Local instabilities of weakly non-parallel large-scale flows: uniform asymptotic expansion

Abstract A uniform asymptotic representation of local instabilities developing in weakly nonparallel large-scale flows that possess vertical and horizontal shear is presented. The analysis extends the comparison equation method of Langer to determine the local eigenfunctions and eigenvalues of the local instabilities. The advantages of the present method over the corresponding WKB analysis (Bar-Sever and Merkine, 1988) are discussed.