# Note on the stability criteria for a new type of helical flows.

@article{Ershkov2019NoteOT, title={Note on the stability criteria for a new type of helical flows.}, author={Sergey V. Ershkov}, journal={arXiv: Fluid Dynamics}, year={2019} }

In this paper, we proceed exploring the case of non-stationary helical flows of the Navier-Stokes equations for incompressible fluids with variable (spatially dependent) coefficient of proportionality between velocity and the curl field of flow. Meanwhile, the system of Navier-Stokes equations (including continuity equation) has been successfully explored previously with respect to the existence of analytical way for presentation of non-stationary helical flows of the aforementioned type. The…

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## References

SHOWING 1-10 OF 11 REFERENCES

### Non-stationary helical flows for incompressible 3D Navier-Stokes equations

- MathematicsAppl. Math. Comput.
- 2016

### Non-stationary Riccati-type flows for incompressible 3D Navier-Stokes equations

- MathematicsComput. Math. Appl.
- 2016

### The Bernoulli Integral for a Certain Class of Non‐Stationary Viscous Vortical Flows of Incompressible Fluid

- Mathematics, Physics
- 2015

It has been shown in our paper [1] that there is a wide class of 3D motions of incompressible viscous fluid which can be described by one scalar function dabbed the quasi‐potential. This class of…

### A note on the hydrodynamics of viscous fluids

- Physics
- 1994

The cross-product of the velocity and the vorticity in a viscous incompressible fluid is formulated and its properties investigated. When the cross-product is identically null, either the flow is…

### An Introduction to Hydrodynamic Stability

- Mathematics
- 2010

In this chapter, our objective is twofold: (1) to describe common physical mechanisms which cause flows to become unstable, and (2) to introduce recent viewpoints on the subject. In the former, we…

### The Navier-Stokes Equations: A Classification of Flows and Exact Solutions

- Physics, Engineering
- 2006

Preface 1. Scope of the book 2. Steady flows bounded by plane boundaries 3. Steady axisymmetric and related flows 4. Unsteady flows bounded by plane boundaries 5. Unsteady axisymmetric and related…

### On a new type of nonstationary helical flows for incompressible 3D Navier-Stokes equations

- Journal of King Saud University – Science (in Press),
- 2018

### Hydrodynamic and hydromagnetic stability, Dover, ISBN 978-0-486-64071-6

- 1961

### A Riccati-type solution of 3D Euler equations for incompressible flow

- MathematicsJournal of King Saud University - Science
- 2020

### Hand-book for Ordinary Differential Eq

- Science
- 1971