Articles | Volume 24, issue 4
Research article
05 Dec 2017
Research article |  | 05 Dec 2017

Analytic solutions for Long's equation and its generalization

Mayer Humi

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Cited articles

Abramowitz, M. and Stegun, I.: Handbook of Mathematical Functions, Dover Publications, New York, 1974.
Akylas, T. R. and Davis, K. S.: Three-dimensional apects of nonlinear stratified flow over topography near the hydrostatic limit, J. Fluid Mech., 428, 81–105, 2001.
Baines, P. G.: Topographic effects in Stratified flows, Cambridge Univ. Press, New York, 1995.
Drazin, P. G.: On the steady flow of a fluid of variable density past an obstacle, Tellus, 13, 239–251, 1961.
Drazin, P. G. and Moore, D. W.: Steady two dimensional flow of fluid of variable density over an obstacle, J. Fluid. Mech., 28, 353–370, 1967.
Short summary
Deriving a generalization of Long's equation to non-isothermal flow shows that Long's equation has (approximate) soliton-like solutions, provides a transformation that linearizes Long's equation (and analytic solutions), and provides analytic solutions for a base flow with shear.