A classical linear stability analysis of normal mode instability of the compressible planar mixing-layer flow of a supercritical fluid

2016 ◽  
Author(s):  
Leonardo S. Alves
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Normal Mode ◽  
Supercritical Fluid ◽  
Linear Stability Analysis ◽  
Mixing Layer ◽  
Mode Instability ◽  
Layer Flow

Nonlinear development and Fourier analysis of the whistler mode instability

1973 ◽  
Vol 9 (3) ◽  
pp. 295-310 ◽  
Author(s):  
S. Cuperman ◽  
Y. Salu
Keyword(s):  
Stability Analysis ◽  
Fourier Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Wave Spectrum ◽  
Equatorial Region ◽  
Anisotropy Ratio ◽  
Mode Instability ◽  
Whistler Mode ◽  
The Waves

The results of the nonlinear computer investigationof the whistler mode instability with the aid of particle-in-cell simulation methods are presented. The electron plasma considered is hot (kT‖ = 20 keV), anisothermal (T⊥/T‖ ≃ 2) and embedded in a static magnetic field such that β‖ = 0.8. A detailed Fourier analysis of the electromagnetic activity developed under the above stated conditions is carried out: the waves are shown to be electron-like and excellent agreement with the linear stability analysis for the first stages of evolution is found. The feed-back effect of the waves on the particles is shown to result in a continuous decrease of the thermal anisotropy ratio T⊥/T‖ corresponding changes in the Fourier spectra of the electromagnetic activity are observed; additional changes in the wave spectrum are introduced by the interaction between various instability modes. At the end of the run (ωpt ⋍600), the state of the system resembles a quasi-stable equilibrium, in which the electromagnetic energy achieves its maximum value: in this state, unlike the equilibrium one usually considered in the linear stability analysis, a thermally anisotropic plasma with T⊥/T‖⋍1·35 appears to be quasi-stable against the whistler mode instability. This last result is relevant for the geostationary magnetospheric conditions (in the equatorial region) where quasi-stationary states with T⊥/T‖ about 1·3 are observed.

Linear stability analysis and structure of the compressible reacting mixing layer

1997 ◽  
Author(s):  
M. Day ◽  
W. Reynolds ◽  
N. Mansour ◽  
M. Day ◽  
W. Reynolds ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Mixing Layer

scholarly journals Linear Stability Effect of Densely Distributed Porous Medium and Coriolis Force on Soret Driven Ferrothermohaline Convection

2018 ◽  
Vol 23 (4) ◽  
pp. 911-928
Author(s):  
R. Sekar ◽  
D. Murugan
Keyword(s):  
Porous Medium ◽  
Stability Analysis ◽  
Linear Stability ◽  
Normal Mode ◽  
Coriolis Force ◽  
Linear Stability Analysis ◽  
Stationary Convection ◽  
Onset Of Convection ◽  
Stability Effect ◽  
Mode Technique

Abstract The effect of Coriolis force on the Soret driven ferrothermohaline convection in a densely packed porous medium has been studied. A linear stability analysis is carried out using normal mode technique. It is found that stationary convection is favorable for the Darcy model, therefore oscillatory instability is studied. A small thermal perturbation is applied to the basic state and linear stability analysis is used for which the normal mode technique is applied. It is found that the presence of a porous medium favours the onset of convection. The porous medium is assumed to be variable and the effect of the permeable parameter is to destabilize the system. The present work has been carried out both for oscillatory as well as stationary instabilities. The results are depicted graphically.

scholarly journals Instability of Lenticular Vortices: Results from Laboratory Experiments, Linear Stability Analysis and Numerical Simulations

Fluids ◽  
2021 ◽  
Vol 6 (11) ◽  
pp. 380
Author(s):  
Noé Lahaye ◽  
Alexandre Paci ◽  
Stefan G. Llewellyn Smith
Keyword(s):  
Stability Analysis ◽  
Numerical Simulations ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Laboratory Experiments ◽  
Lower Layer ◽  
Water Model ◽  
Layer Potential ◽  
Rotating Shallow Water ◽  
Layer Flow

The instability of surface lenticular vortices is investigated using a comprehensive suite of laboratory experiments combined with numerical linear stability analysis as well as nonlinear numerical simulations in a two-layer Rotating Shallow Water model. The development of instabilities is discussed and compared between the different methods. The linear stability analysis allows for a clear description of the origin of the instability observed in both the laboratory experiments and numerical simulations. While global qualitative agreement is found, some discrepancies are observed and discussed. Our study highlights that the sensitivity of the instability outcome is related to the initial condition and the lower-layer flow. The inhibition or even suppression of some unstable modes may be explained in terms of the lower-layer potential vorticity profile.

scholarly journals Instability of a liquid sheet with viscosity contrast in inertial microfluidics

2021 ◽  
Vol 44 (11) ◽  
Author(s):  
Kuntal Patel ◽  
Holger Stark
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Sheet Thickness ◽  
Liquid Sheet ◽  
Interfacial Instability ◽  
Parameter Study ◽  
Inertial Microfluidics ◽  
Inertial Focusing ◽  
Layer Flow

Abstract Flows at moderate Reynolds numbers in inertial microfluidics enable high throughput and inertial focusing of particles and cells with relevance in biomedical applications. In the present work, we consider a viscosity-stratified three-layer flow in the inertial regime. We investigate the interfacial instability of a liquid sheet surrounded by a density-matched but more viscous fluid in a channel flow. We use linear stability analysis based on the Orr–Sommerfeld equation and direct numerical simulations with the lattice Boltzmann method (LBM) to perform an extensive parameter study. Our aim is to contribute to a controlled droplet production in inertial microfluidics. In the first part, on the linear stability analysis we show that the growth rate of the fastest growing mode $$\xi ^{*}$$ ξ ∗ increases with the Reynolds number $$\text {Re}$$ Re and that its wavelength $$\lambda ^{*}$$ λ ∗ is always smaller than the channel width w for sufficiently small interfacial tension $$\Gamma $$ Γ . For thin sheets we find the scaling relation $$\xi ^{*} \propto mt^{2.5}_{s}$$ ξ ∗ ∝ m t s 2.5 , where m is viscosity ratio and $$t_{s}$$ t s the sheet thickness. In contrast, for thicker sheets $$\xi ^{*}$$ ξ ∗ decreases with increasing $$t_s$$ t s or m due to the nearby channel walls. Examining the eigenvalue spectra, we identify Yih modes at the interface. In the second part on the LBM simulations, the thin liquid sheet develops two distinct dynamic states: waves traveling along the interface and breakup into droplets with bullet shape. For smaller flow rates and larger sheet thicknesses, we also observe ligament formation and the sheet eventually evolves irregularly. Our work gives some indication how droplet formation can be controlled with a suitable parameter set $$\{\lambda ,t_{s},m,\Gamma ,\text {Re}\}$$ { λ , t s , m , Γ , Re } . Graphical Abstract

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