An Alternate Approach to the Problem of Stokes’ Flow

1967 ◽  
Vol 34 (1) ◽  
pp. 8-10
Author(s):  
F. Pollock ◽  
R. E. Struzynski
Keyword(s):  
Shear Flow ◽  
Green’S Function ◽  
Flow Pattern ◽  
Green's Function ◽  
Stokes Flow ◽  
Poiseuille Flow ◽  
External Flow ◽  
Uniform Flow ◽  
Uniqueness Of Solution ◽  
Linear Shear

The problem of Stokes’ flow for a sphere in arbitrary external flow pattern is solved using a particular scalar Green’s function. By this method, the uniqueness of solution is clearly shown, and arbitrary flows (linear shear flow, Poiseuille flow, and so on) are seen to be as straightforward as simple uniform flow.

Numerical Prediction of Low Mach Number Jet Noise Ejected From Slit Nozzle

2011 ◽  
Author(s):  
Minoru Yamaguchi ◽  
Yusuke Iwata ◽  
Sadao Akishita ◽  
Yoshifumi Ogami
Keyword(s):  
Mach Number ◽  
Shear Flow ◽  
Green’S Function ◽  
Green's Function ◽  
Jet Noise ◽  
Frequency Range ◽  
Sound Emission ◽  
Low Mach Number ◽  
Number Flow ◽  
Low Mach Number Flow

Prediction of the low Mach number jet noise ejected from rectangular nozzle with high aspect ratio is described. Firstly measurement of the jet noise was conducted in semi-anechoic wind tunnel at the low Mach number flow condition. We were found that the sound power of the jet obeyed 6-th power of jet velocity. This means the jet noise is resulted not from quadrupole distribution in the shear flow of jet, but from dipole distribution on the surface of the exit of the nozzle. The model of vortex sound is applied as the sound generation mechanism at numerical simulation. The sound emission from the vortices in the shear flow is modified with the compact Green’s function representing the scattering effect from the surface of the exit of the nozzle in the lower frequency range. It is also modified with the non-compact Green’s function in the higher frequency range. Lastly calculated sound spectra are compared with measured spectra. The comparison will prove effectiveness of this modeling.

scholarly journals Forced Linear Shear Flows with Rotation: Rotating Couette–Poiseuille Flow, Its Stability, and Astrophysical Implications

2021 ◽  
Vol 922 (2) ◽  
pp. 161
Author(s):  
Subham Ghosh ◽  
Banibrata Mukhopadhyay
Keyword(s):  
Shear Flow ◽  
Couette Flow ◽  
Accretion Disk ◽  
Poiseuille Flow ◽  
Small Region ◽  
Transition To Turbulence ◽  
Plane Couette Flow ◽  
Plane Poiseuille Flow ◽  
Plane Shear ◽  
Linear Shear

Abstract We explore the effect of forcing on the linear shear flow or plane Couette flow, which is also the background flow in the very small region of the Keplerian accretion disk. We show that depending on the strength of forcing and boundary conditions suitable for the systems under consideration, the background plane shear flow, and hence the accretion disk velocity profile, is modified into parabolic flow, which is a plane Poiseuille flow or Couette–Poiseuille flow, depending on the frame of reference. In the presence of rotation, the plane Poiseuille flow becomes unstable at a smaller Reynolds number under pure vertical as well as three-dimensional perturbations. Hence, while rotation stabilizes the plane Couette flow, the same destabilizes the plane Poiseuille flow faster and hence the forced local accretion disk. Depending on the various factors, when the local linear shear flow becomes a Poiseuille flow in the shearing box due to the presence of extra force, the flow becomes unstable even for Keplerian rotation, and hence turbulence will ensue. This helps to resolve the long-standing problem of subcritical transition to turbulence in hydrodynamic accretion disks and the laboratory plane Couette flow.

scholarly journals Motion of a solid particle in a shear flow along a porous slab

2012 ◽  
Vol 713 ◽  
pp. 271-306 ◽  
Author(s):  
Sondes Khabthani ◽  
Antoine Sellier ◽  
Lassaad Elasmi ◽  
François Feuillebois
Keyword(s):  
Shear Flow ◽  
Green’S Function ◽  
Solid Particle ◽  
Green's Function ◽  
Integral Method ◽  
Particle Surface ◽  
Slip Boundary Condition ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Darcy Problem

AbstractThe flow field around a solid particle moving in a shear flow along a porous slab is obtained by solving the coupled Stokes–Darcy problem with the Beavers and Joseph slip boundary condition on the slab interfaces. The solution involves the Green’s function of this coupled problem, which is given here. It is shown that the classical boundary integral method using this Green’s function is inappropriate because of supplementary contributions due to the slip on the slab interfaces. An ‘indirect boundary integral method’ is therefore proposed, in which the unknown density on the particle surface is not the actual stress, but yet allows calculation of the force and torque on the particle. Various results are provided for the normalized force and torque, namely friction factors, on the particle. The cases of a sphere and an ellipsoid are considered. It is shown that the relationships between friction coefficients (torque due to rotation and force due to translation) that are classical for a no-slip plane do not apply here. This difference is exhibited. Finally, results for the velocity of a freely moving particle in a linear and a quadratic shear flow are presented, for both a sphere and an ellipsoid.

scholarly journals Time-evolving bubbles in two-dimensional Stokes flow

1995 ◽  
Vol 301 ◽  
pp. 325-344 ◽  
Author(s):  
Saleh Tanveer ◽  
Giovani L. Vasconcelos
Keyword(s):  
Surface Tension ◽  
Shear Flow ◽  
Exact Solutions ◽  
Stokes Flow ◽  
Mathematical Structure ◽  
The Other ◽  
Two Dimensional ◽  
Slow Viscous Flow ◽  
Expanding Circle ◽  
Linear Shear

A general class of exact solutions is presented for a time-evolving bubble in a two-dimensional slow viscous flow in the presence of surface tension. These solutions can describe a bubble in a linear shear flow as well as an expanding or contracting bubble in an otherwise quiescent flow. In the case of expanding bubbles, the solutions have a simple behaviour in the sense that for essentially arbitrary initial shapes the bubble its asymptote is expanding circle. Contracting bubbles, on the other hand, can develop narrow structures (‘near-cusps’) on the interface and may undergo ‘breakup’ before all the bubble fluid is completely removed. The mathematical structure underlying the existence of these exact solutions is also investigated.

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