Breaking Waves pp 357-366 | Cite as

Processes Leading to Filamentation of a Potential Vorticity Interface over a Topographic Slope

  • R. Grimshaw
  • Z. Yi
Conference paper
Part of the International Union of Theoretical and Applied Mechanics book series (IUTAM)


Using the barotropic, nondivergent model for flow over a topographic slope adjoined by a coastal barrier, a contour dynamics algorithm is developed to describe wave evolution on an interface separating two regions of uniform potential vorticity. We find that wave steepening due to advective nonlinearity is partially controlled by wave dispersion; the usual outcome for even small-amplitude waves is filamentation. A kinematic mechanism proposed by Pullin et al. [1] is used to identify criteria for when filamentation will occur. Of the various parameters in this system, the most important is found to be the ratio of the potential vorticity jump across the interface to the background potential vorticity.


Potential Vorticity Wave Crest Critical Layer Wave Steepen Topographic Slope 
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  1. [1]
    Pullin, D.I., Jacobs, P.A., Grimshaw, R.H.J. and Saffman, P.G., “Instability and filamentation of finite-amplitude waves on vortex layers of finite thickness”, J. Fluid Mech., 209, (1989) 359–384.MathSciNetADSMATHCrossRefGoogle Scholar
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    Grimshaw, R. and Yi, Z., “Evolution of a potential vorticity front over a topographic slope”, J. Phys. Ocean., 21, (1991) 1240–1255.ADSCrossRefGoogle Scholar
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    Send, U., “Vorticity and instability during flow reversals on the continental shelf”, J. Phys. Ocean., 19, (1989) 1620–1633.ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • R. Grimshaw
    • 1
  • Z. Yi
    • 2
  1. 1.School of MathematicsUniversity of New South WalesKensingtonAustralia
  2. 2.NRCMEFHai Dian Division, BeijingP.R. China

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