A Thunderstorm-Generated Solitary Wave Observation Compared with Theory for Nonlinear Waves in a Sheared Atmosphere

Abstract

The theory of internal nonlinear waves in a motionless medium is extended to waves in sheared flow to provide a basis for the interpretation of atmospheric solitary waves. It is shown that if the Scorer parameter is zero in a semi infinite upper region, the integro-differential equation [i.e., the Benjamin-Davis-Ono (BDO) equation] defining the evolution of nonlinear waves in sheared flow is independent of shear and stability in the upper layer. A new type of evolution model is presented, based on the numerical solution of the BDO equation, for the generation of solitary waves by a thunderstorm moving at supercritical speeds. The results of a thorough study of observations of a thunderstorm-generated solitary wave are presented in detail. These observations show that some of the storm's outflow, which was denser than the environment through which the wave propagated, was trapped in the interior of the wave. It is hypothesized that the Coriolis force then caused this denser air to flow along the axis of the wave away from the storm's southern flank for distances in excess of 100 km. Analysis reveals that the temporarily trapped recirculating air in the leading solitary wave is gradually deposited along the ground, forming an advancing shallow layer of denser air behind the wave. The derived wave parameters are then compared with theory. A new type of analysis, based on the separation of the wind change due to vertical transport of horizontal momentum from the observed wind perturbations, results in improved agreement between weakly nonlinear theory and observations. This analysis supports the deduction that wave energy propagates along straight rays, parallel to the plane of recirculating flow, but oblique to the curved wave front. The failure of weakly nonlinear theory to account for all the observed wave characteristics is shown to be caused by the presence of recirculating flow. Comparison with numerical results for strongly nonlinear waves shows reasonably good agreement for all the wave characteristics, except wave speed, which is significantly less than that predicted when wave amplitudes are large. Finally, relations are developed that govern the minimum wave amplitude threshold required for the propagation of solitary waves in waveguides bordered by weakly stratified sheared flow.