Zonal shear flows with a free surface: Hamiltonian formulation and linear and nonlinear stability

References

• Arnol'd , VI . 1978 . Mathematical Methods of Classical Mechanics , New York : Springer-Verlag .
   Google Scholar
• Benzi , R , Pierini , S , Vulpiani , A and Salusti , E . 1982 . On nonlinear hydrodynamic stability of planetary vortices . Geophys. Astrophys. Fluid Dyn. , 20 : 293 – 306 .
   Web of Science ®Google Scholar
• Charney , JG . 1947 . On the scale of atmospheric motions . Geophys. Publ. Kosjones Nor. Vidensk. Akad. Oslo , 17 : 1 – 17 .
   Google Scholar
• Chomaz , JM , Raband , M , Basdevant , C and Couder , Y . 1988 . Experimental and numerical investigation of a forced circular shear layer . J. Fluid Mech. , 187 : 115 – 135 .
   Web of Science ®Google Scholar
• Drazin , PG , Beaumont , DN and Coaker , SA . 1982 . On Rossby waves modified by basic shear and barotropic instability . J. Fluid Mech. , 124 : 439 – 456 .
   Web of Science ®Google Scholar
• Flierl , GR , Stern , ME and Whitehead , JA . 1983 . The physical significance of modons: laboratory experiments and general integral constraints . Dyn. Atmos. Oceans , 7 : 233 – 263 .
   Web of Science ®Google Scholar
• Gnevyshev , VG and Shrira , VI . 1990 . On the evaluation of barotropic–baroclinic instability parameters of zonal flows on a beta-plane . J. Fluid Mech. , 221 : 161 – 181 .
   Web of Science ®Google Scholar
• Hickernell , FJ . 1985 . An upper bound on the growth rate of a linear instability in a homogeneous shear flow . Stud. Appl. Math. , 72 : 87 – 93 .
   Google Scholar
• Howard , LN and Drazin , PG . 1964 . On the instability of a parallel flow of inviscid fluid in a rotating system with variable coriolis parameter . J. Math. Phys. , 43 : 83 – 99 .
   Web of Science ®Google Scholar
• Kuo , HL . 1949 . Dynamic instability of two-dimensional non-divergent flow in a barotropic atmosphere . J. Meteorol. , 6 : 105 – 122 .
   Google Scholar
• Kuo , HL . 1973 . Dynamics of quasi-geostrophic flows and instability theory . Adv. Appl. Mech. , 13 : 247 – 330 .
   Google Scholar
• Lipps , FB . 1962 . The barotropic stability of the mean winds in the atmosphere . J. Fluid Mech. , 12 : 397 – 407 .
   Web of Science ®Google Scholar
• Marcus , PS . 1988 . Numerical simulation of Jupiter's great red spot . Nature , 331 : 693 – 696 .
   Web of Science ®Google Scholar
• Nycander , J . 1988 . New stationary vortex solutions of the Hasegawa–Mima equation . J. Plasma Phys. , 39 : 413 – 430 .
   Web of Science ®Google Scholar
• Pedlosky , J . 1964a . The stability of currents in the atmosphere and the oceans, Part I . J. Atmos. Sci. , 21 : 201 – 219 .
   Web of Science ®Google Scholar
• Pedlosky , J . 1964b . The stability of currents in the atmosphere and the oceans, Part II . J. Atmos. Sci. , 21 : 342 – 353 .
   Web of Science ®Google Scholar
• Ripa , P . 1983 . General stability conditions for zonal flows in a one-layer model on the β-plane or the sphere . J. Fluid Mech. , 126 : 463 – 469 .
   Web of Science ®Google Scholar
• Ripa , P . 1992 . Wave energy-momentum and pseudoenergy-momentum conservation for the layered quasi-geostrophic instability problem . J. Fluid Mech. , 235 : 379 – 398 .
   Web of Science ®Google Scholar
• Ripa , P . 1993 . Arnol'd's second stability theorem for the equivalent barotropic model . J. Fluid Mech. , 257 : 597 – 605 .
   Web of Science ®Google Scholar
• Shivamoggi , BK . 2002 . A generalized class of nonlinear Rossby localized structures in geophysical fluid flows . Chaos Soliton. Fract. , 14 : 469 – 477 .
   Web of Science ®Google Scholar
• Shivamoggi , BK and Rollins , DK . 2001 . Linear stability of zonal shear flows with a free surface . Geophys. Astrophys. Fluid Dyn. , 95 : 31 – 53 .
   Web of Science ®Google Scholar
• Sommeria , J , Meyers , SD and Swinney , HL . 1988 . Laboratory simulation of Jupiter's great red spot . Nature , 331 : 689 – 693 .
   Web of Science ®Google Scholar