Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-18T21:03:50.207Z Has data issue: false hasContentIssue false
  • English
  • Français

The evolution of thermocline waves from an oscillatory disturbance

Published online by Cambridge University Press:  26 April 2006

D. Nicolaou ,
R. Liu  and
T. N. Stevenson
D. Nicolaou
Affiliation:
Department of Engineering, University of Manchester, Oxford Road, Manchester M13 9PL, UK Present address: Department of Mechanical Engineering, University of Liverpool, PO Box 147, Liverpool, L69 3BX, UK.
R. Liu
Affiliation:
Department of Engineering, University of Manchester, Oxford Road, Manchester M13 9PL, UK
T. N. Stevenson
Affiliation:
Department of Engineering, University of Manchester, Oxford Road, Manchester M13 9PL, UK
Get access Rights & Permissions [Opens in a new window]

Abstract

The way in which energy propagates away from a two-dimensional oscillatory disturbance in a thermocline is considered theoretically and experimentally. It is shown how the St. Andrew's-cross-wave is modified by reflections and how the cross-wave can develop into thermocline waves. A linear shear flow is then superimposed on the thermocline. Ray theory is used to evaluate the wave shapes and these are compared to finite-difference solutions of the full Navier–Stokes equations.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 254 , September 1993 , pp. 401 - 416
Copyright
© 1993 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

Appleby, J. C. & Crighton, D. G. 1986 Non Boussinesq effects in the diffraction of internal waves from an oscillating cylinder. Q. J. Mech. Appl. Maths 39, 209.Google Scholar
Bretherton, F. P. 1966 The propagation of groups of internal waves in a shear flow. Q. J. R. Met. Soc. 92, 466.Google Scholar
Gordon, D., Klement, U. R. & Stevenson, T. N. 1975 A viscous internal wave in a stratified fluid whose buoyancy frequency varies with altitude. J. Fluid Mech. 69, 615.Google Scholar
Groen, P. 1948 Contributions to the theory of internal waves. Konin. Neder. Met. Inst. Bilt. Meden-Verhand. Ser. B2.(11).Google Scholar
Harlow, F. H. & Welch, J. E. 1965 Numerical calculation of time-dependent viscous incompressible flow of fluid with a free surface. Phys. Fluids 8, 2182.Google Scholar
Kanellopulos, D. 1982 Internal wave experiments. PhD thesis, University of Manchester.
Kistovich, A. V., Neklyudov, V. I. & Chashechkin, Y. D. 1990 Non-linear two-dimensional internal waves generated by a periodically moving source in an exponentially stratified medium. Izv. Atmos. Ocean. Phys. 26, No. 10.Google Scholar
Koop, C. G. & McGee, B. 1986 Measurements of internal gravity waves in a continuously stratified shear flow. J. Fluid Mech. 172, 453.Google Scholar
Krauss, W. 1966 Methoden und Ergebnisse der Theoretischen Ozeanographie. Interne Wellen 2, 32.Google Scholar
Laws, P., Peat, K. & Stevenson, T. N. 1982 An interferometer to study density stratified flows. J. Phys. E: Sci. Instrum. 15, 1327.Google Scholar
Lighthill, M. J. 1978 Waves in Fluids. Cambridge University Press.
Liu, R. 1989 A numerical and analytical study of internal waves in stratified fluids. PhD thesis, University of Manchester.
Liu, R., Nicolaou, D. & Stevenson, T. N. 1990 Waves from an oscillatory disturbance in a stratified shear flow. J. Fluid Mech. 219, 609.Google Scholar
Liu, R. & Stevenson, T. N. 1989 A finite difference method for modelling internal waves. Aero. Rep. 8908, Dept. of Engng, University of Manchester.
MacIver, R. D. 1988 Experimental investigation of the interaction of internal gravity waves in a thermocline with a linear shear flow. MSc thesis, University of Manchester.
Makarov, S. A., Neklyudov, V. I. & Chashechkin, Y. D. 1990 Spatial structure of two-dimensional monochromatic internal wave beams in an exponentially stratified fluid. Izv. Atmos. Ocean. Phys. 26, No. 7.Google Scholar
Nicolaou, D. 1987 Internal waves around a moving body. PhD thesis, University of Manchester.
Phillips, O. M. 1966 The Dynamics of the Upper Ocean. Cambridge University Press.
Roberts, J. 1975 Internal Gravity Waves in the Ocean. Marcel Dekker.
Stevenson, T. N. 1973 The phase configuration of internal waves around a body moving in a density stratified fluid. J. Fluid Mech. 60, 759.Google Scholar
Stevenson, T. N., Kanellopulos, D. & Constantinides, M. 1986 The phase configuration of trapped internal waves from a body moving in a thermocline. Appl. Sci. Res. 43, 91.Google Scholar
Thomas, N. H. & Stevenson, T. N. 1972 A similarity solution for viscous internal waves. J. Fluid Mech. 54, 495.Google Scholar
Thorpe, S. A. 1968 On the shape of progressive internal waves. Phil. Trans. Roy. Soc. Lond. A 263, 563.Google Scholar
Voisin, B. 1991 Internal wave generation in uniformly stratified fluids. Part 1. Green's function and point sources. J. Fluid Mech. 231, 439.Google Scholar
Young, J. A. & Hirt, C. W. 1972 Numerical calculation of internal wave motions. J. Fluid Mech. 56, 265.Google Scholar