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}
}
  • S. Ershkov
  • Published 9 July 2018
  • Mathematics
  • arXiv: Fluid Dynamics
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

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

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

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

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

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

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

Hand-book for Ordinary Differential Eq

  • Science
  • 1971