D A R G A N M . W . F R I E R S O N U N I V E R S I T Y O F W A S H I N G T O N , D E P A R T M E N T O F A T M O S P H E R I C S C I E N C E S 4 / 5 / 1 1 GFD II: Balance Dynamics ATM S 542Kelvin-Helmholtz Instability Courtesy of Greg HakimBarotropic InstabilityKelvin-Helmholtz InstabilityKelvin-Helmholtz InstabilityKelvin-Helmholtz InstabilityBarotropic InstabilityBarotropic InstabilityBarotropic Instability We studied this: Probably reasonable to assume that smoothed versions of this profile would also be unstable…Barotropic Instability But how about this profile? Velocity doesn’t stay constant at peaks…Barotropic Instability Or this profile? Kind of looks like our example in the bottom half…Barotropic Instability Or these? Both have shear, when can that be tapped by eddies?Barotropic Instability We’ll derive two criteria for barotropic instability: Rayleigh’s criterion Fjortoff’s criterion Former has to do with counter-propagating Rossby waves, latter has to do with zonal wind speeds at location of different waves These are necessary conditions but not sufficient conditions There is no way to say there will definitely be barotropic instability in any given situation without solving the full problem Criteria are extremely useful in practice thoughBack to the Profiles from Before: Zonal winds d^2 u -----
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