Linear instability in two-layer channel flow due to double-diffusive phenomenon

2020 ◽  
Vol 32 (2) ◽  
pp. 024102 ◽  
Author(s):  
Kirti Chandra Sahu
Keyword(s):  
Channel Flow ◽  
Linear Instability ◽  
Double Diffusive

scholarly journals Double-Diffusive Interleaving: Properties of the Steady-State Solution

2015 ◽  
Vol 45 (3) ◽  
pp. 813-835 ◽  
Author(s):  
Yuehua Li ◽  
Trevor J. McDougall
Keyword(s):  
Steady State ◽  
Double Diffusion ◽  
Intermediate Stage ◽  
Steady State Solution ◽  
Finite Amplitude ◽  
Linear Instability ◽  
Vertical Diffusion ◽  
Prandtl Numbers ◽  
Pass Through ◽  
Double Diffusive

AbstractDouble-diffusive interleaving is examined as it progresses from a linear instability toward finite amplitude. When the basic stratification is in the “finger” sense, the initial series of finger interfaces is unstable and one grows in strength at the expense of the others. At an intermediate stage of its development, the interleaving motions pass through a stage when every second interface in the vertical is stable to double diffusion. At a later time this interface turns into a “diffusive” double-diffusive interface. This study takes the fluxes of heat and salt across both the finger and diffusive interfaces to be given by the laboratory flux laws, and the authors ask whether a steady state is possible. It is found that the fluxes across the diffusive interfaces must be many times stronger relative to the corresponding fluxes across the finger interfaces than is indicated from existing flux expressions derived from laboratory experiments. The total effect of the interleaving motion on the vertical fluxes of heat and of salt are calculated for the steady-state solutions. It is found that both the fluxes of heat and salt are upgradient, corresponding to a negative vertical diffusion coefficient for all heat, salt, and density. For moderate to large Prandtl numbers, these negative effective diapycnal diffusivities of heat and salt are approximately equal so that the interleaving process acts to counteract some of the usual turbulent diapycnal diffusivity due to breaking internal waves.

scholarly journals Global Stability For Double-Diffusive Convection In A Couple-Stress Fluid Saturating A Porous Medium

2019 ◽  
Vol 41 (1) ◽  
pp. 13-20
Author(s):  
Shalu Choudhary ◽  
Keyword(s):  
Porous Medium ◽  
Couple Stress ◽  
Linear Instability ◽  
Couple Stress Fluid ◽  
Brinkman Number ◽  
Onset Of Convection ◽  
Instability Theory ◽  
Diffusive Convection ◽  
Solute Gradient ◽  
Double Diffusive

Abstract We show that the global non-linear stability threshold for convection in a double-diffusive couple-stress fluid saturating a porous medium is exactly the same as the linear instability boundary. The optimal result is important because it shows that linearized instability theory has captured completely the physics of the onset of convection. It is also found that couple-stress fluid saturating a porous medium is thermally more stable than the ordinary viscous fluid, and the effects of couple-stress parameter (F ) , solute gradient ( S f ) and Brinkman number ( D a ) on the onset of convection is also analyzed.

scholarly journals Linear instability of shear thinning pressure driven channel flow

2019 ◽  
Vol 270 ◽  
pp. 66-78 ◽  
Author(s):  
H.J. Barlow ◽  
E.J. Hemingway ◽  
A. Clarke ◽  
S.M. Fielding
Keyword(s):  
Channel Flow ◽  
Shear Thinning ◽  
Linear Instability ◽  
Pressure Driven

Double-diffusive Magnetic Layering

2021 ◽  
Vol 922 (2) ◽  
pp. 195
Author(s):  
D. W. Hughes ◽  
N. H. Brummell
Keyword(s):  
Magnetic Field ◽  
Chemical Elements ◽  
Turbulent Transport ◽  
Linear Instability ◽  
Thermosolutal Convection ◽  
Horizontal Magnetic Field ◽  
Diffusive Regime ◽  
Magnetic Buoyancy ◽  
Double Diffusive

Abstract Double-diffusive systems, such as thermosolutal convection, in which the density depends on two components that diffuse at different rates, are prone to both steady and oscillatory instabilities. Such systems can evolve into layered states, in which both components, and also the density, adopt a “staircase” profile. Turbulent transport is enhanced significantly in the layered state. Here we exploit an analogy between magnetic buoyancy and thermosolutal convection in order to demonstrate the phenomenon of magnetic layering. We examine the long-term nonlinear evolution of a vertically stratified horizontal magnetic field in the so-called “diffusive regime,” where an oscillatory linear instability operates. Motivated astrophysically, we consider the case where the viscous and magnetic diffusivities are much smaller than the thermal diffusivity. We demonstrate that diffusive layering can occur even for subadiabatic temperature gradients. Magnetic layering may be relevant for stellar radiative zones, with implications for the turbulent transport of heat, magnetic field, and chemical elements.

scholarly journals Spatio-temporal linear stability of double-diffusive two-fluid channel flow

2012 ◽  
Vol 24 (5) ◽  
pp. 054103 ◽  
Author(s):  
Kirti Chandra Sahu ◽  
Rama Govindarajan
Keyword(s):  
Linear Stability ◽  
Channel Flow ◽  
Fluid Channel ◽  
Spatio Temporal ◽  
Two Fluid ◽  
Double Diffusive

Linear stability analysis of channel flow of viscoelastic Oldroyd-B and FENE-P fluids

2013 ◽  
Vol 737 ◽  
pp. 249-279 ◽  
Author(s):  
Mengqi Zhang ◽  
Iman Lashgari ◽  
Tamer A. Zaki ◽  
Luca Brandt
Keyword(s):  
Relaxation Time ◽  
Kinetic Energy ◽  
Channel Flow ◽  
Time Scale ◽  
Linear Instability ◽  
Additional Parameter ◽  
Normal Velocity ◽  
Opposite Case ◽  
Polymer Relaxation ◽  
Viscoelastic Effects

AbstractWe study the modal and non-modal linear instability of inertia-dominated channel flow of viscoelastic fluids modelled by the Oldroyd-B and FENE-P closures. The effects of polymer viscosity and relaxation time are considered for both fluids, with the additional parameter of the maximum possible extension for the FENE-P. We find that the parameter explaining the effect of the polymer on the instability is the ratio between the polymer relaxation time and the characteristic instability time scale (the frequency of a modal wave and the time over which the disturbance grows in the non-modal case). Destabilization of both modal and non-modal instability is observed when the polymer relaxation time is shorter than the instability time scale, whereas the flow is more stable in the opposite case. Analysis of the kinetic energy budget reveals that in both regimes the production of perturbation kinetic energy due to the work of the Reynolds stress against the mean shear is responsible for the observed effects where polymers act to alter the correlation between the streamwise and wall-normal velocity fluctuations. In the subcritical regime, the non-modal amplification of streamwise elongated structures is still the most dangerous disturbance-growth mechanism in the flow and this is slightly enhanced by the presence of polymers. However, viscoelastic effects are found to have a stabilizing effect on the amplification of oblique modes.

Linear instability of pressure-driven channel flow of a Newtonian and a Herschel-Bulkley fluid

2007 ◽  
Vol 19 (12) ◽  
pp. 122101 ◽  
Author(s):  
K. C. Sahu ◽  
P. Valluri ◽  
P. D. M. Spelt ◽  
O. K. Matar
Keyword(s):  
Channel Flow ◽  
Linear Instability ◽  
Pressure Driven
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