Abstract
The barotropic instability of a boundary jet on a beta plane is consideredwith emphasis on the effect of internal viscosity. An eigenvalue problem for thedisturbance equations and its inviscid version are solved by the aid of numericalmethods, and instability characteristics are determined as functions of the Reynoldsnumber R for various values of the beta-parameter. Typical disturbance structures (eigenfunctions) are also computed.
Numerical examples show that the minimum critical Reynolds number Rcr forinstability is smaller than 100. At a Reynolds number of the order of hundreds, there appears a second mode of instability in addition to the first unstable modeoriginating at Rcr; a kind of ‘resonance’ between the first and second eigenvaluesoccurs at the particular value of R. The neutral stability curves are accordinglymulti-looped. Although each of the two unstable modes asymptotically approachesits inviscid counterpart as R→∞, the asymptotic approach to the inviscid limit israther slow and the effect of varying R is conspicuous even at R-O (104). It isthus demonstrated that the Reynolds number is an essential stability parameter forreal boundary jets.
