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J. Vanneste

1. Introduction The atmosphere and oceans are typical examples of two-time-scale systems. As a result of fast rotation and strong stratification, their dynamics can be separated into a slow, or balanced, part evolving on an advective time scale L / U , and a fast part consisting of inertia–gravity waves (IGWs) evolving on time scales shorter than the inertial period f   −1 . Thus, the Rossby number which gives an estimate of the time-scale separation between the two types of motion, is

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Paul D. Williams, Thomas W. N. Haine, and Peter L. Read

1. Introduction Inertia–gravity waves are observed ubiquitously throughout the stratified parts of the atmosphere (e.g., Eckermann and Vincent 1993 ; Sato et al. 1997 ; Dalin et al. 2004 ) and ocean (e.g., Thorpe 2005 ). Orthodox mechanisms for inertia–gravity wave generation include dynamical instability (e.g., Kelvin–Helmholtz shear instability; Chandrasekhar 1961 ), which is a known source of atmospheric gravity waves ( Fritts 1982 , 1984 ). Another possible mechanism is the

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Chris Snyder, David J. Muraki, Riwal Plougonven, and Fuqing Zhang

. Fluid Mech. , 280 , 303 – 334 . Ford , R. , 1994c : The response of a rotating ellipse of uniform potential vorticity to gravity wave radiation. Phys. Fluids , 6A , 3694 – 3704 . Ford , R. , M. E. McIntyre , and W. A. Norton , 2000 : Balance and the slow quasimanifold: Some explicit results. J. Atmos. Sci. , 57 , 1236 – 1254 . Gill , A. E. , 1982 : Atmosphere–Ocean Dynamics . Academic Press, 662 pp . Griffiths , M. , and M. J. Reeder , 1996 : Stratospheric inertia

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Michael E. McIntyre

vulnerability of small-scale gravity waves to wave capture. For such waves, escape from the prison of a progenitor vortex dipole is unlikely to result in prolonged freedom. Because of the tendency toward passive-tracer behavior, there will be a robust statistical bias toward subsequent wave capture. Such a bias is clear from random-straining models such as that of Haynes and Anglade (1997) . It now seems that this, too, must be part of why atmospheric and oceanic flows often stay close to balance, and that

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Y. D. Afanasyev, P. B. Rhines, and E. G. Lindahl

. Geophys. Res. , 108 . 3322, doi:10.1029/2003JC001979 . Ford , R. , 1994 : Gravity wave radiation from vortex trains in rotating shallow water. J. Fluid Mech. , 281 , 81 – 118 . Ford , R. , M. E. McIntyre , and W. A. Norton , 2000 : Balance and the slow manifold: Some explicit results. J. Atmos. Sci. , 57 , 1236 – 1256 . Griffiths , R. W. , and P. F. Linden , 1981 : The stability of buoyancy-driven coastal currents. Dyn. Atmos. Oceans , 5 , 281 – 306 . Lighthill , J. M

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John A. Knox, Donald W. McCann, and Paul D. Williams

1. Introduction The theory of spontaneous imbalance owes its origins to Lighthill’s (1952) study of aerodynamically generated sound waves and Ford’s (1994) extension of the problem to rotating shallow-water flow and inertia–gravity wave generation. In their analyses, the waves are emitted spontaneously by the vortical flow. This characteristic distinguishes the spontaneous imbalance problem from the initial value imbalance and gravity wave generation of “geostrophic adjustment” ( Rossby

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David A. Schecter

periods. However, the negative radiation torque appeared to be less significant than the expected influence of oceanic surface drag. Despite recent progress, much remains to learn about the SI of intense mesoscale vortices. The extent to which DVRWs (as opposed to continuum perturbations) control IG wave emissions from baroclinic cyclones is unknown. Moreover, the effect of secondary circulation in the basic state is uncertain. The role of moisture is also relatively unexplored. Clearly, moisture

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Vladimir Zeitlin

fundamental parameters: Rossby and Burger numbers. The natural context for studying fast–slow decoupling is geostrophic adjustment of localized disturbances. This fundamental process, ubiquitous in the atmosphere and oceans, consists of the relaxation of any perturbation toward the state of geostrophic equilibrium (balance). Such process is an obvious source of IGW because any initially unbalanced disturbance is getting rid of its unbalanced part by emitting waves. This IGW emission is primary. As will be

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Dong L. Wu and Stephen D. Eckermann

vortex edge, enhanced-amplitude perturbations due to mountain waves are evident over southern South America, the Antarctic Peninsula, and New Zealand, but significant enhancements also occur over broader regions of the Southern Ocean well away from any mountains. The cross sections in Fig. 11 show some of this GW activity emanating from tropopause altitudes, presumably radiated from tropospheric jet stream instabilities associated with baroclinic storm systems that regularly form and propagate

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James J. Riley and Erik Lindborg

regions of the ocean on horizontal scales from those that are not much larger than Ozmidov scale (usually around 0.1–1 m) up to at least a few hundred meters. It is possible that the energy on the few hundred–meter scale is a result of a forward cascade due either to nonlinear internal wave interactions or stratified turbulence at larger scales, or it may be the remnants of turbulent patches, as observed in laboratory experiments (e.g., Spedding 1997 ; Praud et al. 2005 ). In the latter cases at

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