Abstract
Abstract. Weakly nonlinear internal gravity waves are treated in a two-layer fluid with a set of nonlinear Schrodinger equations. The layers have a sharp interface with a jump in buoyancy frequency approximately modeling the tropopause. The waves are periodic in the horizontal but modulated in the vertical and Boussinesq flow is assumed. The equation governing the incident wave packet is directly coupled to the equation for the reflected packet, while the equation governing transmitted waves is only coupled at the interface. Solutions are obtained numerically. The results indicate that the waves create a mean flow that is strong near and underneath the interface, and discontinuous at the interface. Furthermore, the mean flow has an oscillatory component that can contaminate the wave envelope and has a vertical wavelength that decreases as the wave packet interacts with the interface.
Highlights
Earth’s tropopause often has a vertical structure with a very sudden change in the lapse rate with increasing altitude, and a corresponding sudden increase in the buoyancy frequency N
The results indicate that while nonlinear effects are stronger near the interface even with uniform waves, a modulated amplitude results in a localized jet-like mean flow near the interface that can be strong enough to form a critical layer, with important consequences for later waves
The abrupt change in the buoyancy frequency suggests that such observations are related to the dynamics of internal waves near the tropopause
Summary
Earth’s tropopause often has a vertical structure with a very sudden change in the lapse rate with increasing altitude, and a corresponding sudden increase in the buoyancy frequency N. Grimshaw and McHugh (2013) treated weakly nonlinear two-layer horizontally periodic waves for both unsteady and steady flow. Packets of internal waves that propagate at a steep angle to the horizontal will experience a modulational instability, as discussed by Sutherland (2001). The stability of plane monochromatic internal waves propagating at an angle to the horizontal was treated by Shrira (1981) and Tabaei and Akylas (2007), who showed that nonlinearity can lead to instability. The results given below show that the incident and reflected waves combine for a short period to create a strong localized mean flow under the interface that is discontinuous at the interface, as in Grimshaw and McHugh (2013).
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