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Norihiko Sugimoto, Keiichi Ishioka, and Katsuya Ishii

organized as follows. Section 2 describes basic equations and the setup of the nonlinear numerical experiment. Section 3 introduces the Ford–Lighthill equation for the forced-dissipative f -plane shallow water system, in which the source of gravity waves is defined. We also define gravity wave flux and introduce the power law of Fr for gravity wave flux using a scaling analysis. The results of numerical experiments for a wide parameter range of Ro and Fr are shown in section 4 . Here, we also

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

images. Section 3 describes our methodology for quantifying the inertia–gravity wave activity in any given laboratory image. Section 4 estimates the energy flux from the balanced flow into the inertia–gravity waves. Section 5 quantifies the variation of inertia–gravity wave activity with Rossby number. We speculate about the consequences for geophysical flows in section 6 , and we conclude with a summary and discussion in section 7 . 2. Laboratory experiment Figure 2 shows a schematic cross

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Kaoru Sato and Motoyoshi Yoshiki

frequency approaches zero. Another important finding was the dominance of downward energy flux associated with gravity waves in the polar night jet (PNJ) region, suggesting gravity wave sources in the polar stratosphere. Yoshiki and Sato (2000) examined seasonal variation of gravity waves in the polar stratosphere using operational radiosonde data from 33 stations over a period of 10 yr. It was shown that both potential and kinetic energies of gravity waves per unit mass are maximized in austral spring

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David A. Schecter

vorticity reduces to q = ζ / ϕ a in which ϕ a is the constant ambient geopotential. Furthermore, the mean torque per unit mass on the cyclone at the radius r is given to lowest order by in which h φ is the azimuthal average of h . Equation (19) indicates that an MC (in which d q / dr < 0) will lose angular momentum as a DVRW [( q ′) 2 ] grows. It is therefore sensible that the outward angular momentum flux of IG wave radiation acts to amplify the DVRW. b. The growth rate of a DVRW and its

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Yonghui Lin and Fuqing Zhang

conditions are employed for all model domains, and moist processes, surface fluxes, and friction are all neglected in the simulations. For this study, GROGRAT uses as its background atmosphere the 30-km (D2) output of the control simulation of Z04 , but the simulated data are coarsened to 60-km (0.5-km) horizontal (vertical) grids. This coarsened output is further smoothed using a five-point smoother to reduce the smaller-scale background variability though the overall ray-tracing results are hardly

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

heavier layer. A peristaltic pump was used to provide a constant volume flux. The fluid was injected through a thin vertical pipe with a diffuser. The pipe was located adjacent to the wall of the tank such that a baroclinic boundary jet formed readily along the wall. The tank was installed on the rotating table and rotated in an anticlockwise direction with a rate of Ω = 2.32 rad s −1 . The rotating table was driven by a servo-controlled direct-drive direct current motor such that the stability of the

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

extension of this theory to the baroclinic case. Ford’s derivation is based on the flux forms of the momentum and conservation of mass equations in shallow-water flow on the f plane. By forming the divergence and vorticity equations, and then combining them with conservation of mass and its second derivative, Ford obtained the following wave equation: in which g is the acceleration due to gravity, h is the layer depth, and h 0 is the layer depth far from the region of vortical motion; in

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Dong L. Wu and Stephen D. Eckermann

. Eckermann , S. D. , and Coauthors , 2006b : Imaging gravity waves in lower stratospheric AMSU-A radiances. Part 2: Validation case study. Atmos. Chem. Phys. , 6 , 3343 – 3362 . Ern , M. , P. Preusse , M. J. Alexander , and C. D. Warner , 2004 : Absolute values of gravity wave momentum flux derived from satellite data. J. Geophys. Res. , 109 . D20103, doi:10. 1029/2004JD004752 . Fetzer , E. J. , and J. C. Gille , 1994 : Gravity wave variance in LIMS temperatures. Part I

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

, 2005 : A baroclinic instability that couples balanced motions and gravity waves. J. Atmos. Sci. , 62 , 1545 – 1559 . Reeder , M. J. , and M. Griffiths , 1996 : Stratospheric inertia-gravity waves generated in a numerical model of frontogenesis. II: Wave sources, generation mechanisms and momentum fluxes. Quart. J. Roy. Meteor. Soc. , 122 , 1175 – 1195 . Rotunno , R. , W. C. Skamarock , and C. Snyder , 1994 : An analysis of frontogenesis in numerical simulations of baroclinic

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Vladimir Zeitlin

/ c 0 ) r , Eq. (26) takes the form of the Bessel equation: The pressure is proportional to the time derivative of the complex potential for the wave field. Hence, the matching condition is Only the n = 2 harmonics should be present in the wave field, and the following choice of its amplitude ensures the matching (29) : Here, H (2) n is the Hankel function of the second kind, a solution of (28) corresponding to the outward energy flux. 2) The effects of rotation In the rotating case at

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