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## Abstract

In intense tropical cyclones, sea level pressures at the center are 50–100 hPa lower than outside the vortex, but only 10–30 hPa of the total pressure fall occurs inside the eye between the eyewall and the center. Warming by dry subsidence accounts for this fraction of the total hydrostatic pressure fall. Convection in the eyewall causes the warming by doing work on the eye to force the thermally indirect subsidence.

Soundings inside hurricane eyes show warm and dry air aloft, separated by an inversion from cloudy air below. Dewpoint depressions at the inversion level, typically 850–500 hPa, are 10–30 K rather than the ∼100 K that would occur if the air descended from tropopause level without dilution by the surrounding cloud. The observed temperature and dewpoint distribution above the inversion can, however, be derived by ∼100 hPa of undilute dry subsidence from an initial sounding that is somewhat more stable than a moist adiabat. It is hypothesized that the air above the inversion has remained in the eye since it was enclosed when the eyewall formed and that it has subsided at most a few kilometers. The cause of the subsidence is the enclosed air’s being drawn downward toward the inversion level as the air below it flows outward into the eyewall. Shrinkage of the eye’s volume is more than adequate to supply the volume lost as dry air is incorporated into the eyewall or converted to moist air by turbulent mixing across the eye boundary.

The moist air below the inversion is in thermodynamic contact with the sea surface. Its moisture derives from evaporation of seawater inside the eye, frictional inflow of moist air under the eyewall, and from moist downdrafts induced as condensate mixes into the eye. The moist air’s residence time in the eye is much shorter than that of the dry air above the inversion. The height of the inversion is determined by the balance between evaporation, inflow, and inward mixing on one hand and loss to the eyewall updrafts on the other.

## Abstract

In intense tropical cyclones, sea level pressures at the center are 50–100 hPa lower than outside the vortex, but only 10–30 hPa of the total pressure fall occurs inside the eye between the eyewall and the center. Warming by dry subsidence accounts for this fraction of the total hydrostatic pressure fall. Convection in the eyewall causes the warming by doing work on the eye to force the thermally indirect subsidence.

Soundings inside hurricane eyes show warm and dry air aloft, separated by an inversion from cloudy air below. Dewpoint depressions at the inversion level, typically 850–500 hPa, are 10–30 K rather than the ∼100 K that would occur if the air descended from tropopause level without dilution by the surrounding cloud. The observed temperature and dewpoint distribution above the inversion can, however, be derived by ∼100 hPa of undilute dry subsidence from an initial sounding that is somewhat more stable than a moist adiabat. It is hypothesized that the air above the inversion has remained in the eye since it was enclosed when the eyewall formed and that it has subsided at most a few kilometers. The cause of the subsidence is the enclosed air’s being drawn downward toward the inversion level as the air below it flows outward into the eyewall. Shrinkage of the eye’s volume is more than adequate to supply the volume lost as dry air is incorporated into the eyewall or converted to moist air by turbulent mixing across the eye boundary.

The moist air below the inversion is in thermodynamic contact with the sea surface. Its moisture derives from evaporation of seawater inside the eye, frictional inflow of moist air under the eyewall, and from moist downdrafts induced as condensate mixes into the eye. The moist air’s residence time in the eye is much shorter than that of the dry air above the inversion. The height of the inversion is determined by the balance between evaporation, inflow, and inward mixing on one hand and loss to the eyewall updrafts on the other.

## Abstract

This paper revisits calculation of motion for a shallow-water barotropic vortex with fixed mean axisymmetric structure. The algorithm marches the linear primitive equations for the wavenumber 1 asymmetry forward intime using a vortex motion extrapolated from previous calculations. Periodically, it examines the calculated asymmetry for the apparent asymmetry due to mispositioning of the vortex center, repositions the vortex to remove the apparent asymmetry, and passes the corrected vortex motion on to the next cycle.

This approach differs from the author's earlier variational determination of the steady-state motion after initial transients had died away. The steady-state approach demonstrated that the vortex had normal modes at zero frequency and, when an annulus of weak anticyclonic flow encircled the cyclonic inner vortex, at the most anticyclonic rotation frequency of the mean flow. Forcing of the former model led to too rapid steady-state poleward motion on a beta plane.

At least for the linear problem, the key to more realistic simulation of motion and structure is the normal modes' transient response to diverse forcing: environmental potential vorticity gradients, embedded sources and sinks of mass, and initial asymmetries. The beta effect and other environmental potential vorticity gradients excite the normal modes to induce an acceleration of the vortex center toward and to the left of the direction to maximum environmental vorticity. Times ~ 100 days would be required to reach the too fast motions predicted in the earlier work. A rotating mass source-sink pair drives the vortex along a cycloidal track, but does not force the normal modes. A nonrotating source-sink forces a motion from the source toward the sinkand excites the normal modes, leading to motion that persists after the forcing has ceased. Similarly, initial asymmetries that project onto the normal modes maintain themselves for times ≥ 10 days, leading to persistent vortex propagation that evolves as the complex normal-mode frequencies dictate. Understanding of these normal modes can contribute to better tropical cyclone motion forecasts through better initialization of numerical track prediction models.

## Abstract

This paper revisits calculation of motion for a shallow-water barotropic vortex with fixed mean axisymmetric structure. The algorithm marches the linear primitive equations for the wavenumber 1 asymmetry forward intime using a vortex motion extrapolated from previous calculations. Periodically, it examines the calculated asymmetry for the apparent asymmetry due to mispositioning of the vortex center, repositions the vortex to remove the apparent asymmetry, and passes the corrected vortex motion on to the next cycle.

This approach differs from the author's earlier variational determination of the steady-state motion after initial transients had died away. The steady-state approach demonstrated that the vortex had normal modes at zero frequency and, when an annulus of weak anticyclonic flow encircled the cyclonic inner vortex, at the most anticyclonic rotation frequency of the mean flow. Forcing of the former model led to too rapid steady-state poleward motion on a beta plane.

At least for the linear problem, the key to more realistic simulation of motion and structure is the normal modes' transient response to diverse forcing: environmental potential vorticity gradients, embedded sources and sinks of mass, and initial asymmetries. The beta effect and other environmental potential vorticity gradients excite the normal modes to induce an acceleration of the vortex center toward and to the left of the direction to maximum environmental vorticity. Times ~ 100 days would be required to reach the too fast motions predicted in the earlier work. A rotating mass source-sink pair drives the vortex along a cycloidal track, but does not force the normal modes. A nonrotating source-sink forces a motion from the source toward the sinkand excites the normal modes, leading to motion that persists after the forcing has ceased. Similarly, initial asymmetries that project onto the normal modes maintain themselves for times ≥ 10 days, leading to persistent vortex propagation that evolves as the complex normal-mode frequencies dictate. Understanding of these normal modes can contribute to better tropical cyclone motion forecasts through better initialization of numerical track prediction models.

## Abstract

Nonlinear motions of a shallow water barotropic vortex on a *β* plane differ substantially from the analogous linear motions. The nonlinear model described here, in which wavenumber 1–3 asymmetries interact with each other and the mean vortex, predicts that an initially completely cyclonic vortex will accelerate toward the NNW, reaching a speed of 2.5 m s^{−1} at 48 h. During the rest of the 240-h calculation, the speed varies by <0.5 m s^{−1} as the direction turns from NNW to NW. The vortex accelerations are in phase with temporal changes of vortex-relative angular momentum (*L _{R}
*). The turning of the track coincides with a transition of the wavenumber 1 asymmetry from a single dipole to a double dipole. The latter structure appears to be another orthogonal solution of the second-order radial structure equation for a neutral linear normal mode. The corresponding linear model, in which

*β*forces only wavenumber 1, shows only the single dipole structure and straight NNW accelerating motion that reaches a speed of 9 m s

^{−1}at 240 h. The slower motion in the nonlinear model stems from wave-induced changes in the axisymmetric vortex and vacillation between the orthogonal modal structures.

A nonlinear calculation with zero initial *L _{R}
* on a

*β*plane follows a curving path dictated by a barotropically unstable linear mode for the first 144 h. Subsequently, the double dipole structure for that mode appears as the track turns toward the NW and the speed accelerates from 1 to 2 m s

^{−1}. A spatially uniform geostrophic environmental current on an

*f*plane causes vortex motion by advection and by propagation. The potential vorticity (PV) gradient due to the current acts much as

*β*does. Although the PV gradient is typically 0.1 of that due to

*β*, the induced propagation toward high potential vorticity is ½–¼ of that on a

*β*plane because super-position of the vortex on the geopotential gradient amplifies the PV gradient's effect. In a quiescent environment on an

*f*plane, initial asymmetries that project onto the normal modes induce long-lasting motion that retains about half its speed to 240 h. If the initial speed is ≥2 m s

^{−1}, vacillation between orthogonal modal structures may cause dramatic turns and accelerations of the vortex track.

## Abstract

Nonlinear motions of a shallow water barotropic vortex on a *β* plane differ substantially from the analogous linear motions. The nonlinear model described here, in which wavenumber 1–3 asymmetries interact with each other and the mean vortex, predicts that an initially completely cyclonic vortex will accelerate toward the NNW, reaching a speed of 2.5 m s^{−1} at 48 h. During the rest of the 240-h calculation, the speed varies by <0.5 m s^{−1} as the direction turns from NNW to NW. The vortex accelerations are in phase with temporal changes of vortex-relative angular momentum (*L _{R}
*). The turning of the track coincides with a transition of the wavenumber 1 asymmetry from a single dipole to a double dipole. The latter structure appears to be another orthogonal solution of the second-order radial structure equation for a neutral linear normal mode. The corresponding linear model, in which

*β*forces only wavenumber 1, shows only the single dipole structure and straight NNW accelerating motion that reaches a speed of 9 m s

^{−1}at 240 h. The slower motion in the nonlinear model stems from wave-induced changes in the axisymmetric vortex and vacillation between the orthogonal modal structures.

A nonlinear calculation with zero initial *L _{R}
* on a

*β*plane follows a curving path dictated by a barotropically unstable linear mode for the first 144 h. Subsequently, the double dipole structure for that mode appears as the track turns toward the NW and the speed accelerates from 1 to 2 m s

^{−1}. A spatially uniform geostrophic environmental current on an

*f*plane causes vortex motion by advection and by propagation. The potential vorticity (PV) gradient due to the current acts much as

*β*does. Although the PV gradient is typically 0.1 of that due to

*β*, the induced propagation toward high potential vorticity is ½–¼ of that on a

*β*plane because super-position of the vortex on the geopotential gradient amplifies the PV gradient's effect. In a quiescent environment on an

*f*plane, initial asymmetries that project onto the normal modes induce long-lasting motion that retains about half its speed to 240 h. If the initial speed is ≥2 m s

^{−1}, vacillation between orthogonal modal structures may cause dramatic turns and accelerations of the vortex track.

## Abstract

An important limitation of numerical hurricane track forecasts is the difficulty in coaxing the vortex to assume the correct initial motion. Results from a semispectral, barotropic, linear model suggest a remedy. When the model is initialized from axisymmetry and rest in a quiescent environment on a Northern Hemisphere β plane, the vortex moves toward the northwest. The asymmetric streamfunction field is a dipole such that flow between the cyclonic and anticyclonic gyres advects the vortex. This asymmetry appears to reflect a free oscillation because the asymmetric structure, and the induced motion, persists for a long time in the absence of forcing. When the β effect is turned off, the motion continues on an *f* plane, and the dipole can be rotated and scaled to product any desired initial motion.

In the normal-mode interpretation a vortex with cyclonic circulation throughout accelerates poleward rapidly because the β effect forces a neutral mode at zero frequency. A vortex with angular momentum reduced to zero by encirclement of the cyclonic core with an annulus of anticyclonic flow experiences weaker forcing of a mode at the most anticyclonic orbital frequency of the axisymmetric circulation. Although the latter mode has a weak barotropic instability, acceleration along the curving track is slow, so that this vortex is promising for track forecasting. By careful choice of vortex position and the normal-mode asymmetry's amplitude and orientation at some time before the beginning of the forecast calculation, it is possible to “preinitialize” the vortex to pass through a target initial position at the initial time with an arbitrarily chosen initial velocity.

In completely cyclonic vortices that have asymptotic decay of the swirling flow with radius, radial wave energy propagation damps the mode at zero frequency. Experimentation with a variety of axisymmetric vortex structures suggests that, with this single qualification, existence of the previously described modes is a general property of barotropic vortices scaled to resemble hurricanes.

## Abstract

An important limitation of numerical hurricane track forecasts is the difficulty in coaxing the vortex to assume the correct initial motion. Results from a semispectral, barotropic, linear model suggest a remedy. When the model is initialized from axisymmetry and rest in a quiescent environment on a Northern Hemisphere β plane, the vortex moves toward the northwest. The asymmetric streamfunction field is a dipole such that flow between the cyclonic and anticyclonic gyres advects the vortex. This asymmetry appears to reflect a free oscillation because the asymmetric structure, and the induced motion, persists for a long time in the absence of forcing. When the β effect is turned off, the motion continues on an *f* plane, and the dipole can be rotated and scaled to product any desired initial motion.

In the normal-mode interpretation a vortex with cyclonic circulation throughout accelerates poleward rapidly because the β effect forces a neutral mode at zero frequency. A vortex with angular momentum reduced to zero by encirclement of the cyclonic core with an annulus of anticyclonic flow experiences weaker forcing of a mode at the most anticyclonic orbital frequency of the axisymmetric circulation. Although the latter mode has a weak barotropic instability, acceleration along the curving track is slow, so that this vortex is promising for track forecasting. By careful choice of vortex position and the normal-mode asymmetry's amplitude and orientation at some time before the beginning of the forecast calculation, it is possible to “preinitialize” the vortex to pass through a target initial position at the initial time with an arbitrarily chosen initial velocity.

In completely cyclonic vortices that have asymptotic decay of the swirling flow with radius, radial wave energy propagation damps the mode at zero frequency. Experimentation with a variety of axisymmetric vortex structures suggests that, with this single qualification, existence of the previously described modes is a general property of barotropic vortices scaled to resemble hurricanes.

## Abstract

Calculations with a linear semispectral model of a moving tropical-cyclone-like barotropic vortex (Willoughby 1988) show that a vortex with cyclonic circulation throughout exhibits unphysically fast poleward motion on a beta plane, but a vortex with enough anticyclonic circulation at its periphery to make the total relative angular momentum (*L*
_{
R
}) small moves slowly. The high poleward speed arises because the vortex has a linear normal mode at zero frequency, where the beta effect forces asymmetric perturbations. Advection of planetary vorticity by the axisymmetric circulation forces this normal mode at a rate proportional to *L*
_{
R
}. Because the governing equations are third-order in time, as many as three wavenumber-one normal modes are possible. A completely cyclonic vortex has three repeated stable normal modes at zero frequency, whereas one with small *L*
_{
R
} has a single stable mode at zero frequency and a conjugate pair of barotropically unstable modes. The frequency of the unstable modes lies at the most anticyclonic rotation frequency of the axisymmetric circulation, and the growth rate is slow; the *e*-folding time is typically 75 days. If the fluid is made very shallow, the stable normal mode moves away from zero frequency. In this situation, the beta effect fails to force the resonance, and the vortex propagates westward much as a planetary Rossby wave does.

In this model, meridional motion of vortices with *L*
_{
R
} ≠ 0 always acts to adjust *L*
_{
R
} toward zero through conservation of *absolute* angular momentum. Since the asymmetric perturbations are Rossby waves that propagate upon the radial gradient of mean relative vorticity, the mode at zero frequency experiences critical-radius absorption where the mean swirling wind is zero—at the boundary between cyclonic and anticyclonic mean circulation and at the edge of the vortex. Regardless of the sign of *L*
_{
R
}, the wave momentum convergence is concentrated at these critical radii and weakens the circulation while expanding it spatially. When *L*
_{
R
} = 0, waves emanating from the cyclonic and anticyclonic circulations interfere destructively, so that the vortex radiates no angular momentum to its environment.

## Abstract

Calculations with a linear semispectral model of a moving tropical-cyclone-like barotropic vortex (Willoughby 1988) show that a vortex with cyclonic circulation throughout exhibits unphysically fast poleward motion on a beta plane, but a vortex with enough anticyclonic circulation at its periphery to make the total relative angular momentum (*L*
_{
R
}) small moves slowly. The high poleward speed arises because the vortex has a linear normal mode at zero frequency, where the beta effect forces asymmetric perturbations. Advection of planetary vorticity by the axisymmetric circulation forces this normal mode at a rate proportional to *L*
_{
R
}. Because the governing equations are third-order in time, as many as three wavenumber-one normal modes are possible. A completely cyclonic vortex has three repeated stable normal modes at zero frequency, whereas one with small *L*
_{
R
} has a single stable mode at zero frequency and a conjugate pair of barotropically unstable modes. The frequency of the unstable modes lies at the most anticyclonic rotation frequency of the axisymmetric circulation, and the growth rate is slow; the *e*-folding time is typically 75 days. If the fluid is made very shallow, the stable normal mode moves away from zero frequency. In this situation, the beta effect fails to force the resonance, and the vortex propagates westward much as a planetary Rossby wave does.

In this model, meridional motion of vortices with *L*
_{
R
} ≠ 0 always acts to adjust *L*
_{
R
} toward zero through conservation of *absolute* angular momentum. Since the asymmetric perturbations are Rossby waves that propagate upon the radial gradient of mean relative vorticity, the mode at zero frequency experiences critical-radius absorption where the mean swirling wind is zero—at the boundary between cyclonic and anticyclonic mean circulation and at the edge of the vortex. Regardless of the sign of *L*
_{
R
}, the wave momentum convergence is concentrated at these critical radii and weakens the circulation while expanding it spatially. When *L*
_{
R
} = 0, waves emanating from the cyclonic and anticyclonic circulations interfere destructively, so that the vortex radiates no angular momentum to its environment.

## Abstract

More than 900 radial profiles of in situ aircraft observations collected in 19 Atlantic hurricanes and tropical storms over 13 years confirm that the usual mechanism of tropical cyclone intensification involves contracting maxima of the axisymmetric swirling wind. Radar shows that annuli of convective echoes accompany the wind maxima. These features, called convective rings exist and move inward because latent heat released in the rings leads to descent, adiabatic warming, and rapid isobaric height falls in the area they enclose. The radial change in rate of isobaric height fall is concentrated at the inner edge of the wind maximum, causing the gradient wind to increase there and the maximum to contract. Vigorous convection organized in rings invariably causes well defined, inward moving wind maxima, but when convection is weak, the rings are also weak or even absent. In this case, the swirling wind may be nearly constant with radius and change slowly in time.

Hurricanes that have a single, vigorous, axisymmetric convective ring strengthen rapidly. Although a series of minor convective rings may support steady strengthening, development is more generally episodic. When asymmetric convection erupts near the center of tropical storms or weak hurricanes, it may cause intensification to falter and the cyclone tracks to become irregular. In intense hurricanes, outer convective rings may form around the preexistent eyewalls, contract, and strangle the original eyewalls, halting intensification or causing weakening.

## Abstract

More than 900 radial profiles of in situ aircraft observations collected in 19 Atlantic hurricanes and tropical storms over 13 years confirm that the usual mechanism of tropical cyclone intensification involves contracting maxima of the axisymmetric swirling wind. Radar shows that annuli of convective echoes accompany the wind maxima. These features, called convective rings exist and move inward because latent heat released in the rings leads to descent, adiabatic warming, and rapid isobaric height falls in the area they enclose. The radial change in rate of isobaric height fall is concentrated at the inner edge of the wind maximum, causing the gradient wind to increase there and the maximum to contract. Vigorous convection organized in rings invariably causes well defined, inward moving wind maxima, but when convection is weak, the rings are also weak or even absent. In this case, the swirling wind may be nearly constant with radius and change slowly in time.

Hurricanes that have a single, vigorous, axisymmetric convective ring strengthen rapidly. Although a series of minor convective rings may support steady strengthening, development is more generally episodic. When asymmetric convection erupts near the center of tropical storms or weak hurricanes, it may cause intensification to falter and the cyclone tracks to become irregular. In intense hurricanes, outer convective rings may form around the preexistent eyewalls, contract, and strangle the original eyewalls, halting intensification or causing weakening.

## Abstract

Analysis of a large inventory of in situ observations from research aircraft shows that the gradient wind approximates the axisymmetric swirling flow in the free atmosphere within 150 km of the centers of Atlantic hurricanes and tropical storms. In the middle and lower troposphere, the rms difference between the azimuthal cream swirling and gradient winds is typically < 1.5 m s^{−1} with zero bias. This balance prevails only for the azimuthal mean, not locally, nor is balance to be expected in either the surface friction layer or the upper tropospheric outflow layer where the radial flow is comparable with the swirling flow.

It is theoretically possible that axisymmetric supergradient flow may occur in response to rapid radial acceleration where the radial flow slows in the friction layer beneath the eyewall or where it converges into intense diabatically forced updrafts. Nevertheless, the observations in the free lower and midtroposphere show that systematic departures of the azimuthal mean vortex from balance are too small to measure.

## Abstract

Analysis of a large inventory of in situ observations from research aircraft shows that the gradient wind approximates the axisymmetric swirling flow in the free atmosphere within 150 km of the centers of Atlantic hurricanes and tropical storms. In the middle and lower troposphere, the rms difference between the azimuthal cream swirling and gradient winds is typically < 1.5 m s^{−1} with zero bias. This balance prevails only for the azimuthal mean, not locally, nor is balance to be expected in either the surface friction layer or the upper tropospheric outflow layer where the radial flow is comparable with the swirling flow.

It is theoretically possible that axisymmetric supergradient flow may occur in response to rapid radial acceleration where the radial flow slows in the friction layer beneath the eyewall or where it converges into intense diabatically forced updrafts. Nevertheless, the observations in the free lower and midtroposphere show that systematic departures of the azimuthal mean vortex from balance are too small to measure.

## Abstract

A barotropic model of tropical cyclone motion follows from calculation of linear wavenumber-1 perturbations on a moving axisymmetric, maintained vortex. The perturbations are Rossby waves that depend upon the radial gradient of axisymmetric relative vorticity. The vortex has normal modes at zero frequency and at the most anticyclonic orbital frequency; the latter mode is barotropically unstable. The structure of the perturbations is calculable for arbitrary motion of the vortex, but one can select the actual motion in a particular situation because that motion minimizes the Lagrangian of the system.

Motion of tropical cyclones may arise from environmental currents, convection, or the beta effect. In an environmental current that turns as time passes, the motion is nearly the same as the current, except when the frequency matches a normal mode. The effect of convection is simulated by an imposed, rotating mass source-sink pair, which excites both the normal modes and a perturbation that depends upon forcing at Rossby-wave critical radii. The latter response seems to correspond to the trochoidal motion of real tropical cyclones. It has the fastest vortex motion when its frequency is the same as the orbital frequency of the axisymmetric flow where the forcing is imposed. On a beta plane, the vortex motion is poleward with speed proportional to the total relative angular momentum of the vortex. Because of the normal mode at zero frequency, the poleward motion is much too fast when the vortex has cyclonic circulation throughout. This physically unreasonable result highlights the importance of nonlinear processes in tropical cyclone motion.

## Abstract

A barotropic model of tropical cyclone motion follows from calculation of linear wavenumber-1 perturbations on a moving axisymmetric, maintained vortex. The perturbations are Rossby waves that depend upon the radial gradient of axisymmetric relative vorticity. The vortex has normal modes at zero frequency and at the most anticyclonic orbital frequency; the latter mode is barotropically unstable. The structure of the perturbations is calculable for arbitrary motion of the vortex, but one can select the actual motion in a particular situation because that motion minimizes the Lagrangian of the system.

Motion of tropical cyclones may arise from environmental currents, convection, or the beta effect. In an environmental current that turns as time passes, the motion is nearly the same as the current, except when the frequency matches a normal mode. The effect of convection is simulated by an imposed, rotating mass source-sink pair, which excites both the normal modes and a perturbation that depends upon forcing at Rossby-wave critical radii. The latter response seems to correspond to the trochoidal motion of real tropical cyclones. It has the fastest vortex motion when its frequency is the same as the orbital frequency of the axisymmetric flow where the forcing is imposed. On a beta plane, the vortex motion is poleward with speed proportional to the total relative angular momentum of the vortex. Because of the normal mode at zero frequency, the poleward motion is much too fast when the vortex has cyclonic circulation throughout. This physically unreasonable result highlights the importance of nonlinear processes in tropical cyclone motion.

## Abstract

In hurricanes, linear, stationary, asymmetric, inertia-buoyancy oscillations can be resonantly forced at a radius where their tangential wavenumber times the orbital frequency of the mean swirling flow is equal to the local inertia frequency. If the hurricane is advected by an environmental geostrophic steering current without shear, the Coriolis force arising from the motion balances the environmental pressure gradient. However, if the motion of the storm differs from the geostrophic wind or if that wind has a horizontal shear, this balance is disrupted. For a uniform shear, resolution of the imbalance into radial and tangential components leads to a forcing that has a symmetric component and asymmetric components with tangential wavenumbers ±1 and ±2. The symmetric and wavenumber ±1 components have exponential horizontal structure, but the ±2 components have sinusoidal structure and are amplified by the wave action conservation mechanism of Willoughby (1978a,b). These waves resemble the spiral bands observed by research aircraft in Hurricane Anita of 1977.

As is generally the case for resonant forcing, the amplitude of the oscillations is sensitive to the dissipation rate, but for values of this quantity appropriate to cumulus friction and an environmental shear equal to 10% of the Coriolis parameter, the maximum horizontal velocity amplitude in the eye wall is several meters per second.

## Abstract

In hurricanes, linear, stationary, asymmetric, inertia-buoyancy oscillations can be resonantly forced at a radius where their tangential wavenumber times the orbital frequency of the mean swirling flow is equal to the local inertia frequency. If the hurricane is advected by an environmental geostrophic steering current without shear, the Coriolis force arising from the motion balances the environmental pressure gradient. However, if the motion of the storm differs from the geostrophic wind or if that wind has a horizontal shear, this balance is disrupted. For a uniform shear, resolution of the imbalance into radial and tangential components leads to a forcing that has a symmetric component and asymmetric components with tangential wavenumbers ±1 and ±2. The symmetric and wavenumber ±1 components have exponential horizontal structure, but the ±2 components have sinusoidal structure and are amplified by the wave action conservation mechanism of Willoughby (1978a,b). These waves resemble the spiral bands observed by research aircraft in Hurricane Anita of 1977.

As is generally the case for resonant forcing, the amplitude of the oscillations is sensitive to the dissipation rate, but for values of this quantity appropriate to cumulus friction and an environmental shear equal to 10% of the Coriolis parameter, the maximum horizontal velocity amplitude in the eye wall is several meters per second.