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Vladimir Zeitlin

Abstract

This paper provides a brief review of recent results on decoupling of fast [inertia–gravity wave (IGW)] and slow (vortex) motions at small Rossby numbers obtained in the framework of the geostrophic adjustment of localized perturbations. Special attention is paid to the IGW emission and its interpretation in the context of “spontaneous imbalance.” Several mechanisms that lead to spontaneous IGW emission and, thus, to violations of fast–slow splitting at large Rossby numbers are reviewed: Lighthill radiation, symmetric/inertial instability, and ageostrophic shear (Rossby–Kelvin) instability. New results on the saturation of symmetric instability and on the existence of Rossby–Kelvin instability in continuously stratified fluid are presented.

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Noé Lahaye and Vladimir Zeitlin

Abstract

Instabilities of hurricane-like vortices are studied with the help of a rotating shallow-water model, including the effects of moist convection. Linear stability analysis demonstrates that dominant unstable modes are mixed Rossby–inertia–gravity waves. It is shown that, depending on fine details of the vorticity profile, a wavenumber selection of the instability may operate or not, leading in some cases to an unstable mode with a distinctively maximal growth rate and in other cases to an ensemble of unstable modes with close growth rates. Numerical simulations are performed in order to investigate nonlinear saturation of the instability and to understand the dynamical role of moisture. In agreement with previous studies, the authors confirm axisymmetrization of vorticity in the course of the development of the instability, which induces changes of intensity of the hurricane. In “dry” simulations, winds are intensified only inside the radius of maximum wind, while the maximum value of the wind decreases. “Moist precipitating” simulations (with and without evaporation) exhibit a net increase of winds, also at the radius of maximum wind, as compared to the dry simulations. Dynamical effects of moisture on the reorganization of the vortex and on the efficiency of inertia–gravity wave emission are quantified and shown to be considerable. Periodic bursts in the emission of waves related to the development of the unstable modes inside the vortex are evidenced, as well as the appearance of convectively coupled waves in the moist precipitating simulations with evaporation.

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Julien Lambaerts, Guillaume Lapeyre, and Vladimir Zeitlin

Abstract

Dynamical influence of moist convection upon development of the barotropic instability is studied in the rotating shallow-water model. First, an exhaustive linear “dry” stability analysis of the Bickley jet is performed, and the most unstable mode identified in this way is used to initialize simulations to compare the development and the saturation of the instability in dry and moist configurations. High-resolution numerical simulations with a well-balanced finite-volume scheme reveal substantial qualitative and quantitative differences in the evolution of dry and moist-convective instabilities. The moist effects affect both balanced and unbalanced components of the flow. The most important differences between dry and moist evolution are 1) the enhanced efficiency of the moist-convective instability, which manifests itself by the increase of the growth rate at the onset of precipitation, and by a stronger deviation of the end state from the initial one, measured with a number of different norms; 2) a pronounced cyclone–anticyclone asymmetry during the nonlinear evolution of the moist-convective instability, which leads to an additional, with respect to the dry case, geostrophic adjustment, and the modification of the end state; and 3) an enhanced ageostrophic activity in the precipitation zones but also in the nonprecipitating areas because of the secondary geostrophic adjustment.

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Julien Lambaerts, Guillaume Lapeyre, and Vladimir Zeitlin

Abstract

The authors undertake a detailed analysis of the influence of water vapor condensation and latent heat release upon the evolution of the baroclinic instability. The framework consists in a two-layer rotating shallow-water model with moisture coupled to dynamics through mass exchange between the layers due to condensation/precipitation. The model gives all known in literature models of this kind as specific limits. It is fully nonlinear and ageostrophic. The reference state is a baroclinic Bickley jet. The authors first study its “dry” linear instability and then use the most unstable mode to initialize high-resolution numerical simulations of the life cycle of the instability in nonprecipitating (moisture being a passive tracer) and precipitating cases. A new-generation well-balanced finite-volume scheme is used in these simulations.

The evolution in the nonprecipitating case follows the standard cyclonic wave-breaking life cycle of the baroclinic instability, which is reproduced with a high fidelity. In the precipitating case, the onset of condensation significantly increases the growth rate of the baroclinic instability at the initial stages due to production of available potential energy by the latent heat release. Condensation occurs in frontal regions and wraps up around the cyclone, which is consistent with the moist cyclogenesis theory and observations. Condensation induces a clear-cut cyclone–anticyclone asymmetry. The authors explain the underlying mechanism and show how it modifies the equilibration of the flow at the late stages of the saturation of the instability. In spite of significant differences in the evolution, only weak differences in various norms of the perturbations remain between precipitating and nonprecipitating cases at the end of the saturation process.

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Yu Liang, Alexey V. Fedorov, Vladimir Zeitlin, and Patrick Haertel

Abstract

We study the adjustment of the tropical atmosphere to localized surface heating using a Lagrangian atmospheric model (LAM) that simulates a realistic Madden–Julian oscillation (MJO)—the dominant, eastward-propagating mode of tropical intraseasonal variability modulating atmospheric convection. Idealized warm sea surface temperature (SST) anomalies of different aspect ratios and magnitudes are imposed in the equatorial Indian Ocean during MJO-neutral conditions and then maintained for 15 days. The experiments then continue for several more months. Throughout these experiments, we observe a robust generation of an MJO event, evident in precipitation, velocity, temperature, and moisture fields, which becomes a key element of atmospheric adjustment along with the expected Kelvin and Rossby waves. The MJO circulation pattern gradually builds up during the first week, and then starts to propagate eastward at a speed of 5–7 m s−1. The upper-level quadrupole circulation characteristic of the MJO becomes evident around day 14, with two anticyclonic gyres generated by the Gill-type response to convective heating and two cyclonic gyres forced by the excited Kelvin waves and extratropical Rossby wave trains. A moisture budget analysis shows that the eastward propagation of the MJO is controlled largely by the anomalous advection of moisture and by the residual between anomalous moisture accumulation due to converging winds and precipitation. The initial MJO event is followed by successive secondary events, maintaining the MJO for several more cycles. Thus, this study highlights the fundamental role that the MJO can play in the adjustment of the moist equatorial atmosphere to localized surface heating.

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