Three dimensional aspects of symmetric instability
Three dimensional aspects of symmetric instability are investigated using analytic and numerical techniques. The linear stability of a balanced flow with constant vertical shear is studied. In the inviscid case the fastest growing mode is the symmetric mode which is oriented parallel to the basic st...
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University of Reading
1990
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| Online Access: | http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.646003 |
| Summary: | Three dimensional aspects of symmetric instability are investigated using analytic and numerical techniques. The linear stability of a balanced flow with constant vertical shear is studied. In the inviscid case the fastest growing mode is the symmetric mode which is oriented parallel to the basic state isotherms. When the modes are tilted relative to the basic state isotherms the growth rate decreases. Modes with opposite tilts have similar growth rates but different structures; modes with cyclonic tilts have larger amplitude at the boundaries than those with anticyclonic tilts. When the flow is viscous the fastest growing modes are rotated anticyclonically relative to the basic state isotherms. This is attributed to the viscous damping being larger for the cyclonic modes due to their large amplitude near the boundaries. The tilt of the fastest growing mode depends on the viscosity. The larger growth of the anticyclonic modes is maintained into the nonlinear regime. The nonlinear development of the tilted modes proceeds in a similar manner to "nontilted" symmetric instability. The circulations can grow in the presence of structure along the length of the band. The two dimensional symmetrically unstable flow is perturbed with three dimensional disturbances. Growing disturbances retain their three dimensional structure. They can have horizontal tilts which vary with height and change with time. The fastest growth occurs when disturbances have anticyclonic tilts and are elongated in the along front direction. Unstable circulations can grow when the negative potential vorticity is confined in the along front direction. The scale of the region in this direction must exceed the wavelength of the eddies in the across front direction. The unstable circulations develop with the horizontal tilts and wavelengths observed when the unstable region is unconfined. Inertia-gravity waves are excited in the stable regions. |
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