Spinodal instability growth in new stochastic approaches

Resonant excitation of Alfvén waves by fast particles in a finite pressure plasma in a non-uniform magnetic field is studied. Plasma compressibility in the wave field is determined both by the curvature of the magnetic lines of force and finite Larmor radius of fast particles. A general expression for the instability growth rate is obtained and analyzed; the applicability of the results obtained in the previous paper has also been studied. The finite pressure stabilization of the trapped particles instability has been found. The bounce-resonance effects are analyzed.

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Density-driven unstable flows of miscible fluids in a Hele-Shaw cell

Journal of Fluid Mechanics ◽

10.1017/s0022112001006504 ◽

2002 ◽

Vol 451 ◽

pp. 239-260 ◽

Cited By ~ 119

Author(s):

J. FERNANDEZ ◽

P. KUROWSKI ◽

P. PETITJEANS ◽

E. MEIBURG

Keyword(s):

Stokes Equations ◽

Three Dimensional ◽

Brinkman Equation ◽

Length Scale ◽

Dominant Wavelength ◽

Miscible Fluids ◽

Nonlinear Simulations ◽

Instability Growth ◽

Gap Width ◽

Hele Shaw Cell

Density-driven instabilities between miscible fluids in a vertical Hele-Shaw cell are investigated by means of experimental measurements, as well as two- and three-dimensional numerical simulations. The experiments focus on the early stages of the instability growth, and they provide detailed information regarding the growth rates and most amplified wavenumbers as a function of the governing Rayleigh number Ra. They identify two clearly distinct parameter regimes: a low-Ra, ‘Hele-Shaw’ regime in which the dominant wavelength scales as Ra−1, and a high-Ra ‘gap’ regime in which the length scale of the instability is 5±1 times the gap width. The experiments are compared to a recent linear stability analysis based on the Brinkman equation. The analytical dispersion relationship for a step-like density profile reproduces the experimentally observed trend across the entire Ra range. Nonlinear simulations based on the two- and three-dimensional Stokes equations indicate that the high-Ra regime is characterized by an instability across the gap, wheras in the low-Ra regime a spanwise Hele-Shaw mode dominates.

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Theory of the tertiary instability and the Dimits shift within a scalar model

Journal of Plasma Physics ◽

10.1017/s0022377820000823 ◽

2020 ◽

Vol 86 (4) ◽

Cited By ~ 1

Author(s):

Hongxuan Zhu ◽

Yao Zhou ◽

I. Y. Dodin

Keyword(s):

Turbulent Transport ◽

Plasma Phys ◽

Magnetized Plasma ◽

Radial Coordinate ◽

Flow Shear ◽

Zonal Flows ◽

Drift Wave ◽

Zonal Velocity ◽

Instability Growth ◽

Traditional Paradigm

The Dimits shift is the shift between the threshold of the drift-wave primary instability and the actual onset of turbulent transport in a magnetized plasma. It is generally attributed to the suppression of turbulence by zonal flows, but developing a more detailed understanding calls for consideration of specific reduced models. The modified Terry–Horton system has been proposed by St-Onge (J. Plasma Phys., vol. 83, 2017, 905830504) as a minimal model capturing the Dimits shift. Here, we use this model to develop an analytic theory of the Dimits shift and a related theory of the tertiary instability of zonal flows. We show that tertiary modes are localized near extrema of the zonal velocity $U(x)$ , where $x$ is the radial coordinate. By approximating $U(x)$ with a parabola, we derive the tertiary-instability growth rate using two different methods and show that the tertiary instability is essentially the primary drift-wave instability modified by the local $U'' \doteq {\rm d}^2 U/{\rm d} x^2 $ . Then, depending on $U''$ , the tertiary instability can be suppressed or unleashed. The former corresponds to the case when zonal flows are strong enough to suppress turbulence (Dimits regime), while the latter corresponds to the case when zonal flows are unstable and turbulence develops. This understanding is different from the traditional paradigm that turbulence is controlled by the flow shear $| {\rm d} U / {\rm d} x |$ . Our analytic predictions are in agreement with direct numerical simulations of the modified Terry–Horton system.

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Phase behaviors of supercooled water: Reconciling a critical point of amorphous ices with spinodal instability

The Journal of Chemical Physics ◽

10.1063/1.472354 ◽

1996 ◽

Vol 105 (12) ◽

pp. 5099-5111 ◽

Cited By ~ 121

Author(s):

Hideki Tanaka

Keyword(s):

Critical Point ◽

Supercooled Water ◽

Amorphous Ices ◽

Spinodal Instability ◽

Phase Behaviors

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Suppression of Baroclinic Instabilities in Buoyancy-Driven Flow over Sloping Bathymetry

Journal of Physical Oceanography ◽

10.1175/jpo-d-15-0240.1 ◽

2017 ◽

Vol 47 (1) ◽

pp. 49-68 ◽

Cited By ~ 22

Author(s):

Robert D. Hetland

Keyword(s):

Growth Rate ◽

Linear Instability ◽

Linear Stability Theory ◽

Buoyancy Frequency ◽

Bottom Slope ◽

Coriolis Parameter ◽

Plume Front ◽

Instability Theory ◽

Instability Growth ◽

Flow Configurations

AbstractBaroclinic instabilities are ubiquitous in many types of geostrophic flow; however, they are seldom observed in river plumes despite strong lateral density gradients within the plume front. Supported by results from a realistic numerical simulation of the Mississippi–Atchafalaya River plume, idealized numerical simulations of buoyancy-driven flow are used to investigate baroclinic instabilities in buoyancy-driven flow over a sloping bottom. The parameter space is defined by the slope Burger number S = Nf−1α, where N is the buoyancy frequency, f is the Coriolis parameter, and α is the bottom slope, and the Richardson number Ri = N2f2M−4, where M2 = |∇Hb| is the magnitude of the lateral buoyancy gradients. Instabilities only form in a subset of the simulations, with the criterion that SH ≡ SRi−1/2 = Uf−1W−1 = M2f−2α 0.2, where U is a horizontal velocity scale and SH is a new parameter named the horizontal slope Burger number. Suppression of instability formation for certain flow conditions contrasts linear stability theory, which predicts that all flow configurations will be subject to instabilities. The instability growth rate estimated in the nonlinear 3D model is proportional to ωImaxS−1/2, where ωImax is the dimensional growth rate predicted by linear instability theory, indicating that bottom slope inhibits instability growth beyond that predicted by linear theory. The constraint SH 0.2 implies a relationship between the inertial radius Li = Uf−1 and the plume width W. Instabilities may not form when 5Li > W; that is, the plume is too narrow for the eddies to fit.

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The Study of Thermal Conditions on Weibel Instability

Advances in High Energy Physics ◽

10.1155/2015/428013 ◽

2015 ◽

Vol 2015 ◽

pp. 1-6

Author(s):

M. Mahdavi ◽

H. Khanzadeh

Keyword(s):

Growth Rate ◽

Thermal Conditions ◽

Ion Scattering ◽

Weibel Instability ◽

Anisotropic Temperature ◽

Instability Growth ◽

Limiting Condition ◽

Limiting Case ◽

Background Ions ◽

Electromagnetic Instability

Weibel electromagnetic instability has been studied analytically in relativistic plasma with high parallel temperature, where|α=(mc2/T∥)(1+p^⊥2/m2c2)1/2|≪1and while the collision effects of electron-ion scattering have also been considered. According to these conditions, an analytical expression is derived for the growth rate of the Weibel instability for a limiting case of|ζ=α/2(ω′/ck)|≪1, whereω′is the sum of the wave frequency of instability and the collision frequency of electrons with background ions. The results show that in the limiting conditionα≪1there is an unusual situation of the Weibel instability so thatT∥≫T⊥, while in the classic Weibel instabilityT∥≪T⊥. The obtained results show that the growth rate of the Weibel instability will be decreased due to an increase in the number of collisions and a decrease in the anisotropic temperature by the increasing of plasma density, while the increase of the parameterγ^⊥=(1+p^⊥2/m2c2)1/2leads to the increase of the Weibel instability growth rate.

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Ion-driven Instabilities in the Inner Heliosphere. I. Statistical Trends

The Astrophysical Journal ◽

10.3847/1538-4357/ac3081 ◽

2021 ◽

Vol 923 (1) ◽

pp. 116

Author(s):

Mihailo M. Martinović ◽

Kristopher G. Klein ◽

Tereza Ďurovcová ◽

Benjamin L. Alterman

Keyword(s):

Solar Wind ◽

Particle Interaction ◽

Radial Distance ◽

Solar Wind Plasma ◽

Distribution Functions ◽

Nyquist Criterion ◽

Velocity Distribution Functions ◽

Instability Growth ◽

Statistical Trends ◽

The Impact

Abstract Instabilities described by linear theory characterize an important form of wave–particle interaction in the solar wind. We diagnose unstable behavior of solar wind plasma between 0.3 and 1 au via the Nyquist criterion, applying it to fits of ∼1.5M proton and α particle Velocity Distribution Functions (VDFs) observed by Helios I and II. The variation of the fraction of unstable intervals with radial distance from the Sun is linear, signaling a gradual decline in the activity of unstable modes. When calculated as functions of the solar wind velocity and Coulomb number, we obtain more extreme, exponential trends in the regions where collisions appear to have a notable influence on the VDF. Instability growth rates demonstrate similar behavior, and significantly decrease with Coulomb number. We find that for a nonnegligible fraction of observations, the proton beam or secondary component might not be detected, due to instrument resolution limitations, and demonstrate that the impact of this issue does not affect the main conclusions of this work.

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