Energy integral description of the development of Kelvin-Helmholtz billows

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Liu, J. T. C. ; Merkine, L. (2011)

DOI: 10.1111/j.2153-3490.1976.tb00669.xIn this paper we study the development of instability waves in a stratified shear flow which occurs, for instance, in frontal zones and on large scale internal waves where the Richardson number is sufficiently low. The model is based on splitting the flow into the mean flow and instability wave components. The basis for the interaction between the mean flow and the wave is their respective vertically integrated energy flux equations. The wave description is obtained through a shape assumption: the time dependent wave amplitude is determined by its energy equation solved jointly with the mean flow and the vertical shape function is given by the local linear theory. The instability wave kinetic energy development is determined by the balance between energy production from the mean flow and the conversion of fluctuation kinetic to potential energy. From the energy integral considerations, the numerical results show moderately good agreement with observations in our estimate of the lifetime of the wave and the doubling of the thickness of the mean shear layer during this time. The modification of the mean flow velocity and temperature profiles is explained via the effects of the wave generated vertical momentum and heat (or buoyancy) fluxes, respectively.DOI: 10.1111/j.2153-3490.1976.tb00669.x
  • References (45)
    45 references, page 1 of 5

    Atlas, D., Metcalf, J. I., Richter, J. H. & Gosaard, E. E. 1970. The birth of “CAT” and microscale turbulence. J. Atnaos. Sci. 27, 90S913.

    Axford, D. N. 1970. An observation of gravity waves in shear flow in the lower stratospllere. Quart. J. R . Met. SOC.96, 273-286.

    Axford, D. N. 1973. On an observation of turbulent waves on the tropopause surface. Quart. J. R . Met. SOC.99, 438-449.

    Browning, K. A. 1971. Structure of the atmosphere in the vicinity of large amplitude Kelvin-Helmholtz billows. Quart. J. R. Met. SOC.97, 283-299.

    Browning, K. A. & Watkins, C. D. 1970. Observations of clear air turbulence by high power radar. Nature 227, 260-263.

    Browning, K. A., Bryant, G. W., Starr, J. R. & Axford, D. N. 1973. Air motion within KelvinHelmholtz. billows determined from simultaneous Doppler radar and aircraft measurements. Quart. J . R. Met. SOC.99, 608-618.

    Cox, C., Nagata, Y. & Osborn, T. 1969. Ocean fine structure and internal waves. B d l . Jcvpaneee SOC. F h h . Oceanogr. (Special Number, Prof. Uda's Commemorative Papers), pp. 67-71.

    Drazin, P. G. 1970. Kelvin-Helmholtz instability of finite amplitude. J. Fluid Mech. 42, 321-335.

    Dutton, J. A. 1971. Clear-air turbulence, aviation, and atmospheric science. Revs. Qeophys. and Space Phys. 9, 613-657.

    Gossard, E. E., Richter, J. H. & Atlas, D. 1970. Internal waves in the atmosphere from high resolution radar measurements. J. Qeophys. Res. 75, 3523-3536.

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