Abstract
The symmetry reduction equations, similarity solutions, sub-groups and exact solutions of the (3+1)-dimensional nonlinear incompressible non-hydrostatic Boussinesq equations with viscosity (INHBV equations), which describe the atmospheric gravity waves, are researched in this paper. Calculation on symmetry shows that the equations are invariant under the Galilean transformations, scaling transformations, rotational transformations and space-time translations. Three types of symmetry reduction equations and similar solutions for the (3+1)-dimensional INHBV equations are proposed. Traveling wave solutions of the INHBV equations are demonstrated by means of symmetry method. The evolutions on the wind velocities and temperature perturbation are demonstrated by figures.
Highlights
Middle atmospheric meteorology is largely concerned with understanding various types of traveling stratospheric and mesospheric waves
Traveling wave solutions of the INHBV equations are demonstrated by means of symmetry method
Atmospheric gravity waves play an important role in atmospheric dynamics
Summary
Middle atmospheric meteorology is largely concerned with understanding various types of traveling stratospheric and mesospheric waves. Waves generated by flow over mountains, convection and jet-stream instability transport energy and momentum over large distances, serve as the mechanism for coupling different height regions, interact with and produce wind shear and turbulence They can break and produce organized cloud and have a great effect on severe hazardous weather and climate, such as rainstorm of typhoon, deep convection and orographic precipitation.[1,2,3,4]. The governing equations of gravity waves can be considered as the (3+1)-dimensional nonlinear incompressible non-hydrostatic Boussinesq (INHB) equations as follows[5] ut.
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