David A. Schecter

Damping and pumping of a vortex Rossby wave in a monotonic cyclone: Critical layer stirring versus inertia-buoyancy wave emission

This paper further examines the rate at which potential vorticity in the core of a monotonic cyclone becomes vertically aligned and horizontally axisymmetric. We consider the case in which symmetrization occurs by the damping of a discrete vortex Rossby (VR) wave. The damping of the VR wave is caused by its stirring of potential vorticity at a critical radius r*, outside the core of the cyclone. The decay rate generally increases with the radial gradient of potential vorticity at r*. Previous theories for the decay rate were based on “balance models” of the vortex dynamics. Such models filter out inertia–buoyancy (IB) oscillations, i.e., gravity waves. However, if the Rossby number is greater than unity, the core VR wave can excite a frequency-matched outward propagating IB wave, which has positive feedback. To accurately account for this radiation, we here develop a theory for the decay rate that is based on the hydrostatic primitive equations. Starting from conservation of wave activity (angular pseudom...

A Theory for the Vertical Alignment of a Quasigeostrophic Vortex

This article presents a new theory for the rate at which a quasigeostrophic vortex realigns, under conservative dynamics, after being tilted by an episode of external vertical shear. The initial tilt is viewed as the excitation of a three-dimensional ‘‘vortex Rossby mode.’’ This mode, that is, the tilt, decays exponentially with time during its early evolution. The decay rate g is proportional to the potential vorticity gradient at a critical radius, where the fluid rotation is resonant with the mode. The decay rate g also depends on the internal Rossby deformation radius lR, which is proportional to the stratification strength of the atmospheric or oceanic layer containing the vortex. The change of g with lR is sensitive to the form of the vortex. For the case of a ‘‘Rankine-with-skirt’’ vortex, the magnitude of g increases (initially) with increasing lR. On the other hand, for the case of a ‘‘Gaussian’’ vortex, the magnitude of g decreases with increasing lR. The relevance of this theory to tropical cyclogenesis is discussed.

Conditions that inhibit the spontaneous radiation of spiral inertia-gravity waves from an intense mesoscale cyclone

The spontaneous radiation of spiral inertia–gravity (IG) waves from monotonic cyclones is reexamined. Such radiation can occur most significantly in a parameter regime that includes strong supercell mesocyclones and hurricanes. First, linear theory is reviewed. In linear theory, a generic deformation of the cyclone excites discrete vortex Rossby (VR) waves. Each VR wave emits a frequency-matched spiral IG wave into the environment. The emission has positive feedback on the VR wave, causing both to grow. However, the VR wave also deposits wave activity into its critical layer at the radius r * . If the radial gradient of potential vorticity at r * exceeds a threshold, critical layer absorption suppresses the radiative instability. On the other hand, numerical simulations of a shallow-water cyclone show that nonlinear changes to the critical layer can revive a damped VR wave and its radiation field after a brief period of decay. For such revival, it suffices that b/| | 1. This inequality contains two characteristic frequencies. The denominator | | is the absolute value of the (negative) growth rate of the damped wave. The numerator b is the mixing rate of the critical layer, which is proportional to the square root of the initial wave amplitude. After damping is reversed, the radiative VR wave exhibits undulatory growth. Analysis shows that growth proceeds because radiation steadily removes negative wave activity from the cyclone. Secondary amplitude oscillations are due to back-and-forth exchanges of positive wave activity between the VR wave and its critical layer.

Waves in a Cloudy Vortex

Abstract This paper derives a system of equations that approximately govern small-amplitude perturbations in a nonprecipitating cloudy vortex. The cloud coverage can be partial or complete. The model is used to examine moist vortex Rossby wave dynamics analytically and computationally. One example shows that clouds can slow the growth of phase-locked counter-propagating vortex Rossby waves in the eyewall of a hurricane-like vortex. Another example shows that clouds can (indirectly) damp discrete vortex Rossby waves that would otherwise grow and excite spiral inertia–gravity wave radiation from a monotonic cyclone at high Rossby number.

On the symmetrization rate of an intense geophysical vortex

Abstract Numerical models demonstrate that a broad class of geophysical vortices freely evolve toward vertically aligned, axisymmetric states. In principle, this intrinsic drive toward symmetry opposes destructive shearing by the environmental flow. This article examines the case in which a discrete vortex-Rossby-wave dominates a perturbation from symmetry, and symmetrization occurs by decay of the wave. The wave is damped by a resonance with the fluid rotation frequency at a critical radius, r * . The damping rate is proportional to the radial derivative of potential vorticity at r * . Until now, the theory of resonantly damped vortex-Rossby-waves (technically quasi-modes) was formally restricted to slowly rotating vortices, which obey quasigeostrophic (QG) dynamics. This article extends the theory to rapidly rotating vortices. The analysis makes use of the asymmetric balance (AB) approximation. Even at a modest Rossby number (unity), AB theory can predict damping rates that exceed extrapolated QG results by orders of magnitude. This finding is verified upon comparison of AB theory to numerical experiments, based on the primitive equations. The experiments focus on the decay of low azimuthal wave-number asymmetries. A discrete vortex-Rossby-wave can also resonate with an outward propagating inertia-buoyancy wave (Lighthill radiation), inducing both to grow . At large Rossby numbers, this growth mechanism can be dynamically relevant. All balance models, including AB theory, neglect inertia-buoyancy waves, and therefore ignore the possibility of a Rossby-inertia-buoyancy (RIB) instability. This article shows that a large potential vorticity gradient (of the proper sign) at the critical radius r * can suppress the RIB instability, and thereby preserve balanced flow, even at large Rossby numbers.

The Spontaneous Imbalance of an Atmospheric Vortex at High Rossby Number

Abstract This paper discusses recent progress toward understanding the instability of a monotonic vortex at high Rossby number, due to the radiation of spiral inertia–gravity (IG) waves. The outward-propagating IG waves are excited by inner undulations of potential vorticity that consist of one or more vortex Rossby waves. An individual vortex Rossby wave and its IG wave emission have angular pseudomomenta of opposite sign, positive and negative, respectively. The Rossby wave therefore grows in response to producing radiation. Such growth is potentially suppressed by the resonant absorption of angular pseudomomentum in a critical layer, where the angular phase velocity of the Rossby wave matches the angular velocity of the mean flow. Suppression requires a sufficiently steep radial gradient of potential vorticity in the critical layer. Both linear and nonlinear steepness requirements are reviewed. The formal theory of radiation-driven instability, or “spontaneous imbalance,” is generalized in isentropic c...

Infrasound Emitted by Tornado-Like Vortices: Basic Theory and a Numerical Comparison to the Acoustic Radiation of a Single-Cell Thunderstorm

This paper addresses the physics and numerical simulation of the adiabatic generation of infrasound by tornadoes. Classical analytical results regarding the production of infrasound by vortex Rossby waves and by corotating “suction vortices” are reviewed. Conditions are derived for which critical layers damp vortex Rossby waves that would otherwise grow and continually produce acoustic radiation. These conditions are similar to those that theoretically suppress gravity wave radiation from larger mesoscale cyclones, such as hurricanes. To gain perspective, the Regional Atmospheric Modeling System (RAMS) is used to simulate the infrasound that radiates from a single-cell thunderstorm in a shear-free environment. In this simulation, the dominant infrasound in the 0.1–10-Hz frequency band appears to radiate from the vicinity of the melting level, where diabatic processes involving hail are active. It is shown that the 3D Rossby waves of a tornado-like vortex (simulated with RAMS) can generate stronger infrasound if the maximum wind speed of the vortex exceeds a modest threshold. Technical issues regarding the numerical simulation of tornado infrasound are also addressed. Most importantly, it is shown that simulating tornado infrasound likely requires a spatial resolution that is an order of magnitude finer than the current practical limit (10-m grid spacing) for modeling thunderstorms.

Response of a Simulated Hurricane to Misalignment Forcing Compared to the Predictions of a Simple Theory

AbstractThis paper compares the tilt dynamics of a mature tropical cyclone simulated with a conventional cloud model to reduced modeling results and theoretical predictions. The primary experiment involves a tropical cyclone of hurricane strength on the f plane exposed to a finite period of idealized misalignment forcing. A complementary experiment shows how the vortex responds to the same forcing when moisture and symmetric secondary circulation (SSC) are removed from the initial condition. It is found that the applied forcing excites a much stronger tilt mode in the dry nonconvective vortex than in the moist convective hurricane. The evolution of tilt in both experiments agrees reasonably well with a simple linear response theory that neglects the SSC and assumes moisture merely reduces static stability in the vortex core. An additional experiment with suspended cloud water but no substantial SSC supports the theoretical notion that reduction of static stability is sufficient to inhibit the excitation o...

On the Relative Contribution of Inertia–Gravity Wave Radiation to Asymmetric Instabilities in Tropical Cyclone–like Vortices

AbstractIntense atmospheric vortices such as tropical cyclones experience various asymmetric instabilities during their life cycles. This study investigates how vortex properties and ambient conditions determine the relative importance of different mechanisms that can simultaneously influence the growth of an asymmetric perturbation. The focus is on three-dimensional disturbances of barotropic vortices with nonmonotonic radial distributions of potential vorticity. The primary modes of instability are examined for Rossby numbers between 10 and 100 and Froude numbers in the broad neighborhood of unity. This parameter regime is deemed appropriate for tropical cyclone perturbations with vertical length scales ranging from the depth of the vortex to moderately smaller scales. At relatively small Froude numbers, the main cause of instability inferred from analysis typically involves the interaction of vortex Rossby waves with each other and/or critical-layer potential vorticity perturbations. As the Froude numb...

A Method for Diagnosing the Sources of Infrasound in Convective Storm Simulations

Thispaperpresentsaconvenientmethodfordiagnosingthesourcesofinfrasoundin anumericalsimulation of a convective storm. The method is based on an exact acoustic wave equation for the perturbation Exner function P9. One notable source term (Suu) in the P9 equation is commonly associated with adiabatic vortex fluctuations, whereas another (Sm) is directly connected to the heat and mass generated or removed during phase transitions of moisture. Scale estimates suggest that other potential sources are usually unimportant. Simplenumericalsimulationsofadisturbedvortexandevaporatingclouddropletsarecarriedouttoillustrate the infrasound of Suu and Sm. Moreover, the diagnostic method is applied to a towering cumulonimbus simulationthat incorporatesmultiplecategories of ice, liquid, and mixed-phase hydrometeors.The sensitivity of Sm to the modeling of the hail-to-rain category conversion is briefly addressed.