Small-amplitude waves on the surface of a layer of a viscous liquid
Authors:
L. Cortelezzi and A. Prosperetti
Journal:
Quart. Appl. Math. 38 (1981), 375-389
MSC:
Primary 76D99
DOI:
https://doi.org/10.1090/qam/614548
MathSciNet review:
614548
Full-text PDF Free Access
Abstract |
References |
Similar Articles |
Additional Information
Abstract: We study the initial-value problem posed by the small-amplitude waves on the surface of a layer of a viscous fluid of infinite lateral extent. The problem of the motion of the interface is reduced to an integro-differential equation which is solved by means of the Laplace transform. Explicit numerical results for illustrative cases are presented.
H. Lamb, Hydrodynamics, 6th ed., Dover Publications, New York, 1945
- S. Chandrasekhar, Hydrodynamic and hydromagnetic stability, The International Series of Monographs on Physics, Clarendon Press, Oxford, 1961. MR 0128226
- Andrea Prosperetti, Viscous effects on small-amplitude surface waves, Phys. Fluids 19 (1976), no. 2, 195–203. MR 413747, DOI https://doi.org/10.1063/1.861446
- G. F. Carrier and C. T. Chang, On an initial value problem concerning Taylor instability of incompressible fluids, Quart. Appl. Math. 16 (1958), 436–439. MR 101719, DOI https://doi.org/10.1090/S0033-569X-1959-0101719-8
A. Prosperetti, Viscous effects on perturbed spherical flows, Quart. Appl. Math. 34, 339–352 (1977)
R. Menikoff, R. C. Mjolsness, D. H. Sharp, and C. Zemach, Initial-value problem for Rayleigh-Taylor instability of viscous fluids, Phys. Fluids 21, 1674–1687 (1978)
A. Prosperetti, E. Cucchiani, and E. Dei Cas, On the motion of two superposed viscous liquids, Phys. Fluids, in press.
A. Prosperetti, Free oscillations of drops and bubbles: the initial-value problem, submitted to Journal of Fluid Mechanics.
C. A. Truesdell and R. Toupin, The nonlinear field theories of mechanics, in Handbuch der Physik, S. Flugge (ed.), Vol. 3, pt. 3, Springer, Berlin, 1965
R. L. Panton, Potential/complex-lamellar velocity decomposition and its relevance to turbulence, J. Fluid Mech. 88, 97–114 (1978)
L. Cortelezzi and A. Prosperetti, Surface waves generated by a weak vorticity distribution in a viscous liquid, submitted to Phys. Fluids.
C. S. Yih, Fluid mechanics: a concise introduction to the theory, McGraw-Hill, New York, 1969
- F. Durbin, Numerical inversion of Laplace transforms: an efficient improvement to Dubner and Abate’s method, Comput. J. 17 (1974), 371–376. MR 356449, DOI https://doi.org/10.1093/comjnl/17.4.371
H. Lamb, Hydrodynamics, 6th ed., Dover Publications, New York, 1945
S. Chandrasekhar, Hydrodynamic and hydromagnetic stability, Clarendon Press, Oxford, 1961
A. Prosperetti, Viscous effects on small-amplitude surface waves, Phys. Fluids 19, 195–203 (1976)
G. F. Carrier and C. T. Chang, On an initial-value problem concerning Taylor instability of incompressible fluids, Quart. Appl. Math. 16, 436–439 (1959)
A. Prosperetti, Viscous effects on perturbed spherical flows, Quart. Appl. Math. 34, 339–352 (1977)
R. Menikoff, R. C. Mjolsness, D. H. Sharp, and C. Zemach, Initial-value problem for Rayleigh-Taylor instability of viscous fluids, Phys. Fluids 21, 1674–1687 (1978)
A. Prosperetti, E. Cucchiani, and E. Dei Cas, On the motion of two superposed viscous liquids, Phys. Fluids, in press.
A. Prosperetti, Free oscillations of drops and bubbles: the initial-value problem, submitted to Journal of Fluid Mechanics.
C. A. Truesdell and R. Toupin, The nonlinear field theories of mechanics, in Handbuch der Physik, S. Flugge (ed.), Vol. 3, pt. 3, Springer, Berlin, 1965
R. L. Panton, Potential/complex-lamellar velocity decomposition and its relevance to turbulence, J. Fluid Mech. 88, 97–114 (1978)
L. Cortelezzi and A. Prosperetti, Surface waves generated by a weak vorticity distribution in a viscous liquid, submitted to Phys. Fluids.
C. S. Yih, Fluid mechanics: a concise introduction to the theory, McGraw-Hill, New York, 1969
F. Durbin, Numerical inversion of Laplace transforms: an efficient improvement to Dubner and Abate’s method, Comp. J. 17, 371–376 (1974)
Similar Articles
Retrieve articles in Quarterly of Applied Mathematics
with MSC:
76D99
Retrieve articles in all journals
with MSC:
76D99
Additional Information
Article copyright:
© Copyright 1981
American Mathematical Society
