Direct simulation of two-dimensional Bénard flow with free-slip boundary conditions

2021 ◽  
pp. 105040
Author(s):  
Rodrigo Rodakoviski ◽  
Nelson L. Dias
Keyword(s):  
Boundary Conditions ◽  
Two Dimensional ◽  
Direct Simulation ◽  
Slip Boundary Conditions ◽  
Slip Boundary

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.

Reduced-Order Modeling of Low Mach Number Unsteady Microchannel Flows

2014 ◽  
Vol 136 (5) ◽  
Author(s):  
Leila Issa ◽  
Issam Lakkis
Keyword(s):  
Mach Number ◽  
Boundary Conditions ◽  
Stokes Equations ◽  
Solid Boundary ◽  
Two Dimensional ◽  
Slip Boundary Conditions ◽  
Reduced Order ◽  
Low Mach Number ◽  
First Order ◽  
Slip Boundary

We present reduced-order models of unsteady low-Mach-number ideal gas flows in two-dimensional rectangular microchannels subject to first-order slip-boundary conditions. The pressure and density are related by a polytropic process, allowing for isothermal or isentropic flow assumptions. The Navier–Stokes equations are simplified using low-Mach-number expansions of the pressure and velocity fields. Up to first order, this approximation results in a system that is subject to no-slip condition at the solid boundary. The second-order system satisfies the slip-boundary conditions. The resulting equations and the subsequent pressure-flow-rate relationships enable modeling the flow using analog circuit components. The accuracy of the proposed models is investigated for steady and unsteady flows in a two-dimensional channel for different values of Mach and Knudsen numbers.

scholarly journals Lattice-Gas Simulations of Ternary Amphiphilic Fluid Flow in Porous Media

1998 ◽  
Vol 09 (08) ◽  
pp. 1479-1490 ◽  
Author(s):  
P. V. Coveney ◽  
J.-B. Maillet ◽  
J. L. Wilson ◽  
P. W. Fowler ◽  
O. Al-Mushadani ◽  
...  
Keyword(s):  
Porous Media ◽  
Boundary Conditions ◽  
Single Phase ◽  
Lattice Gas ◽  
Flow In Porous Media ◽  
Two Dimensional ◽  
Slip Boundary Conditions ◽  
Dimensional Lattice ◽  
Slip Boundary ◽  
Saturated Rock

We develop our existing two-dimensional lattice-gas model to simulate the flow of single phase, binary immiscible and ternary amphiphilic fluids. This involves the inclusion of fixed obstacles on the lattice, together with the inclusion of "no-slip" boundary conditions. Here we report on preliminary applications of this model to the flow of such fluids within model porous media. We also construct fluid invasion boundary conditions, and the effects of invading aqueous solutions of surfactant on oil-saturated rock during imbibition and drainage are described.

NAVIER–STOKES SYSTEM ON THE FLAT CYLINDER AND UNIT SQUARE WITH SLIP BOUNDARY CONDITIONS

2010 ◽  
Vol 12 (02) ◽  
pp. 325-349 ◽  
Author(s):  
EFIM DINABURG ◽  
DONG LI ◽  
YAKOV G. SINAI
Keyword(s):  
Boundary Conditions ◽  
Initial Velocity ◽  
Stokes System ◽  
Navier Stokes ◽  
Decay Estimates ◽  
Two Dimensional ◽  
Slip Boundary Conditions ◽  
Unit Square ◽  
Slip Boundary

We study the decay of Fourier modes of solutions to the two-dimensional Navier–Stokes System on a flat cylinder and the unit square with slip boundary conditions. Under some suitable assumptions on the initial velocity, we obtain quantitative decay estimates of the Fourier modes.

scholarly journals Bifurcations in a quasi-two-dimensional Kolmogorov-like flow

2017 ◽  
Vol 828 ◽  
pp. 837-866 ◽  
Author(s):  
Jeffrey Tithof ◽  
Balachandra Suri ◽  
Ravi Kumar Pallantla ◽  
Roman O. Grigoriev ◽  
Michael F. Schatz
Keyword(s):  
Boundary Conditions ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Quantitative Agreement ◽  
Navier Stokes ◽  
Dielectric Fluid ◽  
Two Dimensional ◽  
Slip Boundary Conditions ◽  
Slip Boundary ◽  
2D Model

We present a combined experimental and theoretical study of the primary and secondary instabilities in a Kolmogorov-like flow. The experiment uses electromagnetic forcing with an approximately sinusoidal spatial profile to drive a quasi-two-dimensional (Q2D) shear flow in a thin layer of electrolyte suspended on a thin lubricating layer of a dielectric fluid. Theoretical analysis is based on a two-dimensional (2D) model (Suri et al., Phys. Fluids, vol. 26 (5), 2014, 053601), derived from first principles by depth-averaging the full three-dimensional Navier–Stokes equations. As the strength of the forcing is increased, the Q2D flow in the experiment undergoes a series of bifurcations, which is compared with results from direct numerical simulations of the 2D model. The effects of confinement and the forcing profile are studied by performing simulations that assume spatial periodicity and strictly sinusoidal forcing, as well as simulations with realistic no-slip boundary conditions and an experimentally validated forcing profile. We find that only the simulation subject to physical no-slip boundary conditions and a realistic forcing profile provides close, quantitative agreement with the experiment. Our analysis offers additional validation of the 2D model as well as a demonstration of the importance of properly modelling the forcing and boundary conditions.

Travelling waves in two-dimensional reactive Boussinesq systems with no-slip boundary conditions

Nonlinearity ◽  
2006 ◽  
Vol 19 (11) ◽  
pp. 2605-2615 ◽  
Author(s):  
Peter Constantin ◽  
Marta Lewicka ◽  
Lenya Ryzhik
Keyword(s):  
Boundary Conditions ◽  
Travelling Waves ◽  
Two Dimensional ◽  
Slip Boundary Conditions ◽  
Slip Boundary ◽  
Boussinesq Systems
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