Abstract
The instability of oscillatory flows in a two-layer fluid where the two layers differ in density and viscosity has been analysed using a perturbation method for long waves with special interest on effects of viscosity, time scale, density and depth of the fluid. The flow of a fluid with homogeneous density can be unstable, when the kinematic viscosity of the upper fluid layer is different from that of the lower one. Viscosity stratification results in unstable oscillatory flows. Two limiting cases of single-layer flow are also considered.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Batchelor, G. K. (1967): An Introduction to Fluid Dynamics. Cambridge Univ. Press, Cambridge, 615 pp.
Benjamin, T. B. (1960): Effects of a flexible boundary on hydrodynamic stability. J. Fluid Mech.,9, 513–532.
Benjamin, T. B. (1963): The threefold classification of unstable disturbances in flexible surfaces bounding inviscid flows. J. Fluid Mech.,16, 436–450.
Benjamin, T. B. (1966): Fluid flow with flexible boundaries.In, Proceedings of the Eleventh International Congress of Applied Mechanics, Munich (Germany) 1964, ed. byH. Görtler, Springer-Verlag, New York, 109–128.
Conrad, W. andW. O. Criminale, Jr. (1965): The stability of time-dependent laminar flow. Parallel flows. Z. angew. Math. Phys.,16, 233–254.
Drazin, P. G. andL. N. Howard (1966): Hydrodynamic stability of parallel flow of inviscid fluid. Advanc. Appl. Mech.,9, 1–89.
Drazin, P.G. andW.H. Reid (1981): Hydrodynamic Stability. Cambridge Univ. Press, Cambridge, 525 pp.
Hall, P. (1978): The instability of flat Stokes layers. Proc. Roy. Soc. London,A359, 151–166.
Hino, M. and M.Sawamoto (1975): The linear stability problem of oscillatory flows. Proceedings of the 19th Japanese Conference on Hydraulics, 149–154 (in Japanese).
Kamachi, M. (1980): The instability of viscous two-layer oscillatory flows. M. Eng. thesis, Kyushu University, 245 pp.
Kelly, R. E. (1965): The stability of an unsteady Kelvin-Helmholtz flow. J. Fluid Mech.,22, 547–560.
Kerczek, C. V. andS. H. Davis (1974): Linear stability theory of oscillatory Stokes layers. J. Fluid Mech.,64, 753–773.
Landahl, M. T. (1962): On the stability of a laminar incompressible boundary layer over a flexible surface. J. Fluid Mech.,13, 609–632.
Lin, C. C. (1955): The Theory of Hydrodynamic Stability. Cambridge Univ. Press, Cambridge, 155 pp.
Niino, H. (1981): Dynamics of barotropic instability. Tenki,28, 3–32 (in Japanese).
Schlichting, H. (1979): Boundary Layer Theory. 7th ed., McGraw-Hill, New York, 817 pp.
Stuart, J. T. (1963): Hydrodynamic stability, Ch. IXIn, Laminar Boundary Layers ed. byL. Rosenhead, Oxford Univ. Press, Oxford, 687 pp.
Takematsu, M. (1968): Stability of a laminar flow along a flexible boundary (I). Rep. Res. Inst. Appl. Mech., Kyushu University,16, 109–120.
Takematsu, M. (1969): Stability of a laminar flow along a flexible boundary (II). Rep. Res. Inst. Appl. Mech., Kyushu University,17, 25–37.
Takematsu, M. (1970): Stability of a laminar flow along a flexible boundary (III). Rep. Res. Inst. Appl. Mech., Kyushu University,18, 87–100.
Turner, J. S. (1973): Buoyancy Effects in Fluids. Cambridge Univ. Press, Cambridge, 367 pp.
Wylie, C. R. Jr. (1975): Advanced Engineering Mathematics. McGraw-Hill, New York, 937 pp.
Yih, C. S. (1963): Stability of liquid flow down an inclined plane. Phys. Fluids,6, 321–334.
Yih, C. S. (1967): Instability due to viscosity stratification. J. Fluid Mech.,27, 337–352.
Yih, C. S. (1968): Instability of unsteady flows or configurations. Part 1. Instability of a horizontal liquid layer on an oscillating plane. J. Fluid Mech.,31, 737–751.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Kamachi, M., Honji, H. The instability of viscous two-layer oscillatory flows. Journal of the Oceanographical Society of Japan 38, 346–356 (1983). https://doi.org/10.1007/BF02111031
Received:
Revised:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF02111031