The instability of superposed flow
Authors:
S. S. Liang and B. S. Seidel
Journal:
Quart. Appl. Math. 36 (1978), 57-72
MSC:
Primary 76.35
DOI:
https://doi.org/10.1090/qam/475240
MathSciNet review:
475240
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Abstract: The interfacial instability of a stratified two-phase flow is studied. Two independent cases are investigated: first, the instability of an idealized atmosphere (density decreasing exponentially with height) over a liquid; second, the instability of an ideal gas over a liquid. The unbounded and incompressible cases may be obtained by specializing the above results.
G. I. Taylor, Effect of variation in density on the stability of superposed stream of fluid, Proc. Roy. Soc. London A 132 (1931)
H. Jeffrey, On the formation of water waves by wind, Proc. Roy Soc. London A 110 241–7 (1926)
- Carl Eckart, The generation of wind waves on a water surface, J. Appl. Phys. 24 (1953), 1485–1494. MR 60382
- John W. Miles, Generation of surface waves by shear flows, Proc. Sympos. Appl. Math., Vol. XIII, American Mathematical Society, Providence, R.I, 1962, pp. 79–89. MR 0139321
O. M. Phillips, The theory of wind-generated waves, in Advances in hydroscience, Vol. 4, Academic Press, 1967
S. S. Liang and B. S. Seidel, Kelvin-Helmholtz instability of a bounded two-phase flow, in Developments in Mechanics, Vol. 5, Iowa State University, 1969, 135–152
J. F. Sontowski, B. S. Seidel, and W. F. Ames, On the stability of the flow of a stratified gas over a liquid, Quart. Appl. Math. 27, 335–348 (1969)
- I-Dee Chang and Paul E. Russell, Stability of a liquid layer adjacent to a high-speed gas stream, Phys. Fluids 8 (1965), 1018–1026. MR 187527, DOI https://doi.org/10.1063/1.1761350
E. T. Copson, Theory of functions of a complex variable, Oxford, Clarendon Press, 1962
H. Nyquist, Regeneration Theory, Bell System Tech. J. 11, (1934)
H. E. Huppert, On Kelvin-Helmholtz instability in a rotating fluid, J. Fluid Mech. 33 (1968)
W. H. Munk, A critical wind speed for air-sea boundary processes, J. Marine Res. 6 (1947)
Jin Wu, Laboratory studies of wind-wave interaction, J. Fluid Mech. 34 (1968)
A. K. Gupta, M. T. Landahl, and E. L. Mollo-Christensen, Experimental and theoretical investigation of the stability of air flow over a water surface, J. Fluid Mech. 33 (1968)
E. J. Plate, P. C. Chang, and G. M. Hidy, Experiments on the generation of small water waves by wind, J. Fluid Mech. 35 (1969)
J. J. Van Rossum, Experimental investigation of horizontal liquid films, Chem. Eng. Science 11 (1959)
G. I. Taylor, Effect of variation in density on the stability of superposed stream of fluid, Proc. Roy. Soc. London A 132 (1931)
H. Jeffrey, On the formation of water waves by wind, Proc. Roy Soc. London A 110 241–7 (1926)
C. Eckart, The generation of wind waves on a water surface, J. Appl. Phys. 24, 1485–1494 (1953)
J. W. Miles, On the generation of surface waves by shear flows, J. Fluid Mech 7 433–447 (1961)
O. M. Phillips, The theory of wind-generated waves, in Advances in hydroscience, Vol. 4, Academic Press, 1967
S. S. Liang and B. S. Seidel, Kelvin-Helmholtz instability of a bounded two-phase flow, in Developments in Mechanics, Vol. 5, Iowa State University, 1969, 135–152
J. F. Sontowski, B. S. Seidel, and W. F. Ames, On the stability of the flow of a stratified gas over a liquid, Quart. Appl. Math. 27, 335–348 (1969)
I-Dee Chang and P. E. Russell, Stability of a liquid layer adjacent to a high-speed gas stream, Phys. Fluids 8, 1965
E. T. Copson, Theory of functions of a complex variable, Oxford, Clarendon Press, 1962
H. Nyquist, Regeneration Theory, Bell System Tech. J. 11, (1934)
H. E. Huppert, On Kelvin-Helmholtz instability in a rotating fluid, J. Fluid Mech. 33 (1968)
W. H. Munk, A critical wind speed for air-sea boundary processes, J. Marine Res. 6 (1947)
Jin Wu, Laboratory studies of wind-wave interaction, J. Fluid Mech. 34 (1968)
A. K. Gupta, M. T. Landahl, and E. L. Mollo-Christensen, Experimental and theoretical investigation of the stability of air flow over a water surface, J. Fluid Mech. 33 (1968)
E. J. Plate, P. C. Chang, and G. M. Hidy, Experiments on the generation of small water waves by wind, J. Fluid Mech. 35 (1969)
J. J. Van Rossum, Experimental investigation of horizontal liquid films, Chem. Eng. Science 11 (1959)
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Article copyright:
© Copyright 1978
American Mathematical Society
