# On the Applicability of Linear, Axisymmetric Dynamics in Intensifying and Mature Tropical Cyclones

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## Abstract

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## 1. Introduction

## 2. A Forced Axisymmetric Convective Ring Model Revisited

## 3. Forcing the 3DVPAS Model

## 4. Results

## 5. 3DVPAS Dynamics, Sawyer–Eliassen Balance Dynamics, and Their Possible Extensions

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Maximum azimuthally averaged tangential wind velocity and minimum sea level pressure (hourly, dashed lines) in the inner core of the Weather Research and Forecasting (WRF) integration for Hurricane Igor (2010), and corresponding National Hurricane Center Best-Track information (6 hourly, solid lines).

**Figure 2.**Calculated basic-state circular vortex and corresponding forcing terms as output from the WRF model at hour 27 in the simulation of the intensification of Hurricane Igor (2010). This basic state and these forcing terms (held constant) are used in the integration of the linear 3DVPAS model. Shown are the azimuthally-averaged (

**a**) basic-state tangential velocity V at hour 27 (contour interval 5 m ${\mathrm{s}}^{-1}$); (

**b**) basic-state potential temperature $\mathsf{\Theta}$ at hour 27 (contour interval 5 K); (

**c**) diabatic heating-rate forcing $\dot{Q}$ at hour 27 (thick contour interval is 10 K ${\mathrm{h}}^{-1}$, thin curve contour interval is 5 K ${\mathrm{h}}^{-1}$); and (

**d**) tangential momentum forcing ${F}_{\lambda}$ at hour 27 (contour interval 2 m ${\mathrm{s}}^{-1}$ ${\mathrm{h}}^{-1}$, solid positive, dashed negative).

**Figure 3.**Output from the linear 3DVPAS model at 8 h integration time. Shown in a radius-height coordinate system are (

**a**) tangential velocity disturbance ${v}_{0}$ (contour interval every 5 m ${\mathrm{s}}^{-1}$; dashed negative, solid positive); (

**b**) radial velocity disturbance ${u}_{0}$ (contour interval 2 m ${\mathrm{s}}^{-1}$; dashed negative, solid positive); (

**c**) vertical velocity disturbance ${w}_{0}$ (positive contour interval 0.5 m ${\mathrm{s}}^{-1}$, solid; negative contour interval 0.1 m ${\mathrm{s}}^{-1}$, dashed).

**Figure 4.**Linear tendency terms diagnosed from the 3DVPAS model and corresponding nonlinear tendency terms evaluated using the linear solutions at $t=0.4$ h integration time. Shown in a radius-height coordinate system are (

**a**) linear terms from the disturbance tangential velocity equation; (

**b**) nonlinear terms in the disturbance tangential velocity equation (Equation (8)) evaluated using the linear solutions; (

**c**) linear terms in disturbance radial velocity equation; (

**d**) nonlinear terms in disturbance radial velocity equation (Equation (7)) computed using linear solutions. Contour interval for all panels is 5 m ${\mathrm{s}}^{-1}$ ${\mathrm{h}}^{-1}$, solid positive and dashed negative.

**Figure 5.**Linear and nonlinear tendency terms diagnosed from the 3DVPAS model at $t=1.2$ h integration time. The nonlinear tendency terms are evaluated using the linear solutions. Shown in a radius-height coordinate system are (

**a**) sum of linear terms from the disturbance tangential velocity equation; (

**b**) sum of nonlinear terms in the disturbance tangential velocity equation (Equation (8)) evaluated using the linear solutions; (

**c**) sum of linear terms in disturbance radial velocity equation; (

**d**) sum of nonlinear terms in disturbance radial velocity equation (Equation (7)) computed using linear solutions. Contour interval for all panels is 2 m ${\mathrm{s}}^{-1}$ ${\mathrm{h}}^{-1}$; solid positive and dashed negative.

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**MDPI and ACS Style**

Montgomery, M.T.; Smith, R.K. On the Applicability of Linear, Axisymmetric Dynamics in Intensifying and Mature Tropical Cyclones. *Fluids* **2017**, *2*, 69.
https://doi.org/10.3390/fluids2040069

**AMA Style**

Montgomery MT, Smith RK. On the Applicability of Linear, Axisymmetric Dynamics in Intensifying and Mature Tropical Cyclones. *Fluids*. 2017; 2(4):69.
https://doi.org/10.3390/fluids2040069

**Chicago/Turabian Style**

Montgomery, Michael T., and Roger K. Smith. 2017. "On the Applicability of Linear, Axisymmetric Dynamics in Intensifying and Mature Tropical Cyclones" *Fluids* 2, no. 4: 69.
https://doi.org/10.3390/fluids2040069