Numerical simulations and linear stability analysis of transient buoyancy-induced flow in a two-dimensional enclosure

2004 ◽  
pp. 269-274
Author(s):  
C Ihle ◽  
Y Niño ◽  
R Frederick
Keyword(s):  
Stability Analysis ◽  
Numerical Simulations ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Two Dimensional ◽  
Induced Flow ◽  
Buoyancy Induced Flow

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∞.

scholarly journals Revisiting the Meandering Instability During Step-Flow Epitaxy

2019 ◽  
Vol 9 (22) ◽  
pp. 4840
Author(s):  
Yue Chen
Keyword(s):  
Stability Analysis ◽  
Free Boundary ◽  
Boundary Problem ◽  
Linear Stability ◽  
Free Boundary Problem ◽  
Linear Stability Analysis ◽  
Chemical Potential ◽  
Two Dimensional ◽  
Step Flow ◽  
Morphological Instabilities

This paper starts with a generalized Burton, Cabrera and Frank (BCF) model by considering the energetic contribution of the adjacent terraces to the step chemical potential. We use the linear stability analysis of the quasistatic free-boundary problem for a two-dimensional step separated by broad terraces to study the step-meandering instabilities. The results show that the equilibrium adatom coverage has influence on the morphological instabilities.

scholarly journals Linear stability of confined flow around a 180-degree sharp bend

2017 ◽  
Vol 822 ◽  
pp. 813-847 ◽  
Author(s):  
Azan M. Sapardi ◽  
Wisam K. Hussam ◽  
Alban Pothérat ◽  
Gregory J. Sheard
Keyword(s):  
Reynolds Number ◽  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Critical Reynolds Number ◽  
Three Dimensional ◽  
Base Flow ◽  
Two Dimensional ◽  
Two Dimensional Flow ◽  
The Stability

This study seeks to characterise the breakdown of the steady two-dimensional solution in the flow around a 180-degree sharp bend to infinitesimal three-dimensional disturbances using a linear stability analysis. The stability analysis predicts that three-dimensional transition is via a synchronous instability of the steady flows. A highly accurate global linear stability analysis of the flow was conducted with Reynolds number $\mathit{Re}<1150$ and bend opening ratio (ratio of bend width to inlet height) $0.2\leqslant \unicode[STIX]{x1D6FD}\leqslant 5$. This range of $\mathit{Re}$ and $\unicode[STIX]{x1D6FD}$ captures both steady-state two-dimensional flow solutions and the inception of unsteady two-dimensional flow. For $0.2\leqslant \unicode[STIX]{x1D6FD}\leqslant 1$, the two-dimensional base flow transitions from steady to unsteady at higher Reynolds number as $\unicode[STIX]{x1D6FD}$ increases. The stability analysis shows that at the onset of instability, the base flow becomes three-dimensionally unstable in two different modes, namely a spanwise oscillating mode for $\unicode[STIX]{x1D6FD}=0.2$ and a spanwise synchronous mode for $\unicode[STIX]{x1D6FD}\geqslant 0.3$. The critical Reynolds number and the spanwise wavelength of perturbations increase as $\unicode[STIX]{x1D6FD}$ increases. For $1<\unicode[STIX]{x1D6FD}\leqslant 2$ both the critical Reynolds number for onset of unsteadiness and the spanwise wavelength decrease as $\unicode[STIX]{x1D6FD}$ increases. Finally, for $2<\unicode[STIX]{x1D6FD}\leqslant 5$, the critical Reynolds number and spanwise wavelength remain almost constant. The linear stability analysis also shows that the base flow becomes unstable to different three-dimensional modes depending on the opening ratio. The modes are found to be localised near the reattachment point of the first recirculation bubble.

Linear Stability of a Radial Wall Jet

1979 ◽  
Vol 30 (4) ◽  
pp. 544-558 ◽  
Author(s):  
Y Tsuji ◽  
Y Morikawa
Keyword(s):  
Stability Analysis ◽  
Perturbation Method ◽  
Experimental Evidence ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Dimensional Case ◽  
Wall Jet ◽  
Two Dimensional ◽  
Radial Wall ◽  
Sommerfeld Equation

SummaryA linear stability analysis was made for a radial wall jet. A perturbation method against the two-dimensional wall jet was used for the formulation, from which a non-homogeneous Orr-Sommerfeld equation was derived. The computation showed that disturbances are more unstable in the radial wall jet than in the two-dimensional case, which agrees qualitatively with an experimental evidence.

Effect of enclosure height on the structure and stability of shear layers induced by differential rotation

2015 ◽  
Vol 765 ◽  
pp. 45-81 ◽  
Author(s):  
Tony Vo ◽  
Luca Montabone ◽  
Gregory J. Sheard
Keyword(s):  
Stability Analysis ◽  
Shear Layer ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Differential Rotation ◽  
Shear Layers ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Axisymmetric Model ◽  
Two Dimensional Model

AbstractThe structure and stability of Stewartson shear layers with different heights are investigated numerically via axisymmetric simulation and linear stability analysis, and a validation of the quasi-two-dimensional model is performed. The shear layers are generated in a rotating cylindrical tank with circular disks located at the lid and base imposing a differential rotation. The axisymmetric model captures both the thick and thin nested Stewartson layers, which are scaled by the Ekman number ($\mathit{E}\,$) as $\mathit{E}\,^{1/4}$ and $\mathit{E}\,^{1/3}$ respectively. In contrast, the quasi-two-dimensional model only captures the $\mathit{E}\,^{1/4}$ layer as the axial velocity required to invoke the $\mathit{E}\,^{1/3}$ layer is excluded. A direct comparison between the axisymmetric base flows and their linear stability in these two models is examined here for the first time. The base flows of the two models exhibit similar flow features at low Rossby numbers ($\mathit{Ro}$), with differences evident at larger $\mathit{Ro}$ where depth-dependent features are revealed by the axisymmetric model. Despite this, the quasi-two-dimensional model demonstrates excellent agreement with the axisymmetric model in terms of the shear-layer thickness and predicted stability. A study of various aspect ratios reveals that a Reynolds number based on the theoretical Ekman layer thickness is able to describe the transition of a base flow that is reflectively symmetric about the mid-plane to a symmetry-broken state. Additionally, the shear-layer thicknesses scale closely to the expected ${\it\delta}_{vel}\propto A\mathit{E}\,^{1/4}$ and ${\it\delta}_{vort}\propto A\mathit{E}\,^{1/3}$ for shear layers that are not affected by the confinement ($A\mathit{E}\,^{1/4}\lesssim 0.34$ in this system, the ratio of tank height to shear-layer radius). The linear stability analysis reveals that the ratio of Stewartson layer radius to thickness should be greater than $45$ for the stability of the flow to be independent of aspect ratio. Thus, for sufficiently small $A\mathit{E}\,^{1/4}$ and $A\mathit{E}\,^{1/3}$, the flow characteristics remain similar and the linear stability of the flow can be described universally when the azimuthal wavelength is scaled against $A$. The analysis also recovers an asymptotic scaling for the normalized azimuthal wavelength which suggests that ${\it\lambda}_{{\it\theta},c}^{\ast }\propto (|\mathit{Ro}|/\mathit{E}\,^{2})^{-1/5}$ for geometry-independent shear layers at marginal stability.

SYMMETRIC LARGE-SCALE VELOCITY FIELDS IN TWO-DIMENSIONAL THERMAL CONVECTION

1994 ◽  
Vol 04 (05) ◽  
pp. 1369-1374 ◽  
Author(s):  
J. PRAT ◽  
I. MERCADER ◽  
J.M. MASSAGUER
Keyword(s):  
Stability Analysis ◽  
Velocity Field ◽  
Velocity Profile ◽  
Numerical Simulations ◽  
Linear Stability Analysis ◽  
Thermal Convection ◽  
Vertical Profile ◽  
Large Scale ◽  
Velocity Fields ◽  
Two Dimensional

Recent experiments on thermal convection in finite containers [Krishnamurti & Howard, 1981; Howard & Krishnamurti, 1986] show the presence of flows spanning the largest dimension of the container. Numerical simulations of 2D thermal convection showing large-scale flows of this kind have been presented elsewhere [Prat et al., 1993a, 1993b]. In every known example the large scale velocity field has been found to display a vertical profile either antisymmetric or showing rather small departures from antisymmetry. In contrast, theoretical group arguments support the existence of symmetric velocity profiles. In the present paper it will be shown that large-scale velocity fields with vertically symmetric velocity profile do exist. In spite of these flows not being dominant in the range of parameters explored, their geometry and dynamics will be discussed on the basis of a linear stability analysis.

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