Mean zonal flow driven by precession in planetary cores: numerical simulations with a semi-lagrangian scheme

2021 ◽  
Author(s):  
Nathanael Schaeffer ◽  
David Cébron
Keyword(s):  
Shear Flow ◽  
Rotation Axis ◽  
Boundary Layer Equation ◽  
Zonal Flow ◽  
Zonal Flows ◽  
Low Viscosity ◽  
Planetary Cores ◽  
Linear Effects ◽  
Spherical Fluid ◽  
Lagrangian Scheme

<p>We revisit the generation of mean zonal flows in fluid planetary interiors subjected to precession.<br>The main effect of precession on a (nearly) spherical fluid envelope is to make the fluid rotate along an axis tilted with respect to the rotation axis of the solid mantle. This is the so-called "spin-over" response of the fluid.<br> also shows that a steady shear flow develops on top of the spin-over mode due to non-linear effects in the boundary layer equation.<br>This mean zonal shear flow has been studied theoretically and numerically by .</p><p>With faster computers and more efficient codes, we compute this flow down to very low viscosity and compare with the inviscid theory of Busse (1968).<br>In addition we investigate the width and the intensity of the detached shear layer, which is controlled by viscosity and therefore not present in the theory.</p><p>We also use this problem as a benchmark to assess the benefits of using a semi-lagrangian numerical scheme, where solid-body rotation is treated exactly.</p>

scholarly journals The Effect of Quadric Shear Zonal Flows and Beta on the Downstream Development of Unstable Baroclinic Waves

2020 ◽  
Author(s):  
Yu Ying Yang ◽  
Cheng Zhen Guo ◽  
Hong Xin Zhang ◽  
Jian Song
Keyword(s):  
Shear Flow ◽  
Chaotic Behavior ◽  
Great Influence ◽  
Zonal Flow ◽  
Feature Points ◽  
Zonal Flows ◽  
Baroclinic Waves ◽  
Two Layer Model ◽  
The Stability ◽  
Downstream Development

Abstract. In this paper, the influence of quadric shear basic Zonal flows and β on the downstream development of unstable chaotic baroclinic waves is studied from the two-layer model in wide channel controlled by quasi geostrophic potential vorticity equation. Through the obtained Lorentz equation, we focused on the influence of the quadric shear zonal flow (the second derivative of the basic zonal flow is constant) on the downstream development of baroclinic waves. In the absence of zonal shear flow, chaotic behavior along feature points would occur, and the amplitude would change rapidly from one feature to another, that is, it would change very quickly in space. When zonal shear flow is introduced, it will smooth the solution of the equation and reduce the instability, and with the increase of zonal shear flow, the instability in space will increase gradually. So the quadric shear zonal flow has great influence on the stability in space.

scholarly journals Excitation of zonal flow by the modulational instability in electron temperature gradient driven turbulence

2008 ◽  
Vol 74 (3) ◽  
pp. 381-389 ◽  
Author(s):  
Yu. A. ZALIZNYAK ◽  
A. I. YAKIMENKO ◽  
V. M. LASHKIN
Keyword(s):  
Temperature Gradient ◽  
Electron Temperature ◽  
Large Scale ◽  
Modulational Instability ◽  
Zonal Flow ◽  
Finite Amplitude ◽  
Small Scale ◽  
Drift Waves ◽  
Zonal Flows ◽  
Electron Temperature Gradient

AbstractThe generation of large-scale zonal flows by small-scale electrostatic drift waves in electron temperature gradient driven turbulence model is considered. The generation mechanism is based on the modulational instability of a finite amplitude monochromatic drift wave. The threshold and growth rate of the instability as well as the optimal spatial scale of zonal flow are obtained.

scholarly journals Effect of the electron redistribution on the nonlinear saturation of Alfvén eigenmodes and the excitation of zonal flows

2020 ◽  
Vol 86 (3) ◽  
Author(s):  
A. Biancalani ◽  
A. Bottino ◽  
P. Lauber ◽  
A. Mishchenko ◽  
F. Vannini
Keyword(s):  
Magnetic Field ◽  
Zonal Flow ◽  
Large Aspect Ratio ◽  
Nonlinear Saturation ◽  
Energetic Ions ◽  
Electron Population ◽  
Zonal Flows ◽  
Particle In Cell ◽  
Alfven Eigenmodes ◽  
Reversed Shear

Numerical simulations of Alfvén modes driven by energetic particles are performed with the gyrokinetic (GK) global particle-in-cell code ORB5. A reversed shear equilibrium magnetic field is adopted. A simplified configuration with circular flux surfaces and large aspect ratio is considered. The nonlinear saturation of beta-induced Alfvén eigenmodes (BAE) is investigated. The roles of the wave–particle nonlinearity of the different species, i.e. thermal ions, electrons and energetic ions are described, in particular for their role in the saturation of the BAE and the generation of zonal flows. The nonlinear redistribution of the electron population is found to be important in increasing the BAE saturation level and the zonal flow amplitude.

scholarly journals Numerical simulations of vorticity banding of emulsions in shear flows

Soft Matter ◽  
2020 ◽  
Vol 16 (11) ◽  
pp. 2854-2863 ◽  
Author(s):  
Francesco De Vita ◽  
Marco Edoardo Rosti ◽  
Sergio Caserta ◽  
Luca Brandt
Keyword(s):  
Shear Flow ◽  
Numerical Simulations ◽  
Effective Viscosity ◽  
Shear Flows ◽  
Viscosity Ratio ◽  
Low Viscosity

Emulsion under shear flow can exhibit banded structures at low viscosity ratio. When coalescence is favoured, it can stabilize bands generated by migration of droplets. The reduction of the total surface results in a lower effective viscosity state.

A Series of Zonal Jets Embedded in the Broad Zonal Flows in the Pacific Obtained in Eddy-Permitting Ocean General Circulation Models

2005 ◽  
Vol 35 (4) ◽  
pp. 474-488 ◽  
Author(s):  
Hideyuki Nakano ◽  
Hiroyasu Hasumi
Keyword(s):  
General Circulation ◽  
Bottom Topography ◽  
Zonal Flow ◽  
General Circulation Models ◽  
Wind Forcing ◽  
Zonal Flows ◽  
Zonal Jets ◽  
The Pacific ◽  
Ocean General Circulation Models ◽  
Ocean General Circulation

Abstract A series of zonal currents in the Pacific Ocean is investigated using eddy-permitting ocean general circulation models. The zonal currents in the subsurface are classified into two parts: one is a series of broad zonal flows that has the meridional pattern slanting poleward with increasing depth and the other is finescale zonal jets with the meridional scale of 3°–5° formed in each broad zonal flow. The basic pattern for the broad zonal flows is similar between the coarse-resolution model and the eddy-permitting model and is thought to be the response to the wind forcing. A part of the zonal jets embedded in each zonal flow is explained by the anomalous local wind forcing. Most of them, however, seem to be mainly created by the rectification of turbulent processes on a β plane (the Rhines effect), and zonal jets in this study have common features with the zonally elongated flows obtained in previous modeling studies conducted in idealized basins. The position of zonal jets is not stable when the ocean floor is flat, whereas it oscillates only within a few degrees under realistic bottom topography.

Thermal stability in a rotating spherical fluid shell with non-uniform heating

1977 ◽  
Vol 353 (1674) ◽  
pp. 349-362 ◽  
Keyword(s):  
Shear Flow ◽  
Numerical Solutions ◽  
Initial Conditions ◽  
Rapid Change ◽  
Polar Angle ◽  
Quiescent State ◽  
Uniform Heating ◽  
Thermally Induced ◽  
Spherical Fluid ◽  
Geophysical Flow

The theory is developed for the convective stability of a rotating spherical shell of fluid upon which is initially imposed a stable thermally induced shear flow. The fluid shell contains heating sources which are distributed proportional to the sine of the polar angle squared. Thus the analysis has a number of similarities to some geophysical flow situations. It is found that the properties of the solution are strongly dependent on the initial conditions. Thus to obtain further insight concerning the stability of the system numerical solutions are obtained a t two shell thicknesses. The critical values of the Taylor number ( T ) and the Rayleigh number ( C ) are generally similar to those found in previous studies of rotating fluid shells. How ever the effect of the initial shear flow is to reduce the critical value of C for a given T , below that found for uniform heating and an initially quiescent state. The flows obtained at the onset of instability are toroidal cells which vary in number dependent on T and C .A maximum of six cells are found at large values of T . A significant effect of the initial shear flow is the occurrence of a rapid change in stability when the number of toroidal cells changes.

scholarly journals Reduced models of turbulent transport in helical plasmas including effects of zonal flows and trapped electrons

2020 ◽  
Vol 86 (3) ◽  
Author(s):  
S. Toda ◽  
M. Nunami ◽  
H. Sugama
Keyword(s):  
Energy Transport ◽  
Turbulent Transport ◽  
Zonal Flow ◽  
Transport Models ◽  
Nonlinear Simulation ◽  
Ion Energy ◽  
Trapped Electrons ◽  
Zonal Flows ◽  
Reduced Models ◽  
Potential Fluctuation

Using transport models, the impacts of trapped electrons on zonal flows and turbulence in helical field configurations are studied. The effect of the trapped electrons on the characteristic quantities of the linear response for zonal flows is investigated for two different field configurations in the Large Helical Device. The turbulent potential fluctuation, zonal flow potential fluctuation and ion energy transport are quickly predicted by the reduced models for which the linear and nonlinear simulation results are used to determine dimensionless parameters related to turbulent saturation levels and typical zonal flow wavenumbers. The effects of zonal flows on the turbulent transport for the case of the kinetic electron response are much smaller than or comparable to those in an adiabatic electron condition for the two different field configurations. It is clarified that the effect of zonal flows on the turbulent transport due to the trapped electrons changes, depending on the field configurations.

scholarly journals Experimental and numerical study of mean zonal flows generated by librations of a rotating spherical cavity

2010 ◽  
Vol 662 ◽  
pp. 260-268 ◽  
Author(s):  
A. SAURET ◽  
D. CÉBRON ◽  
C. MORIZE ◽  
M. LE BARS
Keyword(s):  
Rate Ratio ◽  
Particle Image ◽  
Numerical Study ◽  
Zonal Flow ◽  
Outer Wall ◽  
Weakly Nonlinear ◽  
Zonal Flows ◽  
Solid Body Rotation ◽  
Weakly Nonlinear Analysis ◽  
Image Velocimetry

We study both experimentally and numerically the steady zonal flow generated by longitudinal librations of a spherical rotating container. This study follows the recent weakly nonlinear analysis of Busse (J. Fluid Mech., vol. 650, 2010, pp. 505–512), developed in the limit of small libration frequency–rotation rate ratio and large libration frequency–spin-up time product. Using particle image velocimetry measurements as well as results from axisymmetric numerical simulations, we confirm quantitatively the main features of Busse's analytical solution: the zonal flow takes the form of a retrograde solid-body rotation in the fluid interior, which does not depend on the libration frequency nor on the Ekman number, and which varies as the square of the amplitude of excitation. We also report the presence of an unpredicted prograde flow at the equator near the outer wall.

Flows in a rotating spherical shell: the equatorial case

1994 ◽  
Vol 276 ◽  
pp. 233-260 ◽  
Author(s):  
A. Colin de Verdière ◽  
R. Schopp
Keyword(s):  
Angular Momentum ◽  
Rotation Axis ◽  
Dynamic Pressure ◽  
Vertical Component ◽  
Low Frequency ◽  
Zonal Flow ◽  
Horizontal Component ◽  
Meridional Plane ◽  
Earth’S Rotation ◽  
Earth's Rotation

It is well known that the widely used powerful geostrophic equations that single out the vertical component of the Earth's rotation cease to be valid near the equator. Through a vorticity and an angular momentum analysis on the sphere, we show that if the flow varies on a horizontal scale L smaller than (Ha)1/2 (where H is a vertical scale of motion and a the Earth's radius), then equatorial dynamics must include the effect of the horizontal component of the Earth's rotation. In equatorial regions, where the horizontal plane aligns with the Earth's rotation axis, latitudinal variations of planetary angular momentum over such scales become small and approach the magnitude of its radial variations proscribing, therefore, vertical displacements to be freed from rotational constraints. When the zonal flow is strong compared to the meridional one, we show that the zonal component of the vorticity equation becomes (2Ω.Δ)u1 = g/ρ0)(∂ρ/a∂θ). This equation, where θ is latitude, expresses a balance between the buoyancy torque and the twisting of the full Earth's vorticity by the zonal flow u1. This generalization of the mid-latitude thermal wind relation to the equatorial case shows that u1 may be obtained up to a constant by integrating the ‘observed’ density field along the Earth's rotation axis and not along gravity as in common mid-latitude practice. The simplicity of this result valid in the finite-amplitude regime is not shared however by the other velocity components.Vorticity and momentum equations appropriate to low frequency and predominantly zonal flows are given on the equatorial β-plane. These equatorial results and the mid-latitude geostrophic approximation are shown to stem from an exact generalized relation that relates the variation of dynamic pressure along absolute vortex lines to the buoyancy field. The usual hydrostatic equation follows when the aspect ratio δ = H/L is such that tan θ/δ is much larger than one. Within a boundary-layer region of width (Ha)1/2 and centred at the equator, the analysis shows that the usually neglected Coriolis terms associated with the horizontal component of the Earth's rotation must be kept.Finally, some solutions of zonally homogeneous steady equatorial inertial jets are presented in which the Earth's vorticity is easily turned upside down by the shear flow and the correct angular momentum ‘Ωr2cos2(θ)+u1rCos(θ)’ contour lines close in the vertical–meridional plane.

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.

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