Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-18T01:17:55.134Z Has data issue: false hasContentIssue false
  • English
  • Français

On internal waves generated by large-amplitude circular and rectilinear oscillations of a circular cylinder in a uniformly stratified fluid

Published online by Cambridge University Press:  01 October 2008

EUGENY V. ERMANYUK  and
NIKOLAI V. GAVRILOV
EUGENY V. ERMANYUK
Affiliation:
Lavrentyev Institute of Hydrodynamics, 630090, Novosibirsk, Russiaermanyuk@hydro.nsc.ru
NIKOLAI V. GAVRILOV
Affiliation:
Lavrentyev Institute of Hydrodynamics, 630090, Novosibirsk, Russiaermanyuk@hydro.nsc.ru
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper presents an experimental study of internal waves generated by circular and rectilinear oscillations of a circular cylinder in a uniformly stratified fluid. The synthetic schlieren technique is used for quantitative analysis of the internal-wave parameters. It is shown that at small oscillation amplitudes, the wave pattern observed for circular oscillations is in good agreement with linear theory: internal waves are radiated in the wave beams passing through the first and third quadrants of a Cartesian coordinate system for the clockwise direction of the cylinder motion, and the intensity of these waves is twice the intensity measured for ‘St Andrew's cross’ waves generated by purely horizontal or vertical oscillations of the same frequency and amplitude. As the amplitude of circular oscillations increases, significant nonlinear effects are observed: (i) a strong density-gradient ‘zero-frequency’ disturbance is generated, and (ii) a region of intense fluid stirring is formed around the cylinder serving as an additional dissipative mechanism that changes the shape of wave envelopes and decreases the intensity of wave motions. In the same range of oscillation amplitudes, the wave generation by rectilinear (horizontal and vertical) oscillations is shown to be by and large a linear process, with moderate manifestations of nonlinearity such as weak ‘zero-frequency’ disturbance and weak variation of the shape of wave envelopes with the oscillation amplitude. Analysis of spatiotemporal images reveals different scenarios of transient effects in the cases of circular and rectilinear oscillations. In general, circular oscillations tend to generate disturbances evolving at longer time scales.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 613 , 25 October 2008 , pp. 329 - 356
Copyright
Copyright © Cambridge University Press 2008

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

REFERENCES

Adrian, R. J. 1991 Particle-imaging techniques for experimental fluid dynamics. Annu. Rev. Fluid. Mech. 23, 261–304.CrossRefGoogle Scholar
Adrian, R. J. 2005 Twenty years of particle image velocimetry. Exps. Fluids 23, 261–304.Google Scholar
Baidulov, V. G. & Chashechkin, Yu. D. 1993 The diffusion effect on the boundary flow in a continuously stratified fluid. Izv. Atmos. Ocean. Phys. 29, 641–647.Google Scholar
Baidulov, V. G. & Chashechkin, Yu. D. 1996 A boundary current induced by diffusion near a motioness horizontal cylinder in a continuously stratified fluid. Izv. Atmos. Ocean. Phys. 32, 751–756.Google Scholar
Balmforth, N. J., Smith, S. G. L. & Young, W. R. 1998 Dynamics of interfaces and layers in a stratified turbulent fluid. J. Fluid Mech. 355, 329–358.CrossRefGoogle Scholar
Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.Google Scholar
Bronshtein, I. N., Gurov, K. P., Kuznetsov, E. B. 1959 A Short Physical–Technical Handbook, vol. 1. Gos. Izdat. Fiz. mat. Lit. (in Russian), Mosow.Google Scholar
Dalziel, S. B. 2000 Synthetic schlieren measurements of internal waves generated by oscillating a square cylinder. Proc. 5th Intl Symp. on Stratified Flows, Vancouver, Canada, 10–13 July 2000, vol. 2, pp. 743–748. University of British Columbia, Vancouver.Google Scholar
Dalziel, S. B., Hughes, G. O. & Sutherland, B. R. 2000 Whole field density measurements by ‘synthetic’ schlieren. Exps. Fluids 28, 322–335.CrossRefGoogle Scholar
Dean, W. R. 1948 On the reflection of surface waves by a submerged circular cylinder. Proc. Camb. Phil. Soc. 44, 483–491.CrossRefGoogle Scholar
Ermanyuk, E. V. 2000 The use of impulse response functions for evaluation of added mass and damping coefficient of a circular cylinder oscillating in a linearly stratified fluid. Exps. Fluids 28, 152–159.CrossRefGoogle Scholar
Ermanyuk, E. V. & Gavrilov, N. V. 2001 Force on a body in a continuously stratified fluid. Part 1. Circular cylinder. J. Fluid Mech. 451, 421–443.CrossRefGoogle Scholar
Ermanyuk, E. V. & Gavrilov, N. V. 2005 Duration of transient processes in the formation of internal-wave beams. Dokl. Phys. 50, 548–550.CrossRefGoogle Scholar
Ermanyuk, E. V. & Gavrilov, N. V. 2007 A note on the propagation speed of a weakly dissipative gravity current. J. Fluid Mech. 574, 393–403.CrossRefGoogle Scholar
Flynn, M. R., Onu, K. & Sutherland, B. R. 2003 Internal wave excitation by a vertically oscillating sphere. J. Fluid Mech. 494, 65–93.CrossRefGoogle Scholar
Garrett, C. & Kunze, E. 2007 Internal tide generaton in the deep ocean. Annu. Rev. Fluid Mech. 39, 57–87.CrossRefGoogle Scholar
Gavrilov, N. V. & Ermanyuk, E. V. 1997 Internal waves generated by circular translational motion of a cylinder in a linearly stratified fluid. J. Appl. Mech. Tech. Phys. 38, 224–227.CrossRefGoogle Scholar
Gostiaux, L. & Dauxois, T. 2007 Laboratory experiments on the generation of internal tidal beams over steep slopes. Phys. Fluids 19, 028102.CrossRefGoogle Scholar
Gostiaux, L., Didelle, H., Mercier, S. & Dauxois, T. 2007 A novel internal waves generator. Exps. Fluids 42, 123–130.CrossRefGoogle Scholar
Hopfinger, E. J. 1987 Turbulence in stratified fluids: a review. J. Geophys. Res. 92, 5287–5303.Google Scholar
Hurley, D. G. 1997 The generation of internal waves by vibrating elliptic cylinders. Part 1. Inviscid solution. J. Fluid Mech. 351, 105–118.CrossRefGoogle Scholar
Hurley, D. G. & Keady, G. 1997 The generation of internal waves by vibrating elliptic cylinders. Part 2. Approximate viscous solution. J. Fluid Mech. 351, 119–138.CrossRefGoogle Scholar
Hurley, D. G. & Hood, M. G. 2001 The generation of internal waves by vibrating elliptic cylinders. Part 3. Angular oscillations and comparison of theory with recent experimental observations. J. Fluid Mech. 433, 61–75.CrossRefGoogle Scholar
Ivey, G. N. & Corcos, G. M. 1982 Boundary mixing in a stratified fluid. J. Fluid Mech. 121, 1–26.CrossRefGoogle Scholar
Linden, P. F. & Weber, J. E. 1977 The formation of layers in a double-diffusive system with a sloping boundary. J. Fluid Mech. 81, 757–773.CrossRefGoogle Scholar
Longuet-Higgins, M. S. 1970 Steady currents induced by oscillations round islands. J. Fluid Mech. 42, 701–720.CrossRefGoogle Scholar
Mowbray, D. E. & Rarity, B. S. H. 1967 A theoretical and experimental investigation of the phase configuration of internal waves of small amplitude in a density-stratified fluid. J. Fluid Mech. 28, 1–16.CrossRefGoogle Scholar
Ogilvie, T. F. 1963 First- and second-order forces on a cylinder submerged under a free surface. J. Fluid Mech. 16, 451–472.CrossRefGoogle Scholar
Onu, K., Flynn, M. R. & Sutherland, B. R. 2003 Schlieren measurement of axisymmetric internal wave amplitudes. Exps. Fluids 35, 24–31.CrossRefGoogle Scholar
Peacock, T. & Tabaei, A. 2005 Visualiation of nonlinear effects in reflecting internal wave beams. Phys. Fluids 17, 061702.CrossRefGoogle Scholar
Phillips, O. M. 1970 On flows induced by diffusion in a stably stratified fluid. Deep-Sea Res. 17, 435–443.Google Scholar
Riley, N. 1971 Stirring of a viscous fluid. Z. Angew. Math. Phys. 22, 645–653.CrossRefGoogle Scholar
Scase, M. M. & Dalziel, S. B. 2006 Internal wave fields generated by a translating body in a stratified fluid: experimental comparison. J. Fluid Mech. 564, 305–331.CrossRefGoogle Scholar
Sturova, I. V. 1994 Plane problem of hydrodynamic rocking of a body submerged in a two-layer fluid without forward speed. Fluid Dyn. 29, 414–423.CrossRefGoogle Scholar
Sturova, I. V. 1999 Problems of radiation and diffraction for a circular cylinder in a stratified fluid. Fluid Dyn. 34, 521–533.Google Scholar
Sutherland, B. R. & Linden, P. F. 2002 Internal wave excitation by a vertically oscillating elliptic cylinder. Phys. Fluids 14 (2), 721–739.CrossRefGoogle Scholar
Sutherland, B. R., Dalziel, S. B., Hughes, G. O. & Linden, P. F. 1999 Visualization and measurement of internal waves by ‘synthetic’ schlieren. Part 1. Vertically oscillating cylinder. J. Fluid Mech. 390, 93–126.CrossRefGoogle Scholar
Sutherland, B. R., Hughes, G. O., Dalziel, S. B. & Linden, P. F. 2000 Internal waves revisited. Dyn. Atmos. Oceans 31, 209–232.CrossRefGoogle Scholar
Thorpe, S. A. 1982 On the layer produced by rapidly oscillating a vertical grid in a uniformly stratified fluid. J. Fluid Mech. 124, 391–409.CrossRefGoogle Scholar
Turner, J. S. 1973 Buoyancy Effects in Fluids. Cambridge University Press.CrossRefGoogle Scholar
Ursell, F. 1950 Surface waves in the presence of a submerged circular cylinder, I and II. Proc. Camb. Phil. Soc. 46, 141–158.CrossRefGoogle Scholar
Vargaftik, N. B. 1963 Handbook on the Thermophysical Properties of Gases and Liquids. Gos. Izdat. Fiz.-Mat. Lit. (in Russian). Moscow.Google Scholar
Vlasenko, V., Stashchuk, N., Hutter, K. 2005 Baroclinic Tides. Theoretical Modeling and Observational Evidence. Cambridge University Press.CrossRefGoogle Scholar
Voisin, B. 2003 Limit states of internal wave beams. J. Fluid Mech. 496, 243–293.CrossRefGoogle Scholar
Westerweel, J. 1997 Fundamentals of digital particle image velocimetry. Meas. Sci. Technol. 8, 1379–1392.CrossRefGoogle Scholar
Wu, J. 1969 Mixed region collapse with internal wave generation in a density-stratified medium. J. Fluid Mech. 35, 531–544.CrossRefGoogle Scholar
Wunsch, C. 1970 On oceanic boundary mixing. Deep-Sea Res. 17, 293–301.Google Scholar
Xu, Y., Boyer, D. L., Fernando, H. J. S. & Zhang, X. 1997 Motion fields generated by the oscillatory motion of a circular cylinder in a linearly stratified fluid. Expl Thermal Fluid Sci. 14, 277–296.CrossRefGoogle Scholar