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The energetics of breaking events in a resonantly forced internal wave field

Published online by Cambridge University Press:  26 April 2006

John R. Taylor
John R. Taylor
Affiliation:
Centre of Water Research, The University of Western Australia, Nedlands, Western Australia, 6009
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Abstract

A series of vertical density profiles was taken in a stratified tank in which a standing internal wave was forced to amplitudes at which it became unstable and, as a result of the instability, localized patches of mixing were generated within the fluid. By resorting the density profiles the available potential energy in the patches could be calculated and, by comparison with the average buoyancy flux in the tank (determined from density profiles taken before and after each mixing run), an average efficiency of utilization of available potential energy, ηAPE, was calculated. Along with previous measurements of the flux Richardson number, Rif, ηAPE was used to show that the mean value of the overturn Froude number, Frf, in the patches was 1, thus implying a balance between the rate of release of available potential energy and dissipation in the mixing patches. On the other hand, the patch-averaged overturn Reynolds number, Ret, was so low that, based on the results of previous laboratory experiments on stratified mixing in the wake of a biplanar grid, most of the patches cannot have been actively mixing at the time of sampling.

It is shown that the temperature and conductivity gradient spectra in different patches can be interpreted in a way consistent with the visualization of mixing events, that is, showing an evolution from the generation of an initially unstable density distribution, through the formation of coherent structures as the fluid restratifies and finally the degeneration of these structures into the finer scales of motion at which mixing occurs.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 239 , June 1992 , pp. 309 - 340
Copyright
© 1992 Cambridge University Press

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References

Chatfield, C.: 1984 The Analysis of Time Series: An Introduction. Chapman and Hall. 286 pp.
Dillon, T. M.: 1982 Vertical overturns: a comparison of Thorpe and Ozmidov length scales. J. Geophys. Res. 87, 9601–9613.Google Scholar
Dillon, T. M.: 1984 The energetics of overturning structures: implications for the theory of fossil turbulence. J. Phys. Oceanogr. 14, 541–549.Google Scholar
Dillon, T. M. & Caldwell, D. R., 1980 The Batchelor spectrum and dissipation in the upper ocean. J. Geophys. Res. 85, 1910–1916.Google Scholar
Fozdar, F. M., Parker, G. J. & Imberger, J., 1985 Matching temperature and conductivity sensor response characteristics. J. Phys. Oceanogr. 15, 1557–1569.Google Scholar
Fritts, D. C.: 1989 Gravity wave saturation, turbulence and diffusion in the atmosphere: observation theory and implications. In Parameterization of Small-Scale Processes, Proc. ‘Aha Hulik'a’ Hawaiian Winter Workshop (ed. P. Müller & D. Henderson), pp. 219–234. University of Hawaii at Manoa.
Gargett, A. E.: 1988 The scaling of turbulence in the presence of stable stratification. J. Geophys. Res. 93, 5021–5036.Google Scholar
Gargett, A. E.: 1989 Ocean turbulence. Ann. Rev. Fluid Mech. 21, 419–451.Google Scholar
Gargett, A. E.: 1990 Reply to comments on “the scaling of turbulence in the presence of vertical stratification’. J. Geophys. Res. 95, 11675–11677.Google Scholar
Gargett, A. E., Osborn, T. R. & Nasmyth, P. W., 1984 Local isotropy and the decay of turbulence in a stratified fluid. J. Fluid Mech. 144, 231–280.Google Scholar
Gregg, M. C.: 1989 Scaling turbulent dissipation in the thermocline. J. Geophys. Res. 94, 9686–9698.Google Scholar
Head, M. J.: 1983 The use of miniature four-electrode conductivity probes for high resolution measurement of turbulent density or temperature variations in salt-stratified water flows. Ph.D. dissertation, University of California, San Diego, 211 pp.
Imberger, J. & Ivey, G. N., 1991 On the nature of turbulence in a stratified fluid. Part 2: application to lakes. J. Phys. Oceanogr. 21, 659–680.Google Scholar
Itsweire, E. C.: 1984 Measurements of vertical overturns in a stably stratified turbulent flow. Phys. Fluids 27, 764–766.Google Scholar
Itsweire, E. C., Helland, K. N. & Van Atta, C. W. 1986 The evolution of grid generated turbulence in a stably stratified fluid. J. Fluid Mech. 162, 229–338.Google Scholar
Ivey, G. N. & Imberger, J., 1991 On the nature of turbulence in a stratified fluid, part I: the energetics of mixing. J. Phys. Oceanogr. 21, 650–658.Google Scholar
Kunze, E., Williams, A. J. & Briscoe, M. G., 1990 Observations of shear and vertical stability from a neutrally buoyant float. J. Geophys. Res. 95, 18127–18142.Google Scholar
Lienhard, J. H. & Van Atta, C. W. 1990 The decay of turbulence in thermally stratified flow. J. Fluid Mech. 210, 57–112.Google Scholar
Linden, P. F.: 1980 Mixing across a density interface produced by grid turbulence. J. Fluid Mech. 100, 691–703.Google Scholar
Mcewan, A. D.: 1983a The kinematics of stratified mixing through internal wavebreaking. J. Fluid Mech. 128, 47–57.Google Scholar
Mcewan, A. D.: 1983b Internal mixing in stratified fluids. J. Fluid Mech. 128, 59–80.Google Scholar
Mcewan, A. D., Mander, D. W. & Smith, R. K., 1972 Forced resonant second-order interaction between damped internal waves. J. Fluid Mech. 55, 589–608.Google Scholar
Mcewan, A. D. & Robinson, R. M., 1975 Parametric instability of internal gravity waves. J. Fluid Mech. 61, 667–687.Google Scholar
Moum, J. N.: 1989 Measuring turbulent fluxes in the ocean – the quest for κρ. In Parameterization of Small-Scale Processes, Proc. ‘Aha Hulik'a’ Hawaiian Winter Workshop (ed. P. Müller & D. Henderson), pp. 145–156. University of Hawaii at Manoa.
Munk, W.: 1981 Internal waves and small-scale processes. In Evolution of Physical Oceanography (ed. B. A. Warren & C. Wunsch). The MIT Press, 623pp.
Oakey, N. S.: 1982 Determination of the rate of dissipation of turbulent energy from simultaneous temperature and velocity shear microstructure shear measurements. J. Phys. Oceanogr. 12, 256–271.Google Scholar
Osborn, T. R.: 1980 Estimates of the local rate of vertical diffusion from dissipation measurements. J. Phys. Oceanogr. 10, 83–89.Google Scholar
Osborn, T. R. & Cox, C. S., 1972 Oceanic fine structure. Geophys. Fluid. Dyn. 3, 321–345.Google Scholar
Rohr, J. J., Itsweire, E. C., Helland, K. N. & Van Atta, C. W. 1988 Growth and decay of turbulence in a stably stratified shear flow. J. Fluid Mech. 195, 77–111.Google Scholar
Stillinger, D. C., Helland, K. N. & Van Atta, C. W. 1983 Experiments on the transition of homogeneous turbulence to internal waves in a stratified fluid. J. Fluid Mech. 131, 91–122.Google Scholar
Tennekes, H. & Lumley, J. L., 1972 A First Course in Turbulence. The MIT Press, 300pp.
Thorpe, S. A.: 1977 Turbulence and mixing in a Scottish loch. Phil. Trans. R. Soc. Lond. A 286, 125–181.Google Scholar
Tryggvason, G. & Unverdi, S. O., 1990 Computations of three-dimensional Rayleigh–Taylor instability. Phys. Fluids A 2, 656–659.Google Scholar
Turner, J. S.: 1979 Buoyancy Effects in Fluids. Cambridge University Press, 368pp.
Van Atta, C. 1990 Comment on “the scaling of turbulence in the presence of vertical stratification.’. J. Geophys. Res 95, 11673–11674.Google Scholar
Yamazaki, H.: 1990 Stratified turbulence near a critical dissipation rate. J. Phys. Oceanogr. 20, 1583–1598.Google Scholar