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.

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>

Zonal flow in toroidal ion temperature gradient mode turbulence

2007 ◽  
Vol 73 (4) ◽  
pp. 565-573 ◽  
Author(s):  
INGMAR SANDBERG ◽  
V. P. PAVLENKO
Keyword(s):  
Temperature Gradient ◽  
Nonlinear Evolution ◽  
Zonal Flow ◽  
Shear Layers ◽  
Ion Temperature ◽  
Ion Temperature Gradient ◽  
Zonal Flows ◽  
Characteristic Oscillation ◽  
The Stability ◽  
Gradient Mode

AbstractThe properties of zonal flows in the toroidal ion temperature gradient mode turbulence are investigated taking into account the polarization drift effects. The stability criterion and the characteristic oscillation frequency of the zonal flow are determined in terms of the spectra of turbulent fluctuations. The nonlinear evolution of zonal flows may lead to the formation of stationary long-lived coherent structures supporting stationary shear layers. These results indicate the existence of regions with reduced levels of anomalous transport attributed to zonal flows generalizing previous findings regarding zonal flows in electron drift turbulence.

scholarly journals The Effect of Beta on the Downstream Development of Unstable, Chaotic Baroclinic Waves

2019 ◽  
Vol 49 (9) ◽  
pp. 2337-2343 ◽  
Author(s):  
Joseph Pedlosky
Keyword(s):  
Chaotic Behavior ◽  
Baroclinic Instability ◽  
Asymptotic Model ◽  
Spatial Change ◽  
Lorenz Equations ◽  
Layer Model ◽  
Additional Mechanism ◽  
Beta Effect ◽  
Two Layer Model ◽  
Downstream Development

AbstractThe weakly unstable, two-layer model of baroclinic instability is studied in a configuration in which the flow is perturbed at the inflow section of a channel by a slow and periodic perturbation. In a parameter regime where the governing equation would be the Lorenz equations for chaos if the development occurs only in time, the solution behavior becomes considerably more complex as a function of time and downstream coordinate. In the absence of the beta effect it has earlier been shown that the chaotic behavior along characteristics renders the solution nearly discontinuous in the slow downstream coordinate of the asymptotic model. The additional presence of the beta effect, although expunging the chaos for large enough values of the beta parameter, also provides an additional mechanism for abrupt spatial change.

The Tangled Tale of Phase Space

2018 ◽  
Author(s):  
David D. Nolte
Keyword(s):  
Phase Space ◽  
Chaotic Behavior ◽  
Three Body Problem ◽  
Henri Poincaré ◽  
History Of ◽  
The Stability ◽  
Three Body ◽  
Space Phase ◽  
Central Paradigm ◽  
System Phase

This chapter presents the history of the development of the concept of phase space. Phase space is the central visualization tool used today to study complex systems. The chapter describes the origins of phase space with the work of Joseph Liouville and Carl Jacobi that was later refined by Ludwig Boltzmann and Rudolf Clausius in their attempts to define and explain the subtle concept of entropy. The turning point in the history of phase space was when Henri Poincaré used phase space to solve the three-body problem, uncovering chaotic behavior in his quest to answer questions on the stability of the solar system. Phase space was established as the central paradigm of statistical mechanics by JW Gibbs and Paul Ehrenfest.

Release Profile of a Model Protein Drug Depending on the Stability of Microspheres Based on Polyelectrolyte Complex

2007 ◽  
Vol 342-343 ◽  
pp. 505-508
Author(s):  
Sung Won Kim ◽  
Yun Sik Nam ◽  
Yeon Jin Min ◽  
Jong Ho Kim ◽  
Kwang Meyong Kim ◽  
...  
Keyword(s):  
Polyelectrolyte Complex ◽  
Coating Layer ◽  
Great Influence ◽  
Release Profile ◽  
Core Material ◽  
Glycol Chitosan ◽  
The Core ◽  
Key Factor ◽  
Model Protein ◽  
The Stability

Stability and disintegration of natural polyelectrolyte complex microspheres for protein drugs delivery have been extensively investigated because of their great influence on the drug release patterns. In this study, we tested stability of microspheres with alginate (Alg) core layered by either chitosan (Chi) or glycol chitosan (GChi) by examining release profiles of fluorophorelabeled bovine serum albumin (BSA) and lysozyme (Lys) from the microspheres. While GChi shell was disintegrated quickly, Chi-shell microspheres showed good stability in PBS. Disintegration of the coated layer induced the core material instable. The results indicated that while the charges of the shell material provided additional diffusion barrier against the protein release, the key factor to hold the proteins inside the microspheres was the integrity of the outer coating layer.

Chaos Control for a Fractional-Order Jerk System via Time Delay Feedback Controller and Mixed Controller

2021 ◽  
Vol 5 (4) ◽  
pp. 257
Author(s):  
Changjin Xu ◽  
Maoxin Liao ◽  
Peiluan Li ◽  
Lingyun Yao ◽  
Qiwen Qin ◽  
...  
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Chaos Control ◽  
Chaotic Behavior ◽  
Control Strategies ◽  
Feedback Controller ◽  
Research Approach ◽  
Controlling Chaos ◽  
The Stability ◽  
Jerk System

In this study, we propose a novel fractional-order Jerk system. Experiments show that, under some suitable parameters, the fractional-order Jerk system displays a chaotic phenomenon. In order to suppress the chaotic behavior of the fractional-order Jerk system, we design two control strategies. Firstly, we design an appropriate time delay feedback controller to suppress the chaos of the fractional-order Jerk system. The delay-independent stability and bifurcation conditions are established. Secondly, we design a suitable mixed controller, which includes a time delay feedback controller and a fractional-order PDσ controller, to eliminate the chaos of the fractional-order Jerk system. The sufficient condition ensuring the stability and the creation of Hopf bifurcation for the fractional-order controlled Jerk system is derived. Finally, computer simulations are executed to verify the feasibility of the designed controllers. The derived results of this study are absolutely new and possess potential application value in controlling chaos in physics. Moreover, the research approach also enriches the chaos control theory of fractional-order dynamical system.

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