Wave-Vortex Interaction in Rotating Shallow Water. Part 1. One Space Dimension

Using a physical space (i.e. non-modal) approach, we investigate interactions between fast inertio-gravity (IG) waves and slow balanced flows in a shallow rotating fluid. Specifically, we consider a train of IG waves impinging on a steady, exactly balanced vortex. For simplicity, the one-dimensional problem is studied first; the limitations of one-dimensionality are offset by the ability to define balance in an exact way. An asymptotic analysis of the problem in the small-amplitude limit is performed to demonstrate the existence of interactions. It is shown that these interactions are not confined to the modification of the wave field by the vortex but, more importantly, that the waves are able to alter in a non-trivial way the potential vorticity associated with that vortex. Interestingly, in this one-dimensional problem, once the waves have traversed the vortex region and have propagated away, the vortex exactly recovers its initial shape and thus bears no signature of the interaction. Furthermore, we prove this last result in the case of arbitrary vortex and wave amplitudes. Numerical integrations of the full one-dimensional shallow-water equations in strongly nonlinear regimes are also performed: they confirm that time-dependent interactions exist and increase with wave amplitude, while at the final state the vortex bears no sign of the interaction. In addition, they reveal that cyclonic vortices interact more strongly with the wave field than anticyclonic ones

Antarctic Climate Response to Stratospheric Ozone Depletion in a Fine Resolution Ocean Climate Model

We investigate the impact of stratospheric ozone depletion on Antarctic climate, paying particular attention to the question of whether eddy parameterizations in the ocean fundamentally alter the results. This is accomplished by contrasting two versions of the Community Climate System Model (version 3.5), one at 0.1° ocean and sea ice resolution and the other at 1° with parameterized ocean eddies. At both resolutions, pairs of integrations are performed: one with high (1960) and one with low (2000) ozone levels. We find that the effect of ozone depletion is to warm the surface and the ocean to a depth of 1000 m and to significantly reduce the sea ice extent. While the ocean warming is somewhat weaker when the eddies are resolved, the total loss of sea ice area is roughly the same in the fine and coarse resolution cases

Nonlinear Geostrophic Adjustment, Cyclone/Anticyclone Asymmetry, and Potential Vorticity Rearrangement

Within the context of the rotating shallow water equations, it is shown how initially unbalanced states possessing certain symmetries dynamically evolve to lose those symmetries during nonlinear geostrophic adjustment. Using conservation law methods, it is demonstrated that the adjustment of equal and opposite (circular) mass imbalances results in a balanced end state where cyclones are stronger than anticyclones; the reverse holds true for momentum imbalances. In both cases, the degree of this asymmetry is shown to be directly proportional to the amount of initial imbalance (a measure of the nonlinearity occurring during time-dependent adjustment). On the other hand, the degree of asymmetry is maximal for imbalances of Rossby deformation scale. As for the potential vorticity, it is shown that its final profile can be noticeably different from its initial one; from an Eulerian perspective, this rearrangement is not confined to uniform shifts of potential vorticity fronts. Direct 2D numerical initial value problems confirm the asymmetry in the predicted final states and establish a relatively fast time scale for adjustment to complete. The robustness of these results is confirmed by studying, in addition, the adjustment of elliptical mass imbalances. The numerical integrations reveal that, during geostrophic adjustment, potential vorticity rearrangement occurs irreversibly on a fast wave time scale

Time-Dependent Fully Nonlinear Geostrophic Adjustment

Shock-capturing numerical methods are employed to integrate the fully nonlinear, rotating 1D shallow-water equations starting from steplike nongeostrophic initial conditions (a Rossby adjustment problem). Such numerical methods allow one to observe the formation of multiple bores during the transient adjustment process as well as their decay due to rotation. It is demonstrated that increasing the rotation and/or the nonlinearity increases the rate of decay. Additionally, the time required for adjustment to be completed and its dependence on nonlinearity is examined; this time is found to be highly measure dependent. Lastly, the final adjusted state of the system is observed through long time integrations. Although the bores that form provide a mechanism for dissipation, their decay results in a final state in very good agreement with the one computed by well-known (dissipationless) conservation methods

The Coherent Structures of Shallowwater Turbulence: Deformationradius Effects, Cyclone/Anticyclone Asymmetry and Gravitywave Generation

Over a large range of Rossby and Froude numbers, we investigate the dynamics of initially balanced decaying turbulence in a shallow rotating fluid layer. As in the case of incompressible two‐dimensional decaying turbulence, coherent vortex structures spontaneously emerge from the initially random flow. However, owing to the presence of a free surface, a wealth of new phenomena appear in the shallow‐water system. The upscale energy cascade, common to strongly rotating flows, is arrested by the presence of a finite Rossby deformation radius. Moreover, in contrast to near‐geostrophic dynamics, a strong asymmetry is observed to develop as the Froude number is increased, leading to a clear dominance of anticyclonic vortices over cyclonic ones, even though no β effect is present in the system. Finally, we observe gravity waves to be generated around the vortex structures, and, in the strongest cases, they appear in the form of shocks. We briefly discuss the relevance of this study to the vortices observed in Jupiter’s atmosphere

Why Might Stratospheric Sudden Warmings Occur with Similar Frequency in El Niño and La Niña Winters?

The effect of El Niño-Southern Oscillation (ENSO) on the frequency and character of Northern Hemisphere major mid-winter stratospheric sudden warmings (SSWs) is evaluated using a meteorological reanalysis data set and comprehensive chemistry-climate models. There is an apparent inconsistency between the impact of opposite phases of ENSO on the seasonal mean vortex and on SSWs: El Niño leads to an anomalously warm, and La Niña leads to an anomalously cool, seasonal mean polar stratospheric state, but both phases of ENSO lead to an increased SSW frequency. A resolution to this apparent paradox is here proposed: the region in the North Pacific most strongly associated with precursors of SSWs is not strongly influenced by El Niño and La Niña teleconnections. In the observational record, both La Niña and El Niño lead to similar anomalies in the region associated with precursors of SSWs and, consistent with this, there is a similar SSW frequency in La Niña and El Niño winters. A similar correspondence between the penetration of ENSO teleconnections into the SSW precursor region and SSW frequency is found in the comprehensive chemistry-climate models. The inability of some of the models to capture the observed relationship between La Niña and SSW frequency appears related to whether the modeled ENSO teleconnections result in extreme anomalies in the region most closely associated with SSWs. Finally, it is confirmed that the seasonal mean polar vortex response to ENSO is only weakly related to the relative frequency of SSWs during El Niño and La Niña

Modeling Evidence that Ozone Depletion Has Impacted Extreme Precipitation in the Austral Summer

The impacts of stratospheric ozone depletion on the extremes of daily precipitation in the austral summer are explored using two global climate models. Both models indicate that stratospheric ozone losses since the late 1970s may have increased the frequency and intensity of very heavy precipitation in austral summer over southern high and subtropical latitudes, and may have decreased the frequency and intensity over southern midlatitudes. This hemispheric wide pattern of extreme precipitation response projects strongly onto a previously identified pattern of seasonal mean precipitation response, both of which are shown to be likely of dynamic rather than thermodynamic origin

Deformation of geometry and bifurcation of vortex rings

We construct a smooth family of Hamiltonian systems, together with a family of group symmetries and momentum maps, for the dynamics of point vortices on surfaces parametrized by the curvature of the surface. Equivariant bifurcations in this family are characterized, whence the stability of the Thomson heptagon is deduced without recourse to the Birkhoff normal form, which has hitherto been a necessary tool.Comment: 26 page