Abstract
The concept of planetary wave breaking (McIntyre andPalmer, 1983; 1984) is critically reviewed. It is concluded that the wave breaking signature is not unique to any particular dynamic event in the stratosphere. Therefore, the classification of stratospheric transport events, such as ‘wave breaking’, groups fundamentally different events together. Better qualification of the wave breaking signature and a more solid theoretical basis of planetary wave breaking must be presented if the concept is to be of significant utility in describing stratospheric tracer transport.
Similar content being viewed by others
References
Beland, M. (1976),Study of the Nonlinear Rossby Wave Critical Line Development in a Barotropic Zonal Flow, J. Atmos. Sci.,33, 2066–2078.
Benjamin, T. B andOliver, P. J. (1982),Hamiltonian Structure, Symmetries and Conservation Laws for Water Waves, J. Fluid. Mech.125, 137–185.
Butchart, N. andRemsberg, E. E. (1986),The Area of the Stratospheric Polar Vortex as a Diagnostic for Tracer Transport on an Isentropic Surface, submitted to J. Atmos. Sci.
Clough, S. A., Grahame, N. S. andO'Neill A. (1985),Potential Vorticity in the Stratosphere Derived Using Data from Satellites, Quart. J. R. Met. Soc.111, 335–358.
Dean, R. G. andDalrymple, R. A.,Water Wave Mechanics for Engineers and Scientists (Prentice-Hall, Englewood Cliffs, New Jersey 1984).
Dunkerton, T. J. andDelisi, D. P. (1986),Evolution of Potential Vorticity in the Winter Stratosphere of January–February 1979, J. Geophys. Res.,91, 1199–1208.
Hess, P. G. andHolton, J. R. (1985),The Origin of Temporal Variance in Long-Lived Trace Constituents in the Summer Stratosphere, J. Atmos. Sci.42, 1455–1463.
Hsu, C.-P. F. (1980),Air Parcel Motions During a Numerically Simulated Sudden Stratospheric Warming, J. Atmos. Sci.37, 2768–2792.
Hoskins, B. J., McIntyre, M. E. andRobertson, A. W. (1985),On the Use and Significance of Isentropic Potential Vorticity Maps, Quart. J. R. Met. Soc.,111, 877–946.
Killworth, P. D. andMcIntyre, M. E. (1985),Do Rossby-Wave Critical Layers Absorb, Reflect, or Over-Reflect?, J. Fluid Mech.,161, 449–492.
Lamb, H.,Hydrodynamics, (Dover, New York 1945).
Leovy, C. B., Sun, C.-R., Hitchman, M. H., Remsberg E. E., Russell III, J. M., Gordly, L. L., Gille, J. C. andLyjak, L. V. (1985),Transport of Ozone in the Middle Stratosphere: Evidence for Planetary Wave Breaking, J. Atmos. Sci.42, 230–244.
Longuet-Higgins, M. S.,On Breaking Waves. InProceedings of the Symposium on Waves on Water of Variable Depth,Lecture Notes in Physics no. 64 (Springer, Berlin 1977) pp. 129–130.
Longuet-Higgins, M. S. (1978a),The Instabilities of Gravity Waves of Finite Amplitude in Deep Water I. Superharmonics, Proc. R. Soc. Lond. A360, 471–488.
Longuet-Higgins, M. S. (1978b),The Instabilities of Gravity Waves of Finite Amplitude in Deep Water II. Subharmonics, Proc. R. Soc. Lond. A360, 489–505.
Longuet-Higgins, M. S. (1980a),A Technique for Time-dependent Free-Surface Flows, Proc. R. Soc. Lond. A371, 441–451.
Longuet-Higgins, M. S. (1980b),On the Forming of Sharp Corners at a Free Surface, Proc. R. Soc. Lond. A371, 453–478.
Longuet-Higgins, M. S. (1981),On the Overturning of Gravity Waves, Proc. R. Soc. Lond. A376, 377–400.
Longuet-Higgins, M. S. (1982),Parametric Solutions for Breaking Waves, J. Fluid Mech.121, 402–424.
Longuet-Higgins, M. S. andCokelet, E. D. (1976),The Deformation of Steep Surface Waves on Water I. A Numerical Method of Computation, Proc. R. Soc. Lond. A350, 1–26.
Longuet-Higgins, M. S. andCokelet, E. D. (1978),The Deformation of Steep Surface Waveson Water, Proc. R. Soc. Lond. A364, 1–28.
Matsuno, T. andNakamura K. (1979),The Eulerian-and Lagrangian-Meridional Circulations in the Stratosphere at the Time of a Sudden Warming, J. Atmos. Sci.36, 640–654.
McIntyre, M. E. andPalmer, T. N. (1983),Breaking Planetary Waves in the Stratosphere, Nature305, 593–600.
McIntyre, M. E. andPalmer, T. N. (1984),The ‘Surf Zone’ in the Stratosphere, J. Atmos. Terrest. Phys.46, 825–849.
Mied, R. P. andLindeman, G. J. (1984),Mass Transfer between Gulf Stream Rings, J. Geophys. Res.89, 6365–6372.
Price, R. K. (1971),The Breaking of Water Waves, J. Geophys. Res.76, 1576–1581.
Rood, R. B. (1983),Transport and the Seasonal Variation of Ozone, Pure Appl. Geophys.121, 1049–1064.
Rood, R. B. andSchoeberl, M. R. (1983),Ozone Transport by Diabatic and Planetary Wave Circulations on a β-Plane, J. Geophys. Res.88, 8491–8504.
Stewartson, K. (1978),The Evolution of the Critical Layer of a Rossby Wave, Geophys. Astrophys. Fluid Dynamics9, 185–200.
Stiassnie, M. andPeregrine D. H. (1980),Shoaling of Finite-Amplitude Surface Waves on Water of Slowlyvarying Depth, J. Fluid Mech.97, 783–805.
Stokes G. G. (1880),On the Theory of Oscillatory Waves. Appendix B: Considering Relative to the Greatest Height of Oscillatory Irrotational Waves which can be Propagated without Change of Form, Math. Phys. Papers1, 225–228.
Stordal, F., Isaken, I. S. A. andHorntveth, K. (1985),A Diabatic Circulation Two-Dimensional Model with Photochemistry: Simulations of Ozone and Long-Lived Tracers with Surface Sources, J. Geophys. Res.90, 5757–5776.
Thom, R. (1975),Structural Stability and Morphogenesis (W. A. Benjamin, Reading, Massachusetts 1975).
Vinje, T. andBrevig, P. Breaking Waves on Finite Water Depths. A Numerical Study (Ship Res. Inst. of Norway, Rep. R111.81, 1981).
Wang, P.-H. andMcCormack, M. P. (1985),Variations in Stratospheric Aerosol Optical Depth During Northern Warnings, J. Geophys. Res.90, 10597–10606.
Warn, T. andWarn, H. (1978),The Evolution of a Nonlinear Critical Level, Stud. Appl. Math.59, 37–71.
Welander, P. (1955),Studies on the General Development of Motion in a Two-Dimensional, Ideal Fluid, Tellus7, 141–156.
Whitham, G. B.,Linear and Nonlinear Waves (John Wiley and Sons, New York 1974).
Wu, J. (1979),Oceanic Whitecaps and Sea State, J. Phys. Oceanogr.9, 1064–1068.
Zeeman, E. C.,Breaking of Waves InProceedings of the Symposium on Differential Equations and Dynamical Systems,Lecture Notes in Mathematics no. 206 (Springer, Berlin 1971), pp. 2–6.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Rood, R.B. A critical analysis of the concept of planetary wave breaking. PAGEOPH 123, 733–755 (1985). https://doi.org/10.1007/BF00878405
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00878405