Oblique interactions of internal solitary waves in the lower atmosphere

Abstract

Internal solitary waves frequently occur in the atmosphere. On rare occasions, they create the awe-inspiring spectacle known, for example, as the Morning Glory Clouds, a spectacular roll cloud, or series of roll clouds predictably appearing in the southern part of the Gulf of Carpentaria. Nevertheless, solitary wave–wave interactions have rarely been studied and documented; thus, we here focus on the long-time evolution of the superposition of two solitons featuring an X-shape and, more complicated, the interactions between three solitons initially posing as a Y-shape. To better understand the underlying dynamics of these phenomena, we derive a bidirectional and isotropic theoretical equation in a two-layer fluid system with variable bottom topography. This is accomplished by using its Hamiltonian structure and the Taylor expansion of the Dirichlet–Neumann operator for the potential theory. Essentially, the derived equation is an extension of the widely recognized Benjamin–Ono equation at two horizontal dimensions, and thereby, it possesses plane soliton solutions propagating in any horizontal direction. It is noted that the initial angles play an essential role in the oblique wave–wave interactions, manifested as the determination of waveforms, amplitudes, and the emergence of the Mach stem. In addition, the wave evolution is slightly modulated by the topographic effects, partly due to invoking the assumption of small topography.