Conditions That Inhibit the Spontaneous Radiation of Spiral Inertia–Gravity Waves from an Intense Mesoscale Cyclone

David A. Schecter Department of Atmospheric Science, Colorado State University, Fort Collins, Colorado

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Michael T. Montgomery Department of Atmospheric Science, Colorado State University, Fort Collins, Colorado

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Abstract

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 Ωb/|γ| ≳ 1. This inequality contains two characteristic frequencies. The denominator |γ| is the absolute value of the (negative) growth rate of the damped wave. The numerator Ωb 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.

Corresponding author address: Dr. David Schecter, Department of Atmospheric Science, Colorado State University, Foothills Campus, Mail 1371, Fort Collins, CO 80523-1371. Email: schecter@atmos.colostate.edu

Abstract

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 Ωb/|γ| ≳ 1. This inequality contains two characteristic frequencies. The denominator |γ| is the absolute value of the (negative) growth rate of the damped wave. The numerator Ωb 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.

Corresponding author address: Dr. David Schecter, Department of Atmospheric Science, Colorado State University, Foothills Campus, Mail 1371, Fort Collins, CO 80523-1371. Email: schecter@atmos.colostate.edu

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