Downstream decay of linear trapped lee waves in the presence of a stratosphere

It has long been known that, in the presence of a stratosphere aloft, trapped lee wave energy may leak upwards due to the increased Scorer parameter in this upper layer. Nevertheless, the impact of the stratosphere on trapped wave structure has not been studied in detail.  We provide such an analysis and show that the behavior of leaky trapped waves is not simply a trivial extension of the non-leaky solution.

We present linear solutions of trapped waves in three or more layer atmospheres, with two layer results for comparison. For each basic profile, we compute solutions for a range of tropopause heights and stratospheric static stabilities (Ns). The rate of leakage due to the stratosphere is shown to be maximized for values of Ns marginally above the threshold value for leakage, with a decreasing trend in the rate of decay as Ns is further increased. Changes in the resonant wavelength also occur in relation to stratospheric stability, with the shortest values occurring at the threshold value in Ns for leakage.

Further, the rate of downstream decay generated by the stratosphere is increased as we model more realistic profiles. Upward leakage, and thus downstream decay, is significant when the waves are trapped by stability concentrated in an elevated inversion, with these realistic inversions producing rapid decay.

Forward free tropospheric wind shear plays an important role in the process. Stronger shear lowers the thickness of the elevated inversion required for a resonant wave duct to exist - allowing potentially stronger downstream decay. However for a given stable layer, stronger wind shear results in weaker stratospheric leakage due to a greater exponential decay of wave amplitude with height through the free troposphere.