Dynamic properties of ηi-mode weak turbulence

1996 ◽  
Vol 55 (1) ◽  
pp. 47-58 ◽  
Author(s):  
Alireza Pakyari ◽  
Vladimir P. Pavlenko
Keyword(s):  
Dynamic Properties ◽  
Fluid Model ◽  
Linear Instability ◽  
Linear Growth Rate ◽  
Cascade Process ◽  
Zonal Flows ◽  
Elementary Estimate ◽  
Model Equations ◽  
Wavenumber Region ◽  
Nonlinear Mode Coupling

The turbulence of the toroidal ηi mode has a forward spectral cascade. This means that most of the energy initially placed in the low-wavenumber region (the linear instability region) will be spread out towards high-wavenumber modes. Therefore the linear instability may be reduced by this energy cascade. An elementary estimate of the critical amplitude for nonlinear mode coupling to balance the linear growth rate is given. As a consequence of three wave cascade process derivable from the fully toroidal fluid model equations, the formation of zonal flows ηi-mode turbulence is predicted.

Lattice Boltzmann Simulation of Two-Fluid Model Equations

2008 ◽  
Vol 47 (23) ◽  
pp. 9165-9173 ◽  
Author(s):  
Krishnan Sankaranarayanan ◽  
Sankaran Sundaresan
Keyword(s):  
Lattice Boltzmann ◽  
Fluid Model ◽  
Lattice Boltzmann Simulation ◽  
Two Fluid Model ◽  
Model Equations ◽  
Two Fluid

scholarly journals Collisionless kinetic-fluid model of zonal flows in toroidal plasmas

2007 ◽  
Vol 14 (2) ◽  
pp. 022502 ◽  
Author(s):  
H. Sugama ◽  
T.-H. Watanabe ◽  
W. Horton
Keyword(s):  
Fluid Model ◽  
Zonal Flows ◽  
Toroidal Plasmas

Analysis of Flow-Induced Vibration Due to Stratified Wavy Two-Phase Flow

2016 ◽  
Vol 138 (9) ◽  
Author(s):  
Shuichiro Miwa ◽  
Takashi Hibiki ◽  
Michitsugu Mori
Keyword(s):  
Two Phase Flow ◽  
Dynamic Properties ◽  
Fluid Model ◽  
Dominant Frequency ◽  
Phase Flow ◽  
Flow Induced Vibration ◽  
Two Phase ◽  
Pipe Bend ◽  
Experimental Database ◽  
Force Fluctuation

Fluctuating force induced by horizontal gas–liquid two-phase flow on 90 deg pipe bend at atmospheric pressure condition is considered. Analysis was conducted to develop a model which is capable of predicting the peak force fluctuation frequency and magnitudes, particularly at the stratified wavy two-phase flow regime. The proposed model was developed from the local instantaneous two-fluid model, and adopting guided acoustic theory and dynamic properties of one-dimensional (1D) waves to consider the collisional force due to the interaction between dynamic waves and structure. Comparing the developed model with experimental database, it was found that the main contribution of the force fluctuation due to stratified wavy flow is from the momentum and pressure fluctuations, and collisional effects. The collisional effect is due to the fluid–solid interaction of dynamic wave, which is named as the wave collision force. Newly developed model is capable of predicting the force fluctuations and dominant frequency range with satisfactory accuracy for the flow induced vibration (FIV) caused by stratified wavy two-phase flow in 52.5 mm inner diameter (ID) pipe bend.

Inverse cascade of kinetic energy in two-dimensional β-Plane magnetohydrodynamic turbulence

2020 ◽  
Author(s):  
Timofey Zinyakov ◽  
Arakel Petrosyan
Keyword(s):  
Numerical Simulation ◽  
Kinetic Energy ◽  
Cascade Process ◽  
Two Dimensional ◽  
Mhd Turbulence ◽  
Self Similarity ◽  
Magnetohydrodynamic Turbulence ◽  
Zonal Flows ◽  
Inverse Cascade ◽  
Kolmogorov Spectrum

<p>Numerical studies of two-dimensional β-plane homogeneous magnetohydrodynamic turbulence are presented. The study of the fundamental properties of such turbulence allows understanding the evolution of various astrophysical objects from the Sun and stars to planetary systems, galaxies, and galaxy clusters. Energy spectra and cascade process in two-dimensional β-plane MHD are studied.</p><p>In this work the equations of two-dimensional magnetohydrodynamics with the Coriolis force in the β-plane approximation are used for the qualitative analysis and numerical simulation of processes in plasma astrophysics. The equations are solved on a square box of edge size 2π with periodic boundary conditions applying a the pseudospectral method using the 2/3 rule for dealiasing. The results of numerical simulation of two-dimensional β-plane MHD turbulence with a spatial resolution of 1024 × 1024 and 4096 × 4096 with different Rossby parameters β and different Reynolds numbers are presented.</p><p>It is found that only unsteady zonal flows with complex temporal dynamics are formed in two-dimensional β-plane magnetohydrodynamic turbulence. It is shown that flow nonstationarity is due to the appearance of isotropic magnetic islands caused by the Lorentz force in the system. The formation of Iroshnikov–Kraichnan spectrum is shown in the early stages of evolution of two-dimensional β-plane magnetohydrodynamic turbulence. The self-similarity of the decay of Iroshnikov–Kraichnan spectrum is studied. On long time scale violation of self-similarity of the decay and formation of Kolmogorov spectrum is discovered. The inverse cascade of kinetic energy, which is characteristic of the detected Kolmogorov spectrum, provides the formation of zonal flows.</p><p>This work was supported by the Russian Foundation for Basic Research (project no. 19-02-00016).</p>

Electromagnetic gyrokinetic simulation of turbulence in torus plasmas

2015 ◽  
Vol 81 (2) ◽  
Author(s):  
A. Ishizawa ◽  
S. Maeyama ◽  
T.-H. Watanabe ◽  
H. Sugama ◽  
N. Nakajima
Keyword(s):  
Temperature Gradient ◽  
Turbulent Transport ◽  
Zonal Flow ◽  
Linear Instability ◽  
Conserved Quantity ◽  
The Other ◽  
Ion Temperature ◽  
Zonal Flows ◽  
Tearing Modes ◽  
Other Hand

Gyrokinetic simulations of electromagnetic turbulence in magnetically confined torus plasmas including tokamak and heliotron/stellarator are reviewed. Numerical simulation of turbulence in finite beta plasmas is an important task for predicting the performance of fusion reactors and a great challenge in computational science due to multiple spatio-temporal scales related to electromagnetic ion and electron dynamics. The simulation becomes further challenging in non-axisymmetric plasmas. In finite beta plasmas, magnetic perturbation appears and influences some key mechanisms of turbulent transport, which include linear instability and zonal flow production. Linear analysis shows that the ion-temperature gradient (ITG) instability, which is essentially an electrostatic instability, is unstable at low beta and its growth rate is reduced by magnetic field line bending at finite beta. On the other hand, the kinetic ballooning mode (KBM), which is an electromagnetic instability, is destabilized at high beta. In addition, trapped electron modes (TEMs), electron temperature gradient (ETG) modes, and micro-tearing modes (MTMs) can be destabilized. These instabilities are classified into two categories: ballooning parity and tearing parity modes. These parities are mixed by nonlinear interactions, so that, for instance, the ITG mode excites tearing parity modes. In the nonlinear evolution, the zonal flow shear acts to regulate the ITG driven turbulence at low beta. On the other hand, at finite beta, interplay between the turbulence and zonal flows becomes complicated because the production of zonal flow is influenced by the finite beta effects. When the zonal flows are too weak, turbulence continues to grow beyond a physically relevant level of saturation in finite-beta tokamaks. Nonlinear mode coupling to stable modes can play a role in the saturation of finite beta ITG mode and KBM. Since there is a quadratic conserved quantity, evaluating nonlinear transfer of the conserved quantity from unstable modes to stable modes is useful for understanding the saturation mechanism of turbulence.

scholarly journals Magmatic channelisation by reactive and shear-driven instabilities at mid-ocean ridges: a combined analysis

2021 ◽  
Author(s):  
D W Rees Jones ◽  
H Zhang ◽  
R F Katz
Keyword(s):  
Seismic Anisotropy ◽  
Linear Instability ◽  
Linear Growth Rate ◽  
Reactive Flow ◽  
High Porosity ◽  
Ridge Axis ◽  
Feedback Mechanisms ◽  
Solid Flow ◽  
Melt Extraction ◽  
Ocean Ridges

Summary It is generally accepted that melt extraction from the mantle at mid-ocean ridges is concentrated in narrow regions of elevated melt fraction called channels. Two feedback mechanisms have been proposed to explain why these channels grow by linear instability: shear flow of partially molten mantle and reactive flow of the ascending magma. These two mechanisms have been studied extensively, in isolation from each other, through theory and laboratory experiments as well as field and geophysical observations. Here, we develop a consistent theory that accounts for both proposed mechanisms and allows us to weigh their relative contributions. We show that interaction of the two feedback mechanisms is insignificant and that the total linear growth rate of channels is well-approximated by summing their independent growth rates. Furthermore, we explain how their competition is governed by the orientation of channels with respect to gravity and mantle shear. By itself, analysis of the reaction-infiltration instability predicts the formation of tube-shaped channels. We show that with the addition of even a small amount of extension in the horizontal, the combined instability favours tabular channels, consistent with the observed morphology of dunite bodies in ophiolites. We apply the new theory to mid-ocean ridges by calculating the accumulated growth and rotation of channels along streamlines of the solid flow. We show that reactive flow is the dominant instability mechanism deep beneath the ridge axis, where the most unstable orientation of high-porosity channels is sub-vertical. Channels are then rotated by the solid flow away from the vertical. The contribution of the shear-driven instability is confined to the margins of the melting region. Within the limitations of our study, the shear-driven feedback does not appear to be responsible for significant melt focusing or for the shallowly dipping seismic anisotropy that has been obtained by seismic inversions.

Numerical Convection Algorithms and Their Role in Eulerian CFD Reactor Simulations

2002 ◽  
Vol 1 (1) ◽  
Author(s):  
Hugo A. Jakobsen
Keyword(s):  
Fluid Model ◽  
Time Integration ◽  
Higher Order ◽  
Computational Time ◽  
Implicit Time ◽  
Modified Method ◽  
Integration Schemes ◽  
Time Integration Schemes ◽  
Model Equations ◽  
Time Required

In this paper a comparative convection algorithm study is presented. The performance of a large number of schemes is compared evaluating the predicted solutions for a standard benchmarking test problem. The nature of the errors caused by the numerical approximations to the convection term is highlighted. Although there is no algorithm that performs the best in general, several conclusions can be made. The tests performed show that the 1st order upwind scheme and several variations of this scheme are very diffusive and should be avoided. Most stable 2nd order schemes seem to be much more accurate, whereas the accuracy gained by higher order schemes (3rd order and 4th order) may be a little more costly. Implicit time integration schemes are usually not as efficient as the corresponding explicit schemes due to the computational time required on the iterative process. With larger time steps the accuracy of implicit schemes decrease rapidly. The choice of proper higher order schemes (2nd order schemes) is then seemingly determined by the trade-off between accuracy and computational time. The conservative methods like the UTOPIA, the QUICK-1D combined with a limiter, and a limited number of FCT and TVD formulations may be sufficient solving the multi-fluid model equations. For advective terms (e.g., as occur in the temperature equation) the non-flux-based modified method of characteristics is very fast, but also other higher order (2nd order) schemes performed well.

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