Analysis and direct numerical simulation of the flow at a gravity-current head. Part 2. The lobe-and-cleft instability

2000 ◽  
Vol 418 ◽  
pp. 213-229 ◽  
Author(s):  
CARLOS HÄRTEL ◽  
FREDRIK CARLSSON ◽  
MATTIAS THUNBLOM
Keyword(s):  
Numerical Simulation ◽  
Stability Analysis ◽  
Direct Numerical Simulation ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Gravity Current ◽  
Leading Edge ◽  
Two Dimensional ◽  
Amplification Rate ◽  
The Stability

Results are presented from a linear-stability analysis of the flow at the head of two-dimensional gravity-current fronts. The analysis was undertaken in order to clarify the instability mechanism that leads to the formation of the complex lobe-and-cleft pattern which is commonly observed at the leading edge of gravity currents propagating along solid boundaries. The stability analysis concentrates on the foremost part of the front, and is based on direct numerical simulation data of two-dimensional lock-exchange flows which are described in the companion paper, Härtel et al. (2000). High-order compact finite differences are employed to discretize the stability equations which results in an algebraic eigenvalue problem for the amplification rate, that is solved in an iterative fashion. The analysis reveals the existence of a vigorous linear instability that acts in a localized way at the leading edge of the front and originates in an unstable stratification in the flow region between the nose and stagnation point. It is shown that the amplification rate of this instability as well as its spanwise length scale depend strongly on Reynolds number. For validation, three-dimensional direct numerical simulations of the early stages of the frontal instability are performed, and close agreement with the results from the linear-stability analysis is demonstrated.

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.

The effect of interruption probability in lattice model of two-lane traffic flow with passing

2016 ◽  
Vol 27 (05) ◽  
pp. 1650050 ◽  
Author(s):  
Guanghan Peng
Keyword(s):  
Numerical Simulation ◽  
Stability Analysis ◽  
Traffic Flow ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Stability Condition ◽  
Lattice Model ◽  
Mkdv Equation ◽  
Reaction Coefficient ◽  
The Stability

A new lattice model is proposed by taking into account the interruption probability with passing for two-lane freeway. The effect of interruption probability with passing is investigated about the linear stability condition and the mKdV equation through linear stability analysis and nonlinear analysis, respectively. Furthermore, numerical simulation is carried out to study traffic phenomena resulted from the interruption probability with passing in two-lane system. The results show that the interruption probability with passing can improve the stability of traffic flow for low reaction coefficient while the interruption probability with passing can destroy the stability of traffic flow for high reaction coefficient on two-lane highway.

Direct Numerical Simulation and Linear Stability Analysis of the Flow in a Pebble Bed

2014 ◽  
Author(s):  
P. Ward ◽  
Y. Hassan ◽  
E. Merzari ◽  
P. Fischer
Keyword(s):  
Numerical Simulation ◽  
Stability Analysis ◽  
Direct Numerical Simulation ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
National Laboratory ◽  
Argonne National Laboratory ◽  
Flow Patterns ◽  
Face Centered Cubic ◽  
Pebble Bed

The flow in a tightly packed array of spheres is important to various engineering fields. In nuclear engineering applications, for instance, researchers have proposed core geometries of the pebble bed reactor (PBR) type cooled by gas or molten salt. Proper core cooling, both at operation and during accident conditions, is a key issue that must be addressed in any reactor design; and the limited amount of data available for the complicated geometry of PBR cores makes this task even more complex. A detailed understanding of coolant flow patterns and properties must be developed in order to meet safety requirements and ensure core longevity. We address this issue by using the spectral-element computational fluid dynamics code Nek5000, developed at Argonne National Laboratory, to conduct both large eddy simulation (LES) and direct numerical simulation (DNS) of fluid flow through a single face-centered cubic sphere lattice with periodic boundary conditions. Moreover, a statistical analysis of the flow field and a global linear stability analysis of the laminar flow were performed in order to investigate the mechanism of laminar-turbulent transition in this geometry. One of the main objectives of the present study is, in fact, to determine how the Reynolds number affects the development of asymmetries within the flow patterns.

A Study of the Lateral Stability of Railroad Vehicles Using a Nonlinear Constrained Multibody Formulation

2001 ◽  
Author(s):  
Davide Valtorta ◽  
Khaled E. Zaazaa ◽  
Ahmed A. Shabana ◽  
Jalil R. Sany
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Linear Theory ◽  
Linear Stability Analysis ◽  
Numerical Study ◽  
Operating Conditions ◽  
Lateral Stability ◽  
Railroad Vehicles ◽  
Contact Formulation ◽  
The Stability

Abstract The lateral stability of railroad vehicles travelling on tangent tracks is one of the important problems that has been the subject of extensive research since the nineteenth century. Early detailed studies of this problem in the twentieth century are the work of Carter and Rocard on the stability of locomotives. The linear theory for the lateral stability analysis has been extensively used in the past and can give good results under certain operating conditions. In this paper, the results obtained using a linear stability analysis are compared with the results obtained using a general nonlinear multibody methodology. In the linear stability analysis, the sources of the instability are investigated using Liapunov’s linear theory and the eigenvalue analysis for a simple wheelset model on a tangent track. The effects of the stiffness of the primary and secondary suspensions on the stability results are investigated. The results obtained for the simple model using the linear approach are compared with the results obtained using a new nonlinear multibody based constrained wheel/rail contact formulation. This comparative numerical study can be used to validate the use of the constrained wheel/rail contact formulation in the study of lateral stability. Similar studies can be used in the future to define the limitations of the linear theory under general operating conditions.

scholarly journals Towards the Understanding of Humpback Whale Tubercles: Linear Stability Analysis of a Wavy Flat Plate

Fluids ◽  
2020 ◽  
Vol 5 (4) ◽  
pp. 212
Author(s):  
Miles Owen ◽  
Abdelkader Frendi
Keyword(s):  
Reynolds Number ◽  
Stability Analysis ◽  
Flat Plate ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Critical Reynolds Number ◽  
Global Analysis ◽  
Leading Edge ◽  
Local Analysis ◽  
Mean Flow

The results from a temporal linear stability analysis of a subsonic boundary layer over a flat plate with a straight and wavy leading edge are presented in this paper for a swept and un-swept plate. For the wavy leading-edge case, an extensive study on the effects of the amplitude and wavelength of the waviness was performed. Our results show that the wavy leading edge increases the critical Reynolds number for both swept and un-swept plates. For the un-swept plate, increasing the leading-edge amplitude increased the critical Reynolds number, while changing the leading-edge wavelength had no effect on the mean flow and hence the flow stability. For the swept plate, a local analysis at the leading-edge peak showed that increasing the leading-edge amplitude increased the critical Reynolds number asymptotically, while the leading-edge wavelength required optimization. A global analysis was subsequently performed across the span of the swept plate, where smaller leading-edge wavelengths produced relatively constant critical Reynolds number profiles that were larger than those of the straight leading edge, while larger leading-edge wavelengths produced oscillating critical Reynolds number profiles. It was also found that the most amplified wavenumber was not affected by the wavy leading-edge geometry and hence independent of the waviness.

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.

The Stability of a Radial Wall Jet

1977 ◽  
Vol 28 (4) ◽  
pp. 247-258 ◽  
Author(s):  
Yutaka Tsuji ◽  
Yoshinobu Morikawa ◽  
Masaaki Sakou
Keyword(s):  
Linear Stability ◽  
Water Flow ◽  
Wall Jet ◽  
Two Dimensional ◽  
Radial Wall ◽  
Linear Region ◽  
Stability Calculation ◽  
Amplification Rate ◽  
Vortex Patterns ◽  
The Stability

SummaryMeasured stability characteristics in a radial wall jet were compared with calculated results for a two-dimensional wall jet. It was found that the stability of the radial wall jet is similar in many respects to that of the two-dimensional wall jet. An exception is that the local amplification rate of the disturbance velocity is much higher than in the two-dimensional case. It was also found that quarter-harmonics appear in the non-linear region, as well as half-harmonics, and that their amplitude distributions show profiles similar to that of the fundamental component. Further, vortex patterns were visualised in water flow, and results corresponding to measurements in air flow and to the linear stability calculation were obtained.

Non-parallel linear stability analysis of the vertical boundary layer in a differentially heated cavity

1997 ◽  
Vol 352 ◽  
pp. 265-281 ◽  
Author(s):  
A. M. H. BROOKER ◽  
J. C. PATTERSON ◽  
S. W. ARMFIELD
Keyword(s):  
Boundary Layer ◽  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Navier Stokes ◽  
Parabolized Stability Equations ◽  
The Stability ◽  
Flow Quantity ◽  
Energy Equations ◽  
Made In

A non-parallel linear stability analysis which utilizes the assumptions made in the parabolized stability equations is applied to the buoyancy-driven flow in a differentially heated cavity. Numerical integration of the complete Navier–Stokes and energy equations is used to validate the non-parallel theory by introducing an oscillatory heat input at the upstream end of the boundary layer. In this way the stability properties are obtained by analysing the evolution of the resulting disturbances. The solutions show that the spatial growth rate and wavenumber are highly dependent on the transverse location and the disturbance flow quantity under consideration. The local solution to the parabolized stability equations accurately predicts the wave properties observed in the direct simulation whereas conventional parallel stability analysis overpredicts the spatial amplification and the wavenumber.

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