Two regimes of self-propelled motion of a torus rotating about its centerline in a viscous incompressible fluid at intermediate Reynolds numbers

2012 ◽  
Vol 24 (5) ◽  
pp. 053603 ◽  
Author(s):  
N. P. Moshkin ◽  
Pairin Suwannasri
Keyword(s):  
Incompressible Fluid ◽  
Viscous Incompressible Fluid ◽  
Reynolds Numbers

The stability of Poiseuille flow in a pipe

1969 ◽  
Vol 36 (2) ◽  
pp. 209-218 ◽  
Author(s):  
A. Davey ◽  
P. G. Drazin
Keyword(s):  
Incompressible Fluid ◽  
Poiseuille Flow ◽  
Viscous Incompressible Fluid ◽  
Reynolds Numbers ◽  
Numerical Calculations ◽  
Circular Pipe ◽  
Asymptotic Results ◽  
The Stability

Numerical calculations show that the flow of viscous incompressible fluid in a circular pipe is stable to small axisymmetric disturbances at all Reynolds numbers. These calculations are linked with known asymptotic results.

scholarly journals Controllability of low Reynolds numbers swimmers of ciliate type

2020 ◽  
Vol 26 ◽  
pp. 31
Author(s):  
Jérôme Lohéac ◽  
Takéo Takahashi
Keyword(s):  
Rigid Body ◽  
Incompressible Fluid ◽  
Control Problem ◽  
Vector Fields ◽  
Viscous Incompressible Fluid ◽  
Exact Controllability ◽  
Reynolds Numbers ◽  
Low Reynolds Numbers ◽  
Minimal Dimension ◽  
Stokes Fluid

We study the locomotion of a ciliated microorganism in a viscous incompressible fluid. We use the Blake ciliated model: the swimmer is a rigid body with tangential displacements at its boundary that allow it to propel in a Stokes fluid. This can be seen as a control problem: using periodical displacements, is it possible to reach a given position and a given orientation? We are interested in the minimal dimension d of the space of controls that allows the microorganism to swim. Our main result states the exact controllability with d = 3 generically with respect to the shape of the swimmer and with respect to the vector fields generating the tangential displacements. The proof is based on analyticity results and on the study of the particular case of a spheroidal swimmer.

On stability of parallel flow of an incompressible fluid of variable density and viscosity

1962 ◽  
Vol 58 (4) ◽  
pp. 646-661 ◽  
Author(s):  
P. G. Drazin
Keyword(s):  
Incompressible Fluid ◽  
Water Waves ◽  
Salt Water ◽  
Reynolds Numbers ◽  
Variable Density ◽  
Stability Equation ◽  
Wave Disturbances ◽  
Long Wave ◽  
Vertical Variations ◽  
The Stability

ABSTRACTSome aspects of generation of water waves by wind and of turbulence in a heterogeneous fluid may be described by the theory of hydrodynamic stability. The technical difficulties of these problems of instability have led to obscurities in the literature, some of which are elucidated in this paper. The stability equation for a basic steady parallel horizontal flow under the influence of gravity is derived carefully, the undisturbed fluid having vertical variations of density and viscosity. Methods of solution of the equation for large Reynolds numbers and for long-wave disturbances are described. These methods are applied to simple models of wind blowing over water and of fresh water flowing over salt water.

Slender-body theory for slow viscous flow

1976 ◽  
Vol 75 (4) ◽  
pp. 705-714 ◽  
Author(s):  
Joseph B. Keller ◽  
Sol I. Rubinow
Keyword(s):  
Integral Equation ◽  
Incompressible Fluid ◽  
Viscous Incompressible Fluid ◽  
Unit Length ◽  
The Body ◽  
Slender Body ◽  
Slow Flow ◽  
Slender Body Theory ◽  
Slow Viscous Flow ◽  
Body Theory

Slow flow of a viscous incompressible fluid past a slender body of circular crosssection is treated by the method of matched asymptotic expansions. The main result is an integral equation for the force per unit length exerted on the body by the fluid. The novelty is that the body is permitted to twist and dilate in addition to undergoing the translating, bending and stretching, which have been considered by others. The method of derivation is relatively simple, and the resulting integral equation does not involve the limiting processes which occur in the previous work.

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