweg-de Vries equation is derived.

On the production and interaction of planetary solitary waves: Applications to the Jovian atmosphere

We present further evidence that strengthens the case for our interpretation of many features in the Jovian atmosphere as solitary Rossby waves (solitons). These include: a mechanism whereby such waves can evolve from the instability of the basic shear flows; further interpretation of the interaction between observed features, and comparison with calculations of the interaction between planetary solitons of a restricted class; and calculations of the morphology for a type of shear flow other than the type considered originally by Maxworthy and Redekopp.

On the theory of solitary Rossby waves

The evolution of long, finite amplitude Rossby waves in a horizontally sheared zonal current is studied. The wave evolution is described by the Korteweg–de Vries equation or the modified Korteweg-de Vries equation depending on the atmospheric stratification. In either case, the cross-stream modal structure of these waves is given by the long-wave limit of the neutral eigensolutions of the barotropic stability equation. Both non-singular and singular eigensolutions are considered and the appropriate analysis is developed to yield a uniformly valid description of the motion in the critical-layer region where the wave speed matches the flow velocity. The analysis demonstrates that coherent, propagating, eddy structures can exist in stable shear flows and that these eddies have peculiar interaction properties quite distinct from the traditional views of turbulent motion.