# Stabilization of Isolated Vortices in a Rotating Stratified Fluid

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## Abstract

**:**

## 1. Introduction

## 2. Instability of a Gaussian Vortex

## 3. Theoretical Model of a Stable Vortex

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**The initial radial PV/f profiles along isopycnals. (

**a**) for a Gaussian vortex (Equation (1)); and (

**b**) for a PV-corrected state described in Section 3.

**Figure 2.**Evolution of a Gaussian meddy. The horizontal sections of relative vorticity at mid-depth ($z={z}_{0}$) normalized by the Coriolis parameter ($\varsigma /f$) are shown at t = 0.9, 1.1, 1.3, and 1.5 years in (

**a**–

**d**), respectively.

**Figure 3.**Time records of (

**a**) the maximum relative vorticity normalized by the Coriolis parameter and (

**b**) the net kinetic energy normalized by its initial value. Note the dramatic increase in both maximal vorticity and kinetic energy associated with the eddy breakdown.

**Figure 4.**Zonal horizontal sections through the vortex center at t = 1 year (

**a**,

**c**) and t = 2 years (

**b**,

**d**). Relative vorticity at mid-depth ($z={z}_{0}$) normalized by the Coriolis parameter is shown in (

**a**,

**c**). Potential vorticity normalized by the background PV at mid-depth ($z={z}_{0}$) is shown in (

**b**,

**d**). Red curves represent the initial Gaussian vortex.

**Figure 5.**The vertical sections of vortex stretching ${N}^{2}/{N}_{0}^{2}$ through the centers of the original vortex and smaller ones after breaking at times corresponding to Figure 2. (

**a**) t = 0.9 years; (

**b**) t = 1.3 years; and (

**c**) t = 2 years.

**Figure 6.**(

**a**) the isopycnal displacement the vortex axis as a function of depth; and (

**b**) azimuthal velocity at mid-level ($z={z}_{0}$) as a function of radius for the Gaussian (

**red**curve), PV-corrected (

**blue**curves) and PV-corrected vortices without mirror image adjustment (

**green**curves).

**Figure 7.**Evolution of the PV-corrected meddy. The horizontal sections of PV at mid-depth ($z={z}_{0}$) normalized by the background value (

**a**) initial; (

**b**) t = 15 years; and (

**c**) the vertical section of PV through the vortex center along the dashed line at (b).

**Figure 8.**The same as in Figure 2 but for the PV-corrected experiment in the small computational domain. Note the weak instability. (

**a**) t = 0.9 years; (

**b**) t = 1.1 years; (

**c**) t = 1.3 years; (

**d**) t = 1.5 years.

**Figure 9.**The same as in Figure 2 but for the PV-corrected experiment without mirror image adjustment. Note the weak instability of the meddy, which becomes visible by t = 5 years and produces an elliptic rotating vortex. (

**a**) t = 5 years; (

**b**) t = 9 years; (

**c**) t = 13 years; (

**d**) t = 17 years.

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**MDPI and ACS Style**

Sutyrin, G.G.; Radko, T.
Stabilization of Isolated Vortices in a Rotating Stratified Fluid. *Fluids* **2016**, *1*, 26.
https://doi.org/10.3390/fluids1030026

**AMA Style**

Sutyrin GG, Radko T.
Stabilization of Isolated Vortices in a Rotating Stratified Fluid. *Fluids*. 2016; 1(3):26.
https://doi.org/10.3390/fluids1030026

**Chicago/Turabian Style**

Sutyrin, Georgi G., and Timour Radko.
2016. "Stabilization of Isolated Vortices in a Rotating Stratified Fluid" *Fluids* 1, no. 3: 26.
https://doi.org/10.3390/fluids1030026