Spatial decay bounds in a channel flow of 2-D Boussinesq fluid with variable thermal diffusivity

2018 ◽  
Vol 41 (11) ◽  
pp. 4287-4304
Author(s):  
Yuanfei Li ◽  
Changhao Lin
Keyword(s):  
Thermal Diffusivity ◽  
Channel Flow ◽  
Spatial Decay ◽  
Decay Bounds ◽  
Boussinesq Fluid

scholarly journals Spatial decay bounds for the channel flow of the Boussinesq equations

2011 ◽  
Vol 381 (1) ◽  
pp. 87-109 ◽  
Author(s):  
Yan Liu ◽  
Yuanfei Li ◽  
Yiwu Lin ◽  
Zhengan Yao
Keyword(s):  
Channel Flow ◽  
Boussinesq Equations ◽  
Spatial Decay ◽  
Decay Bounds

SPATIAL DECAY BOUNDS IN THE CHANNEL FLOW OF AN INCOMPRESSIBLE VISCOUS FLUID

2004 ◽  
Vol 14 (06) ◽  
pp. 795-818 ◽  
Author(s):  
CHANGHAO LIN ◽  
LAWRENCE E. PAYNE
Keyword(s):  
Laminar Flow ◽  
Viscous Fluid ◽  
Channel Flow ◽  
Exponential Decay ◽  
Transient Flow ◽  
Incompressible Viscous Fluid ◽  
Spatial Decay ◽  
Decay Bounds ◽  
Channel Boundary ◽  
Entrance Velocity

In this paper, we study the transient flow of an incompressible viscous fluid in a semi-infinite channel assuming adherence at the channel boundary. We show that under appropriate restrictions on the data if the fluid is initially at rest and the channel entrance velocity and/or channel width are sufficiently small, the solution will tend exponentially to a transient laminar flow as the distance form the entry section tends to infinity. In fact explicit exponential decay bounds are obtained.

Convection in an imposed magnetic field. Part 1. The development of nonlinear convection

1981 ◽  
Vol 108 ◽  
pp. 247-272 ◽  
Author(s):  
N. O. Weiss
Keyword(s):  
Magnetic Field ◽  
Thermal Diffusivity ◽  
Rayleigh Number ◽  
Numerical Experiments ◽  
Dynamical Regime ◽  
Two Dimensional ◽  
Nonlinear Convection ◽  
Boussinesq Fluid ◽  
Chandrasekhar Number ◽  
Steady Convection

Nonlinear two-dimensional magnetoconvection in a Boussinesq fluid has been studied in a series of numerical experiments with values of the Chandrasekhar number Q ≤ 4000 and the ratio ζ of the magnetic to the thermal diffusivity in the range 1 ≥ ζ ≥ 0·025. If the imposed field is strong enough, convection sets in as overstable oscillations which give way to steady convection as the Rayleigh number R is increased. In the dynamical regime that follows, magnetic flux is concentrated into sheets at the sides of the cells, from which the motion is excluded.

Horizontal convection is non-turbulent

2002 ◽  
Vol 466 ◽  
pp. 205-214 ◽  
Author(s):  
F. PAPARELLA ◽  
W. R. YOUNG
Keyword(s):  
Thermal Diffusivity ◽  
Energy Dissipation ◽  
Rayleigh Number ◽  
Prandtl Number ◽  
Numerical Solutions ◽  
Inviscid Limit ◽  
Two Dimensional ◽  
Uniform Temperature ◽  
Horizontal Convection ◽  
Boussinesq Fluid

Consider the problem of horizontal convection: a Boussinesq fluid, forced by applying a non-uniform temperature at its top surface, with all other boundaries insulating. We prove that if the viscosity, ν, and thermal diffusivity, κ, are lowered to zero, with σ ≡ ν/κ fixed, then the energy dissipation per unit mass, κ, also vanishes in this limit. Numerical solutions of the two-dimensional case show that despite this anti-turbulence theorem, horizontal convection exhibits a transition to eddying flow, provided that the Rayleigh number is sufficiently high, or the Prandtl number σ sufficiently small. We speculate that horizontal convection is an example of a flow with a large number of active modes which is nonetheless not ‘truly turbulent’ because ε→0 in the inviscid limit.

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