Shear instability in spherical linear shallow water system is investigated using wind profiles observed near Venus cloud top. Results from two different wind profiles are presented. The first profile has a uniform zonal wind velocity between 60N and 60S with wind decreasing poleward of these latitudes; it is barotropically and inertially stable. The other has a zonal wind velocity of 100ms-1 at the equator and high-latitude jets of 160ms-1 at around 60N and 60S; it satisfies sufficient condition for both barotropic and inertial instability.
For the former profile, the most preferred growing mode appears at a zonal number of m=2 and (gH)2(2aΩ)-1=0.11. It has an e-folding time of about 100 days and an equivalent depth corresponding to a vertical wavelength of ~1km near the cloud top. In a frequency - Lamb-parameter diagram, this mode corresponds to an intersection of the Kelvin mode curve and the continuous modes region, which ranges from the frequency corresponding to minimum basic angular velocity to that of maximum basic angular velocity. The intersections of eastward propagating gravity mode curves and continuous mode region sometimes generate another growing mode, whereas the intersections of westward propagating gravity mode curves and continuous mode region do not generate growing mode.
For the latter profile, the most preferred growing mode appears at a zonal number of m=1 and (gH)2(2aΩ)-1 >0.1. It has an e-folding time of about 2 days and an equivalent depth corresponding to a vertical wavelength of below ~2km near the cloud top. This mode corresponds to an intersction of modified Rossby mode curve and continuous modes region.
In these growing modes, angular momentum is conveyed equatorward. This particular feature is expected for explaining the superrotation of Venus atmosphere.
Using the concept of resonance between different neutral modes,the cause of these growing modes is discussed. For the former profile, for example, the eastward propagating gravity modes and Kelvin mode having positive pseudo angular momentum resonate with continuous modes, which originally have negative (i.e. opposite sign) pseudo angular momentum. On the other hand, the westward propagating gravity modes, which originally have negative pseudo angular momentum cannot resonate with continuous modes with negative (i.e. same sign) pseudo angular momentum. |
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