Leaky trapped mountain lee waves are investigated by examining the structure of individual linear modes in multilayer atmospheres. When the static stability and cross-mountain wind speed are constant in the topmost unbounded layer, modes that decay exponentially downstream also grow exponentially with height. This growth with height occurs because packets containing relatively large-amplitude waves follow ray paths through the stratosphere, placing them above packets entering the stratosphere

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... rther downstream that contain relatively low-amplitude waves. Nevertheless, if the trapped wave train is generated by a compact source, all waves disappear above some line parallel to the group velocity that passes just above the source region. The rate of downstream decay due to leakage into the stratosphere is strongly dependent on the atmospheric structure. Downstream dissipation is often significant under realistic atmospheric conditions, which typically include elevated inversions and strong upper-tropospheric winds. On the other hand, idealized profiles with constant Scorer parameters throughout each of two tropospheric layers can exhibit a wide range of behaviors when capped by a third stratospheric layer with typical real-world static stability. Assuming the Scorer parameter in the stratosphere is a little larger than the minimum value necessary to allow a particular mode to propagate vertically, the rate of downstream decay is more sensitive to changes in the height of the tropopause than to further increases in the stability of the stratosphere. Downstream decay is minimized when the tropopause is high and the horizontal wavelength is short. * Current affiliation: Atmospheric Sciences,