Numerical simulation of soliton destruction of internal gravity waves in the upper atmosphere

Internal gravity waves (IGW) in the atmosphere can break, forming secondary waves of smaller scales, up to the formation of wave turbulence. Experimentally, it is difficult to trace the process of wave destruction in detail, since waves usually propagate over long distances. The scale of the secondary waves formed may differ from the scale of the primary wave by orders of magnitude. To verify numerical studies of wave propagation and destruction, it is useful to have analytical estimates for the conditions of destruction, the time of destruction, and the scale of secondary waves formed. The combination of analytical and numerical approaches makes it possible to better study the process of wave propagation and destruction in detail.

     A direct numerical solution of hydrodynamic equations for atmospheric gas is performed using a high-resolution model. A comparison of the results of these numerical calculations with the results of the analysis of the derived KdW-Burgers equation for atmospheric layers showed a fairly good agreement. The preferred heights, near which IGWs can break, approximately correspond to the heights of the change in the sign of the horizontal velocity in the wave. The parameters of small-scale solitary secondary waves (solitons) formed in calculations based on complete hydrodynamic equations, are in good agreement with estimates based on the analysis of the KdW-Burgers equation. The latter equation does not describe the propagation of secondary waves over time into other atmospheric layers, as well as fluctuations, tilts, and deformation of the layered structure created by the primary wave, due to the approximations used in the derivation of the KDW-Burgers equation.

     Long IGW have a layered structure: temperature, density, and horizontal velocity perturbations alternate signs with height. It is shown that the destruction of waves manifests itself inside the layers created by the primary waves. Small-scale isolated secondary waves appear in the layers. In this case, each of the secondary waves formed perturbations in several layers. The layered structure of the long IGW persists for a long time, despite the formation of secondary waves, but the layers can undulate, change thickness and tilt. Calculations of wave destruction based on the numerical solution of complete hydrodynamic equations for atmospheric gas are performed. A comparison of the results of these numerical calculations with the results of an analysis of the system of hydrodynamic equations based on the KdW-Buregs equation derived for the layers showed that the model equation as a whole correctly describes the dynamics of waves. The parameters of small-scale isolated secondary waves formed in calculations with complete hydrodynamic equations are in good agreement with estimates based on the analysis of the KdW-Burgers equation.