On Whether Inertio-Gravity Waves are Absorbed or Reflected when their Intrinsic Frequency is Doppler-Shifted towards?

[摘要] Inertio-gravity waves of intrinsic frequency ω propagate through a shear flow in a stratified, rotating fluid with Coriolis parameter f. The question of when a surface ω=f is an absorber (as found by Jones 1967 and Miyahara 1976) and when it is a reflector (as for equatorially-trapped waves) is addressed by means of calculations based on ray tracing for a vertically-sheared mean flow at large Richardson number. These calculations show that the rays reflect-or more properly refract-away from the surface ω=f, in all cases except the f-plane case studied by Jones. However, on a β-plane with limitingly small the time for a wave packet to get away from the surface ω=f becomes arbitrarily long. This means that for sufficiently small β there is absorption in practice if not in principle, since some dissipation will always be present. For parameters typical of mountain lee waves in mid-latitudes, for example, molecular dissipation alone would be more than enough to destroy a wave packet near ω=f, the appropriate dimensionless values of β being extremely small in such cases.We thus suggest that the absorption found by Miyahara (1976) in a numerical model with finite dissipation and small β should not be regarded as surprising, nor as conflicting with the conclusions of earlier work by Matsuno (1966), Lindzen (1970) and others on equatorial trapping of waves for values of β which are effectively much larger.

[学科分类] 大气科学