scholarly journals Stability of a Double-Diffusive Interface in the Diffusive Convection Regime

2012 ◽  
Vol 42 (5) ◽  
pp. 840-854 ◽  
Author(s):  
J. R. Carpenter ◽  
T. Sommer ◽  
A. Wüest
Keyword(s):  
Boundary Layer ◽  
Stability Analysis ◽  
Numerical Simulations ◽  
Linear Stability ◽  
Boundary Layers ◽  
Linear Stability Analysis ◽  
Direct Numerical Simulations ◽  
Diffusive Convection ◽  
Diffusive Interface ◽  
Double Diffusive

Abstract In this paper, the authors explore the conditions under which a double-diffusive interface may become unstable. Focus is placed on the case of a cold, freshwater layer above a warm, salty layer [i.e., the diffusive convection (DC) regime]. The “diffusive interface” between these layers will develop gravitationally unstable boundary layers due to the more rapid diffusion of heat (the destabilizing component) relative to salt. Previous studies have assumed that a purely convective-type instability of these boundary layers is what drives convection in this system and that this may be parameterized by a boundary layer Rayleigh number. The authors test this theory by conducting both a linear stability analysis and direct numerical simulations of a diffusive interface. Their linear stability analysis reveals that the transition to instability always occurs as an oscillating diffusive convection mode and at boundary layer Rayleigh numbers much smaller than previously thought. However, these findings are based on making a quasi-steady assumption for the growth of the interfaces by molecular diffusion. When diffusing interfaces are modeled (using direct numerical simulations), the authors observe that the time dependence is significant in determining the instability of the boundary layers and that the breakdown is due to a purely convective-type instability. Their findings therefore demonstrate that the relevant instability in a DC staircase is purely convective.

scholarly journals Simulations of a double-diffusive interface in the diffusive convection regime

2012 ◽  
Vol 711 ◽  
pp. 411-436 ◽  
Author(s):  
J. R. Carpenter ◽  
T. Sommer ◽  
A. Wüest
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Molecular Diffusion ◽  
Layer Structure ◽  
Previous Theory ◽  
Convection Regime ◽  
Graphic Interface ◽  
Diffusive Convection ◽  
Diffusive Interface ◽  
Double Diffusive

AbstractThree-dimensional direct numerical simulations are performed that give us an in-depth account of the evolution and structure of the double-diffusive interface. We examine the diffusive convection regime, which, in the oceanographically relevant case, consists of relatively cold fresh water above warm salty water. A ‘double-boundary-layer’ structure is found in all of the simulations, in which the temperature ($T$) interface has a greater thickness than the salinity ($S$) interface. Therefore, thin gravitationally unstable boundary layers are maintained at the edges of the diffusive interface. The $TS$-interface thickness ratio is found to scale with the diffusivity ratio in a consistent manner once the shear across the boundary layers is accounted for. The turbulence present in the mixed layers is not able to penetrate the stable stratification of the interface core, and the $TS$-fluxes through the core are given by their molecular diffusion values. Interface growth in time is found to be determined by molecular diffusion of the $S$-interface, in agreement with a previous theory. The stability of the boundary layers is also considered, where we find boundary layer Rayleigh numbers that are an order of magnitude lower than previously assumed.

Stability and dynamics of the laminar wake past a slender blunt-based axisymmetric body

2011 ◽  
Vol 676 ◽  
pp. 110-144 ◽  
Author(s):  
P. BOHORQUEZ ◽  
E. SANMIGUEL-ROJAS ◽  
A. SEVILLA ◽  
J. I. JIMÉNEZ-GONZÁLEZ ◽  
C. MARTÍNEZ-BAZÁN
Keyword(s):  
Stability Analysis ◽  
Numerical Simulations ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Velocity Ratio ◽  
Reynolds Numbers ◽  
Base Flow ◽  
Direct Numerical Simulations ◽  
The Body ◽  
Stream Velocity

We investigate the stability properties and flow regimes of laminar wakes behind slender cylindrical bodies, of diameter D and length L, with a blunt trailing edge at zero angle of attack, combining experiments, direct numerical simulations and local/global linear stability analyses. It has been found that the flow field is steady and axisymmetric for Reynolds numbers below a critical value, Recs (L/D), which depends on the length-to-diameter ratio of the body, L/D. However, in the range of Reynolds numbers Recs(L/D) < Re < Reco(L/D), although the flow is still steady, it is no longer axisymmetric but exhibits planar symmetry. Finally, for Re > Reco, the flow becomes unsteady due to a second oscillatory bifurcation which preserves the reflectional symmetry. In addition, as the Reynolds number increases, we report a new flow regime, characterized by the presence of a secondary, low frequency oscillation while keeping the reflectional symmetry. The results reported indicate that a global linear stability analysis is adequate to predict the first bifurcation, thereby providing values of Recs nearly identical to those given by the corresponding numerical simulations. On the other hand, experiments and direct numerical simulations give similar values of Reco for the second, oscillatory bifurcation, which are however overestimated by the linear stability analysis due to the use of an axisymmetric base flow. It is also shown that both bifurcations can be stabilized by injecting a certain amount of fluid through the base of the body, quantified here as the bleed-to-free-stream velocity ratio, Cb = Wb/W∞.

Characterisation of a Wavy Convective Instability in Poiseuille-Rayleigh-Be´nard Flows: Linear Stability Analysis and Non Linear Numerical Simulations Under Random Excitations

2010 ◽  
Author(s):  
Xavier Nicolas ◽  
Shihe Xin ◽  
Noussaiba Zoueidi
Keyword(s):  
Stability Analysis ◽  
Numerical Simulations ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Convective Instability ◽  
Random Excitation ◽  
Time Development ◽  
Direct Numerical Simulations ◽  
Channel Inlet ◽  
Non Linear

The aim of the present paper is to characterize a secondary convective instability of Poiseuille-Rayleigh-Be´nard (PRB) mixed convection flows in air that takes the shape of wavy thermoconvective rolls, for 70≤Re≤300 and 3000<Ra<15000. At first, the linear stability analysis by Clever and Busse [JFM, 1991] in the case of PRB flows between two infinite plates is extended to the case of confined channels with a 10 transversal aspect ratio. In the second part, using 3D non linear direct numerical simulations, the space and time development of the chaotic wavy rolls obtained by maintaining a permanent random excitation at channel inlet is analyzed. As the perturbation is designed to cover all the modes, it is possible to detect the modes that are naturally amplified by the flow and those that are damped. It is shown that the wavy roll characteristics obtained in this way vary a lot with Ra increasing and stabilize for Ra>3Ra*. Comparisons with the experiments by Pabiou et al. [JFM, 2005] are proposed.

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