Variable Coefficient KdV Equation and the Analytical Diagnoses of a Dipole Blocking Life Cycle

A variable coefficient Korteweg de Vries (VCKdV) system is derived by considering the time-dependent basic flow and boundary conditions from the well-known Euler equation with an earth rotation term. The analytical solution obtained from the VCKdV equation can be successfully used to explain fruitful phenomena in fluid and other physical fields, for instance, the atmospheric blocking phenomena. In particular, a dipole blocking case happened during 9 April 1973 to 18 April 1973 read out from the National Center for Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR) reanalysis data is well described by the analytical solution.

[1]  D. Luo.  A barotropic envelope Rossby soliton model for block-eddy interaction. Part II: Role of westward-traveling planetary waves , 2005 .

[2]  Robert R. Long,et al.  Solitary Waves in the Westerlies , 1964 .

[3]  D. Korteweg,et al.  XLI. On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves , 1895 .

[4]  P. Malanotte‐Rizzoli,et al.  Nonlinear Stationary Rossby Waves on Nonuniform Zonal Winds and Atmospheric Blocking. Part I: The Analytical Theory , 1984 .

[5]  H. Tanaka.  A Numerical Simulation of Amplification of Low-Frequency Planetary Waves and Blocking Formations by the Upscale Energy Cascade , 1991 .

[6]  D. Luo.  Envelope solitary Rossby waves and modulational instabilities of uniform Rossby wave trains in two space dimensions , 1996 .

[7]  T. Kakutani,et al.  Second Order K-dV Soliton on a Nonlinear Transmission Line , 1984 .

[8]  Daniel F. Rex,et al.  Blocking Action in the Middle Troposphere and its Effect upon Regional Climate I. An Aerological Study of Blocking Action. , 1950 .

[9]  N. Flytzanis,et al.  Kink, breather and asymmetric envelope or dark solitons in nonlinear chains. I. Monatomic chain , 1985 .

[10]  Hiroshi L. Tanaka.  Numerical Simulation of a Life-Cycle of Atmospheric Blocking and the Analysis of Potential Vorticity , 1998 .

[11]  N. Zabusky,et al.  Interaction of "Solitons" in a Collisionless Plasma and the Recurrence of Initial States , 1965 .

[12]  Daniel F. Rex,et al.  Blocking Action in the Middle Troposphere and its Effect upon Regional Climate II. The Climatology of Blocking Action , 1950 .

[13]  D. Luo.  Derivation of a higher order nonlinear Schrödinger equation for weakly nonlinear Rossby waves , 2001 .

[14]  S. Colucci,et al.  Planetary-Scale Climatology of Explosive Cyclogenesis and Blocking , 1996 .

[15]  D. Luo,et al.  A Barotropic Envelope Rossby Soliton Model for Block Eddy Interaction. Part I: Effect of Topography , 2005 .

[16]  Roger Grimshaw,et al.  The Effect of Topography on the Dynamics of Interacting Solitary Waves in the Context of Atmospheric Blocking , 1999 .

[17]  F. Huang,et al.  Interaction between antecedent planetary‐scale envelope soliton blocking anticyclone and synoptic‐scale eddies: Observations and theory , 2001 .

[18]  J. Marshall,et al.  A Theoretical and Diagnostic Study of Solitary Waves and Atmospheric Blocking , 1989 .

[19]  R. Grimshaw,et al.  The formation of coherent structures in the context of blocking , 1999 .

[20]  N. N. Rao,et al.  DUST -ACOUSTIC WAVES IN DUSTY PLASMAS , 1990 .