A mechanism for the barotropic equilibration of baroclinic waves

Abstract The barotropic instability of finite amplitude waves is suggested as a mechanism for explaining the equilibration of a baroclinic wave growing in a meridionally independent vertical shear flow. A quasigeostrophic two-layer channel model on an f-plane is used to give evidence for this hypothesis. Three solutions with different flow symmetries are adopted for the analysis. Numerical simulations reveal that the flow symmetry of the initial small amplitude perturbation can have a large impact on wave structure evolution and energetics. The flow symmetry of the first solution forces the wave to excite symmetric life cycles with baroclinic growth and baroclinic decay. The flow symmetries of the other solutions enable the wave to undergo an asymmetric life cycle with baroclinic growth followed by a barotropic decay that occurs when the fundamental wave has a sufficiently large aspect ratio. Accordingly, a linear-stability analysis of a steady barotropic wave reveals an increasing destabilization with in...

[1]  M. McIntyre,et al.  On the Representation of Rossby Wave Critical Layers and Wave Breaking in Zonally Truncated Models. , 1987 .

[2]  R. Young,et al.  Nonlinear Baroclinic Instability on the Sphere: Multiple Life Cycles with Surface Drag and Thermal Damping , 1992 .

[3]  J. Pedlosky,et al.  A Numerical Study of Baroclinic Instability at Large Supereriticality , 1986 .

[4]  B. Boville.  Amplitude Vacillation on a β-Plane , 1980 .

[5]  N. Nakamura.  Momentum flux, flow symmetry, and the nonlinear barotropic governor , 1993 .

[6]  J. Hart.  Wavenumber Selection in Nonlinear Baroclinic Instability , 1981 .

[7]  J. Hart.  A laboratory study of baroclinic instability , 1972 .

[8]  R. Pfeffer,et al.  Time-Dependent Modes of Behavior of Thermally Driven Rotating Fluids , 1980 .

[9]  L. Gray,et al.  Concerning the effect of surface drag on the circulation of a baroclinic planetary atmosphere , 1986 .

[10]  B. Hoskins,et al.  The Life Cycles of Some Nonlinear Baroclinic Waves , 1978 .

[11]  C. Schär,et al.  The Palette of Fronts and Cyclones within a Baroclinic Wave Development , 1991 .

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

[13]  E. T. Eady,et al.  Long Waves and Cyclone Waves , 1949 .

[14]  H. Kuo.  Dynamics of Quasigeostrophic Flows and Instability Theory , 1973 .

[15]  M. Rosenbluth,et al.  Analytical model of the tilting'' instability , 1994 .

[16]  Norman A. Phillips,et al.  Energy Transformations and Meridional Circulations associated with simple Baroclinic Waves in a two-level, Quasi-geostrophic Model , 1954 .

[17]  J. G. Charney,et al.  THE DYNAMICS OF LONG WAVES IN A BAROCLINIC WESTERLY CURRENT , 1947 .

[18]  B. Hoskins,et al.  Eliassen-Palm Cross Sections for the Troposphere , 1980 .

[19]  A. Hollingsworth,et al.  On the Simplest Example of the Barotropic Instability of Rossby Wave Motion , 1973 .

[20]  Ragnar Fjørtoft,et al.  On the Changes in the Spectral Distribution of Kinetic Energy for Twodimensional, Nondivergent Flow , 1953 .

[21]  R. Grotjahn.  Baroclinic instability in a long wave environment. Part I: Review , 1984 .

[22]  Brian F. Farrell,et al.  Optimal Excitation of Baroclinic Waves , 1989 .

[23]  L. Howard,et al.  Large-scale flow generation in turbulent convection. , 1981, Proceedings of the National Academy of Sciences of the United States of America.

[24]  E. Lorenz.  Barotropic Instability of Rossby Wave Motion , 1972 .

[25]  Ruby Krishnamurti,et al.  Large-scale flow in turbulent convection: a mathematical model , 1986, Journal of Fluid Mechanics.

[26]  Noboru Nakamura,et al.  Nonlinear Equilibration of Two-Dimensional Eady Waves , 1989 .

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

[28]  Brian J. Hoskins,et al.  Stability of the Rossby-Haurwitz wave , 1973 .

[29]  M. Mundt,et al.  Secondary instability, EOF reduction, and the transition to baroclinic chaos , 1994 .

[30]  Jerry F. Magnan,et al.  Transitions between baroclinic flow regimes , 1986 .

[31]  W. Randel,et al.  The observed life cycle of a baroclinic instability , 1985 .

[32]  I. Held,et al.  Barotropic Decay of Baroclinic Waves in a Two-Layer Beta-Plane Model , 1989 .