Secondary fluid flows driven electromagnetically in a two-dimensional extended duct

2005 ◽  
Vol 461 (2058) ◽  
pp. 1659-1683 ◽  
Author(s):  
Zhi-Min Chen ◽  
W.G Price
Keyword(s):  
Steady State ◽  
Laboratory Experiments ◽  
Fluid Motion ◽  
Fluid Flows ◽  
Two Dimensional ◽  
Slip Boundary Conditions ◽  
Slip Boundary ◽  
Wave Numbers ◽  
Motion Problem ◽  
Secondary Fluid

This study focuses on two-dimensional fluid flows in a straight duct with free-slip boundary conditions applied on the channel walls y =0 and y =2 πN with N >1. In this extended wall-bounded fluid motion problem, secondary fluid flow patterns resulting from steady-state and Hopf bifurcations are examined and shown to be dependent on the choice of longitudinal wave numbers. Some secondary steady-state flows appear at specific wave numbers, whereas at other wave numbers, both secondary steady-state and self-oscillation flows coexist. These results, derived through analytical arguments and truncation series approximation, are confirmed by simple numerical experiments supporting the findings observed from laboratory experiments.

Microscopic Slip Boundary Conditions in Unsteady Fluid Flows

2019 ◽  
Vol 123 (26) ◽  
Author(s):  
J. A. de la Torre ◽  
D. Duque-Zumajo ◽  
D. Camargo ◽  
Pep Español
Keyword(s):  
Boundary Conditions ◽  
Fluid Flows ◽  
Slip Boundary Conditions ◽  
Slip Boundary ◽  
Unsteady Fluid

scholarly journals Generalized Navier–Stokes equations with nonlinear anisotropic viscosity

2019 ◽  
Vol 17 (06) ◽  
pp. 977-1003
Author(s):  
H. B. de Oliveira
Keyword(s):  
Stokes Equations ◽  
Fluid Flows ◽  
Ekman Layer ◽  
Navier Stokes ◽  
Slip Boundary Conditions ◽  
Very Weak Solutions ◽  
Navier Stokes Equations ◽  
Slip Boundary ◽  
Nonlinear Viscosity ◽  
Anisotropic Viscosity

The purpose of this work is to study the generalized Navier–Stokes equations with nonlinear viscosity that, in addition, can be fully anisotropic. Existence of very weak solutions is proved for the associated initial and boundary-value problem, supplemented with no-slip boundary conditions. We show that our existence result is optimal in some directions provided there is some compensation in the remaining directions. A particular simplification of the problem studied here, reduces to the Navier–Stokes equations with (linear) anisotropic viscosity used to model either the turbulence or the Ekman layer in atmospheric and oceanic fluid flows.

Transition and turbulence in horizontal convection: linear stability analysis

2017 ◽  
Vol 821 ◽  
pp. 31-58 ◽  
Author(s):  
Pierre-Yves Passaggia ◽  
Alberto Scotti ◽  
Brian White
Keyword(s):  
Stability Analysis ◽  
Rayleigh Number ◽  
Boundary Conditions ◽  
Stokes Equations ◽  
Critical Rayleigh Number ◽  
Base Flow ◽  
Two Dimensional ◽  
Slip Boundary Conditions ◽  
Slip Boundary ◽  
Horizontal Convection

The linear instability mechanisms of horizontal convection in a rectangular cavity forced by a horizontal buoyancy gradient along its surface are investigated using local and global stability analyses for a Prandtl number equal to unity. The results show that the stability of the base flow, a steady circulation characterized by a narrow descending plume and a broad upwelling region, depends on the Rayleigh number, $Ra$. For free-slip boundary conditions at a critical value of $Ra\approx 2\times 10^{7}$, the steady base flow becomes unstable to three-dimensional perturbations, characterized by counter-rotating vortices originating within the plume region. A Wentzel–Kramers–Brillouin (WKB) method applied along closed streamlines demonstrates that this instability is of a Rayleigh–Taylor type and can be used to accurately reconstruct the global instability mode. In the case of no-slip boundary conditions, the base flow also becomes unstable to a self-sustained two-dimensional instability whose critical Rayleigh number is $Ra\approx 1.7\times 10^{8}$. Beyond this critical $Ra$, two-dimensional equilibrium stationary states of the Navier–Stokes equations are computed using the selective frequency damping method. The two-dimensional onset of instability is shown to be characterized by a family of modes also originating within the plume. A local spatio-temporal stability analysis shows that the flow becomes absolutely unstable at the origin of the plume. Taken together, these results illustrate the mechanisms behind the onset of turbulence that has been observed in horizontal convection.

scholarly journals Correlation between No-Slip and Slip Boundary Conditions Associated with A Two-Dimensional Navier-Stokes Flows in a Plane Diffuser

2021 ◽  
Vol 65 (1) ◽  
pp. 1-23
Author(s):  
Ranis Ibragimov ◽  
◽  
Vesselin Vatchev ◽  
Keyword(s):  
Boundary Conditions ◽  
Small Perturbation ◽  
Taylor Series Expansion ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Slip Boundary Conditions ◽  
Viscous Effects ◽  
Stokes Flows ◽  
Slip Boundary ◽  
Two Parameters

We examine the viscous effects of slip boundary conditions for the model describing two-dimensional Navier-Stokes flows in a plane diffuser. It is shown that the velocity profile is related to a half period shifted Weierstrass function with two parameters. This allows to approximate the explicit solution by a Taylor series expansion with two new micro- parameters, that can be measured in physical experiments. It is shown that the assumption for no-slip boundary conditions is stable in the sense that a small perturbation of the boundary values result in a small perturbation in the solutions.

Newtonian and viscoelastic fluid flows through an abrupt 1:4 expansion with slip boundary conditions

2020 ◽  
Vol 32 (4) ◽  
pp. 043103 ◽  
Author(s):  
L. L. Ferrás ◽  
A. M. Afonso ◽  
M. A. Alves ◽  
J. M. Nóbrega ◽  
F. T. Pinho
Keyword(s):  
Boundary Conditions ◽  
Viscoelastic Fluid ◽  
Fluid Flows ◽  
Slip Boundary Conditions ◽  
Slip Boundary
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