The Sine-Gordon Equation as a Model for a Rapidly Rotating Baroclinic Fluid

Recent work has shown that the Sine-Gordon and SIT equations describe the evolution of the envelope of baroclinic wave packets in a two-layer rapidly rotating fluid. The significance of this result is discussed with reference to the optical SIT problem and it is shown how this type of rotating fluid behaves in a simple way as a two-level pseudospin system. The periodic behaviour of the Sine-Gordon equation which is more appropriate for experimental situations is discussed. Experimental and numerical evidence suggests that recurrence of initial states occurs; behaviour which is strikingly similar to the FPU problem of solid state physics.

[1]  J. Pedlosky.  Finite-Amplitude Baroclinic Wave Packets , 1972 .

[2]  Peter D. Lax,et al.  Almost Periodic Solutions of the KdV Equation , 1976 .

[3]  A. Scott,et al.  The soliton: A new concept in applied science , 1973 .

[4]  Norman A. Phillips,et al.  A SIMPLE THREE-DIMENSIONAL MODEL FOR THE STUDY OF LARGE-SCALE EXTRATROPICAL FLOW PATTERNS , 1951 .

[5]  P. J. Mason,et al.  Baroclinic waves in a container with sloping end walls , 1975, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[6]  Alan R. Bishop,et al.  Solitons and Condensed Matter Physics , 1978 .

[7]  John D. Gibbon,et al.  AnN-soliton solution of a nonlinear optics equation derived by a general inverse method , 1973 .

[8]  S. Leibovich.  Weakly non-linear waves in rotating fluids , 1970, Journal of Fluid Mechanics.

[9]  John Whitehead,et al.  Finite bandwidth, finite amplitude convection , 1969, Journal of Fluid Mechanics.

[10]  Raymond Hide,et al.  An experimental study of thermal convection in a rotating liquid , 1958, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[11]  Mark J. Ablowitz,et al.  Method for Solving the Sine-Gordon Equation , 1973 .

[12]  R. Hide.  Some experiments on thermal convection in a rotating liquid , 1953 .

[13]  R. Miura.  The Korteweg–deVries Equation: A Survey of Results , 1976 .

[14]  Joseph Pedlosky,et al.  Finite-Amplitude Baroclinic Waves , 1970 .

[15]  M. Ablowitz,et al.  The Inverse scattering transform fourier analysis for nonlinear problems , 1974 .

[16]  R. Pfeffer,et al.  Wave Dispersion in a Rotating, Differentially Heated Cylindrical Annulus Of Fluid. , 1968 .

[17]  G. Lamb.  Analytical Descriptions of Ultrashort Optical Pulse Propagation in a Resonant Medium , 1971 .

[18]  J. Pedlosky.  Geophysical Fluid Dynamics , 1979 .

[19]  Raymond Hide,et al.  Sloping convection in a rotating fluid , 1975 .

[20]  L. Redekopp,et al.  On the theory of solitary Rossby waves , 1977, Journal of Fluid Mechanics.