Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-18T15:11:08.284Z Has data issue: false hasContentIssue false
  • English
  • Français

Mass transport induced by standing interfacial waves

Part of: Incompressible viscous fluids

Published online by Cambridge University Press:  26 February 2010

D. J. Crampin  and
B. D. Dore
D. J. Crampin
Affiliation:
Department of Mathematics, The University of Reading, Whiteknights, Reading.
B. D. Dore
Affiliation:
Department of Mathematics, The University of Reading, Whiteknights, Reading.
Get access

Abstract

A higher-order, double boundary-layer theory is employed to investigate the mass transport velocity due to two-dimensional standing waves in a system consisting of two semi-infinite, homogeneous fluids of different densities and viscosities. For moderately large wave amplitudes, the leading correction to the tangential mass transport velocity near the interface is extremely significant and may typically contribute about 20% of the total velocity.

MSC classification

Secondary: 76D10: Boundary-layer theory, separation and reattachment, higher-order effects
Type
Research Article
Information
Mathematika , Volume 26 , Issue 2 , December 1979 , pp. 224 - 235
Copyright
Copyright © University College London 1979

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

1.Dore, B. D.. “On mass transport induced by interfacial oscillations at a single frequency”, Proc. Camb. Phil. Soc., 74 (1973), 333–347.CrossRefGoogle Scholar
2.Dore, B. D.. “Double boundary layers in standing interfacial waves”, J. Fluid Mech, 76 (1976), 819–828.Google Scholar
3.Stuart, J. T.. Laminar boundary layers, chap. 7 (1963, Oxford University Press).Google Scholar
4.Stuart, J. T.. “Double boundary layers in oscillatory viscous flow”, J. Fluid Mech, 24 (1966), 673–687.Google Scholar
5.Riley, N.. “Oscillating viscous flows”, Mathematika, 12 (1965), 161–175.Google Scholar
6.Riley, N.. “Oscillatory viscous flows. Review and extension”, J. lnst. Math. Appl., 3 (1967), 419–434.CrossRefGoogle Scholar
7.Davidson, B. J. and Riley, N.. “Jets induced by oscillatory motion”, J. Fluid. Meek, 53 (1972), 287–303.Google Scholar
8.Riley, N., “The steady streaming induced by a vibrating cylinder”, J. Fluid Mech, 68 (1975), 801–812.CrossRefGoogle Scholar
9.Bertelsen, A. F.. “An experimental investigation of high Reynolds number steady streaming generated by oscillating cylinders”, J. Fluid Mech, 64 (1974), 589–597.Google Scholar
10.Longuet-Higgins, M. S.. “Mass transport in water waves”, Phil. Trans. Roy. Soc. London, A245 (1953), 535–581.Google Scholar
11.Dore, B. D.. “A double boundary-layer model of mass transport in interfacial waves”, J. Eng. Math., 12 (1978), 289–301.CrossRefGoogle Scholar
12.Dore, B. D.. “Some effects of the air-water interface on gravity waves”, Geophys. Astrophys. Fluid Dyn., 10 (1978), 215–230.CrossRefGoogle Scholar
13.Batchelor, G. K.. An introduction to fluid dynamics (1967, Cambridge University Press).Google Scholar