Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-18T19:18:28.239Z Has data issue: false hasContentIssue false
  • English
  • Français

Effects of plane progressive irrotational waves on thermal boundary layers

Published online by Cambridge University Press:  29 March 2006

James Witting
James Witting
Affiliation:
Applied Mathematics Division, Argonne National Laboratory, Argonne, Ill. 60439 Present address: Office of Naval Research, Arlington, Va. 22217.
Get access Rights & Permissions [Opens in a new window]

Abstract

The average changes in the structure of thermal boundary layers at the surface of bodies of water produced by various types of surface waves are computed. the waves are two-dimensional plane progressive irrotational waves of unchanging shape. they include deep-water linear waves, deep-water capillary waves of arbitrary amplitude, stokes waves, and the deep-water gravity wave of maximum amplitude.

The results indicate that capillary waves can decrease mean temperature gradients by factors of as much as 9·0, if the average heat flux at the air-water interface is independent of the presence of the waves. Irrotational gravity waves can decrease the mean temperature gradients by factors no more than 1·381.

Of possible pedagogical interest is the simplicity of the heat conduction equation for two-dimensional steady irrotational flows in an inviscid incompressible fluid if the velocity potential and the stream function are taken to be the independent variables.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 50 , Issue 2 , 29 November 1971 , pp. 321 - 334
Copyright
© 1971 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Boussinesq, J. J. 1905 J. Math. Pures Appl. Ser. 6, 1, 285.
Crapper, G. D. 1957 J. Fluid Mech. 2, 532.
Gradshteyn, I. S. & Ryzhik, I. M. 1965 Table of Integrals, Series, and Products, 4th edition (translation ed. A. Jeffrey). Academic.
Grosh, R. J. & Cess, R. D. 1958 Trans. Am. Soc. Mech. Engrs 80, 667.
Havelock, T. H. 1918 Proc. Roy. Soc. A, 95, 38.
Hill, R. H. 1970 U.S. Naval Research Laboratory Report, no. 7212.
Lamb, H. 1932 Hydrodynamics, 6th edn. Dover.
Mcalister, E. D. & McLeish, W. 1969 J. Geophys. Res. 74, 3408.
Mcgoldrick, L. F. 1965 J. Fluid Mech. 21, 305.
Michell, J. H. 1893 Phil. Mag. (5), 36, 430.
O'Brien, E. E. 1967 J. Fluid Mech. 28, 295.
Omholt, T. 1970 The effects of progressive waves on convective transfers. Ph.D. Thesis, State University of New York at Stony Brook.
Osborne, M. F. M. 1964 Dt. Hydrogr. Z. 17, 115.
Osborne, M. F. M. 1965 Dt. Hydrogr. Z. 18, 1.
Stokes, G. G. 1847 Trans. Cambridge Phil. Soc. 8, 411 (also in Mathematical and Physical Papers, 1, 197, Cambridge University Press 1880).
Stokes, G. G. 1880 Mathematical and Physical Papers, 1, 314. Cambridge University Press.
Wilton, J. R. 1914 Phil. Mag. (6), 27, 385.