# Analytical Approximations of Dispersion Relations for Internal Gravity Waves Equation with Shear Flows

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## Abstract

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## 1. Introduction

## 2. Statement of the Problem

## 3. Basic Properties of Dispersion Curves

## 4. Analytical Approximation of Dispersion Relations

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**Phase structure for the first model of shear flows. The phase structure consists of curved triangles embedded in the wave wedges with their vertex lying nearer to the origin.

**Figure 3.**Phase structure for the second model of shear flows. The wave pattern looks like a system of longitudinal and transverse waves.

**Figure 4.**Phase structure for the third model of shear flows. The wave pattern looks like closed (symmetric or asymmetric) ellipsoids.

**Figure 5.**Dispersion curves and its approximations for the first model, lines 1—first mode, lines 2—second mode.

**Figure 6.**Dispersion curves and its approximations for the second model, lines 1—first mode, lines 2—second mode.

**Figure 7.**Dispersion curves and its approximations for the third model, lines 1—first mode, lines 2—second mode.

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**MDPI and ACS Style**

Bulatov, V.; Vladimirov, Y.
Analytical Approximations of Dispersion Relations for Internal Gravity Waves Equation with Shear Flows. *Symmetry* **2020**, *12*, 1865.
https://doi.org/10.3390/sym12111865

**AMA Style**

Bulatov V, Vladimirov Y.
Analytical Approximations of Dispersion Relations for Internal Gravity Waves Equation with Shear Flows. *Symmetry*. 2020; 12(11):1865.
https://doi.org/10.3390/sym12111865

**Chicago/Turabian Style**

Bulatov, Vitaly, and Yury Vladimirov.
2020. "Analytical Approximations of Dispersion Relations for Internal Gravity Waves Equation with Shear Flows" *Symmetry* 12, no. 11: 1865.
https://doi.org/10.3390/sym12111865