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Vladimir Zeitlin

adjustment in the equatorial tangent plane, see Le Sommer et al. (2004) ]. In this approach, the slow dynamics appears from the removal of resonances in the fast one by fast-time averaging. The nonlinear geostrophic adjustment of localized (finite energy) initial perturbations was considered by this method within the following models of increasing complexity: rotating shallow water (RSW), 2-layer RSW (2RSW) with a flat bottom and rigid lid boundary conditions, and hydrostatic primitive equations (HSPEs

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

directions and 15 km in the vertical. Vertical velocity is zero on the rigid upper and lower boundaries and the horizontal boundary conditions are periodic. The model includes a sponge layer above 12.5 km where the damping rate increases linearly from zero at the bottom of the layer to 10 −4 s −1 at the model top. For general aspects of the solution, we performed low-resolution runs, with 128 points in each horizontal direction and 64 points in the vertical, giving a grid spacing of 23.4 km

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David A. Schecter

temperature) of the atmosphere increases monotonically with altitude and that the axisymmetric PV distribution q ( r , θ ) of the unperturbed cyclone decreases monotonically with radius on a surface of constant θ . With suitable boundary conditions, such a vortex is stable in the context of balanced dynamics ( Montgomery and Shapiro 1995 ; Ren 1999 ). On the other hand, stability is not guaranteed when IG waves are allowed to interact with DVRWs—in which case SI can occur. a. PV and angular

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Shuguang Wang, Fuqing Zhang, and Chris Snyder

conditions ( Grell et al. 1994 ). A sponge layer is also included near the bottom boundary for MDJET. MM5 is configured to have zero tendencies at lateral boundaries. The MM5 built-in diffusion scheme (i.e., the deformation-dependent fourth-order form) is applied at interior points for all simulations. 3. Simulated gravity waves from jet dipoles This section discusses differences in gravity waves between SFJET and MDJET. It is suggested that wave generation is closely related to localized jets. The shift

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

waves. Starting with linearized equations of motion for a homogeneous density layer of depth H 0 , with boundary conditions We look for the solution in the form of horizontally propagating harmonics with vertical structure determined by their z -dependent amplitudes A single equation for pressure is then obtained with boundary conditions ∂ z p 0 (− H 0 ) = 0 and ∂ z p 0 (0) = ( ω 2 / g ) p 0 (0). Here ω ′= ω / f is the dimensionless frequency. The solution of (5.4) is given by with dispersion

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James J. Riley and Erik Lindborg

case, since the flows in this range are clearly highly anisotropic, and since other physics, namely stable density stratification, are strongly influencing the dynamics. Lindborg performed three-dimensional numerical simulations of forced, strongly stratified flow subject to the above conditions, and found inertial ranges as predicted (see Fig. 2 ). The constants were found to be C K ≈ C P ≈ 0.5. Riley and deBruynKops (2003) performed direct numerical simulations of decaying, strongly

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K. Ngan, P. Bartello, and D. N. Straub

, spontaneous imbalance may occur even for unbalanced motion of arbitrarily small amplitude ( Ford et al. 2000 ; Vanneste and Yavneh 2004 ), by contrast with the classic Rossby adjustment (or “dam break”) problem (e.g., Gill 1982 ), in which the adjustment occurs on the fast time scale and depends crucially on the (unbalanced) initial conditions. Indeed the phenomenon of spontaneous imbalance is essentially independent of the definition of balance that one chooses to adopt [ Vanneste and Yavneh (2004

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

1938 ; Cahn 1945 ) and from boundary condition perturbations leading to topographically forced gravity waves ( Smith 1979 ). Instead, it is fundamentally rooted in the “universal ‘internal’ . . . nonlinearity of atmospheric motions,” as demonstrated by Medvedev and Gavrilov (1995) in their independent extension of Lighthill’s theory. While the weakness of spontaneous emission in Lighthill–Ford theory is sometimes emphasized, in this paper we stress the fact that the theory does indeed predict

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Michael E. McIntyre

), together with compatible smoothness conditions (Gevrey regularity) and triply periodic boundary conditions as in V06 , V07 , and V08 . However, with nondiffusive, ideal-fluid flow and a velocity field that is less smooth (such as would be expected, for instance, with isentropic distributions of PV that have jump discontinuities), the projection integral might instead diminish algebraically with R . Here, the R dependence would be that of a set of ideal-fluid cases computed over a finite time

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Gregory J. Hakim

equation and the quasigeostrophic (QG) system, the dynamics compress naturally on this variable. Furthermore, two basic facts elevate the status of PV among other control variables. The first fact is that linear modes of the primitive equations for states of rest are distinguished, exactly, by linearized PV, 1 and therefore linear inertia–gravity waves are effectively filtered through a PV inversion decompression algorithm. Second, for adiabatic and inviscid conditions, PV is conserved on fluid

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