Normal-Mode Analysis of a Baroclinic Wave-Mean Oscillation

2006 ◽  
Vol 63 (11) ◽  
pp. 2795-2812 ◽  
Author(s):  
Christopher L. Wolfe ◽  
Roger M. Samelson
Keyword(s):  
Normal Mode Analysis ◽  
Normal Modes ◽  
Generalized Solution ◽  
Horizontal Resolution ◽  
Basic Flow ◽  
Mode Analysis ◽  
Baroclinic Wave ◽  
Mean Oscillation ◽  
The Stability ◽  
Time Periodic

Abstract The stability of a time-periodic baroclinic wave-mean oscillation in a high-dimensional two-layer quasigeostrophic spectral model is examined by computing a full set of time-dependent normal modes (Floquet vectors) for the oscillation. The model has 72 × 62 horizontal resolution and there are 8928 Floquet vectors in the complete set. The Floquet vectors fall into two classes that have direct physical interpretations: wave-dynamical (WD) modes and damped-advective (DA) modes. The WD modes (which include two neutral modes related to continuous symmetries of the underlying system) have large scales and can efficiently exchange energy and vorticity with the basic flow; thus, the dynamics of the WD modes reflects the dynamics of the wave-mean oscillation. These modes are analogous to the normal modes of steady parallel flow. On the other hand, the DA modes have fine scales and dynamics that reduce, to first order, to damped advection of the potential vorticity by the basic flow. While individual WD modes have immediate physical interpretations as discrete normal modes, the DA modes are best viewed, in sum, as a generalized solution to the damped advection problem. The asymptotic stability of the time-periodic basic flow is determined by a small number of discrete WD modes and, thus, the number of independent initial disturbances, which may destabilize the basic flow, is likewise small. Comparison of the Floquet exponent spectrum of the wave-mean oscillation to the Lyapunov exponent spectrum of a nearby aperiodic trajectory suggests that this result will still be obtained when the restriction to time periodicity is relaxed.

scholarly journals Thermosolutal Instability in Compressible Viscoelastic Dusty Fluid through Porous Medium

2013 ◽  
Vol 18 (1) ◽  
pp. 99-112 ◽  
Author(s):  
P. Kumar ◽  
H. Mohan
Keyword(s):  
Porous Medium ◽  
Viscoelastic Fluid ◽  
Normal Mode Analysis ◽  
Suspended Particles ◽  
Mode Analysis ◽  
Stationary Convection ◽  
Linearized Stability ◽  
Medium Permeability ◽  
The Stability ◽  
Solute Gradient

Thermosolutal instability in a compressible Walters B’ viscoelastic fluid with suspended particles through a porous medium is considered. Following the linearized stability theory and normal mode analysis, the dispersion relation is obtained. For stationary convection, the Walters B’ viscoelastic fluid behaves like a Newtonian fluid and it is found that suspended particles and medium permeability have a destabilizing effect whereas the stable solute gradient and compressibility have a stabilizing effect on the system. Graphs have been plotted by giving numerical values to the parameters to depict the stability characteristics. The stable solute gradient and viscoelasticity are found to introduce oscillatory modes in the system which are non-existent in their absence.

scholarly journals Normal Mode Analysis as a Routine Part of a Structural Investigation

Molecules ◽  
2019 ◽  
Vol 24 (18) ◽  
pp. 3293 ◽  
Author(s):  
Jacob A. Bauer ◽  
Jelena Pavlović ◽  
Vladena Bauerová-Hlinková
Keyword(s):  
Normal Mode ◽  
Structural Study ◽  
Computer Technology ◽  
Structural Investigation ◽  
Normal Mode Analysis ◽  
Computational Cost ◽  
Normal Modes ◽  
Mode Analysis ◽  
Computationally Expensive ◽  
The Web

Normal mode analysis (NMA) is a technique that can be used to describe the flexible states accessible to a protein about an equilibrium position. These states have been shown repeatedly to have functional significance. NMA is probably the least computationally expensive method for studying the dynamics of macromolecules, and advances in computer technology and algorithms for calculating normal modes over the last 20 years have made it nearly trivial for all but the largest systems. Despite this, it is still uncommon for NMA to be used as a component of the analysis of a structural study. In this review, we will describe NMA, outline its advantages and limitations, explain what can and cannot be learned from it, and address some criticisms and concerns that have been voiced about it. We will then review the most commonly used techniques for reducing the computational cost of this method and identify the web services making use of these methods. We will illustrate several of their possible uses with recent examples from the literature. We conclude by recommending that NMA become one of the standard tools employed in any structural study.

Linearized theory of inhomogeneous multiple ‘water-bag’ plasmas

1973 ◽  
Vol 9 (2) ◽  
pp. 235-247 ◽  
Author(s):  
H. W. Bloomberg ◽  
H. L. Berk
Keyword(s):  
Boundary Conditions ◽  
Normal Mode ◽  
Normal Mode Analysis ◽  
Mode Analysis ◽  
Special Boundary ◽  
Finite Region ◽  
Trapped Particles ◽  
Linearized Theory ◽  
Beam Approximation ◽  
The Stability

The problem of the stability of inhomogeneous, electrostatic, multiple water-bag plasmas is considered. Equations are derived for general stationary water-bag equilibria, as well as for the corresponding perturbations. Particular attention is directed to systems with trapped particles in periodic equilibria, and special boundary conditions for the perturbation equations at the trapped-particle turning points are introduced. A normal-mode analysis is carried out for a configuration involving trapped particles occupying a finite region in the vicinity of the trough of an equilibrium wave (BGK mode). The results confirm the validity of the bunched-beam approximation.

Singular Vectors and Time-Dependent Normal Modes of a Baroclinic Wave-Mean Oscillation

2008 ◽  
Vol 65 (3) ◽  
pp. 875-894 ◽  
Author(s):  
Christopher L. Wolfe ◽  
Roger M. Samelson
Keyword(s):  
Degrees Of Freedom ◽  
Channel Model ◽  
Normal Modes ◽  
Time Dependent ◽  
Inner Product ◽  
Time Interval ◽  
Baroclinic Wave ◽  
Singular Vectors ◽  
Mean Oscillation ◽  
Local Attractor

Abstract Linear disturbance growth is studied in a quasigeostrophic baroclinic channel model with several thousand degrees of freedom. Disturbances to an unstable, nonlinear wave-mean oscillation are analyzed, allowing the comparison of singular vectors and time-dependent normal modes (Floquet vectors). Singular vectors characterize the transient growth of linear disturbances in a specified inner product over a specified time interval and, as such, they complement and are related to Lyapunov vectors, which characterize the asymptotic growth of linear disturbances. The relationship between singular vectors and Floquet vectors (the analog of Lyapunov vectors for time-periodic systems) is analyzed in the context of a nonlinear baroclinic wave-mean oscillation. It is found that the singular vectors divide into two dynamical classes that are related to those of the Floquet vectors. Singular vectors in the “wave dynamical” class are found to asymptotically approach constant linear combinations of Floquet vectors. The most rapidly decaying singular vectors project strongly onto the most rapidly decaying Floquet vectors. In contrast, the leading singular vectors project strongly onto the leading adjoint Floquet vectors. Examination of trajectories that are near the basic cycle show that the leading Floquet vectors are geometrically tangent to the local attractor while the leading initial singular vectors point off the local attractor. A method for recovering the leading Floquet vectors from a small number of singular vectors is additionally demonstrated.

scholarly journals ProMode-Oligomer: Database of Normal Mode Analysis in Dihedral Angle Space for a Full-Atom System of Oligomeric Proteins

2012 ◽  
Vol 6 (1) ◽  
pp. 9-19 ◽  
Author(s):  
Hiroshi Wako ◽  
Shigeru Endo
Keyword(s):  
Normal Mode ◽  
Protein Complexes ◽  
Normal Mode Analysis ◽  
Normal Modes ◽  
Point Of View ◽  
Mode Analysis ◽  
Dihedral Angles ◽  
Oligomeric Proteins ◽  
Displacement Vectors ◽  
Atom System

The database ProMode-Oligomer (http://promode.socs.waseda.ac.jp/promode_oligomer) was constructed by collecting normal-mode-analysis (NMA) results for oligomeric proteins including protein-protein complexes. As in the ProMode database developed earlier for monomers and individual subunits of oligomers (Bioinformatics vol. 20, pp. 2035–2043, 2004), NMA was performed for a full-atom system using dihedral angles as independent variables, and we released the results (fluctuations of atoms, fluctuations of dihedral angles, correlations between atomic fluctuations, etc.). The vibrating oligomer is visualized by animation in an interactive molecular viewer for each of the 20 lowest-frequency normal modes. In addition, displacement vectors of constituent atoms for each normal mode were decomposed into two characteristic motions in individual subunits, i.e., internal and external (deformation and rigid-body movements of the individual subunits, respectively), and then the mutual movements of the subunits and the movement of atoms around the interface regions were investigated. These results released in ProMode-Oligomer are useful for characterizing oligomeric proteins from a dynamic point of view. The analyses are illustrated with immunoglobulin light- and heavy-chain variable domains bound to lysozyme and to a 12-residue peptide.

scholarly journals The effect of compressibility, rotation and magnetic field on thermal instability of Walters’ fluid permeated with suspended particles in porous medium

2014 ◽  
Vol 18 (suppl.2) ◽  
pp. 539-550 ◽  
Author(s):  
Kumar Aggarwal ◽  
Anushri Verma
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Normal Mode Analysis ◽  
Suspended Particles ◽  
Elastic Parameter ◽  
Mode Analysis ◽  
Medium Permeability ◽  
Stabilizing Effect ◽  
Model Fluid ◽  
The Stability

The purpose of this paper is to study the effects of compressibility, rotation, magnetic field and suspended particles on thermal stability of a layer of visco-elastic Walters? (model) fluid in porous medium. Using linearized theory and normal mode analysis, dispersion relation has been obtained. In case of stationary convection, it is found that the rotation has stabilizing effect on the system. The magnetic field may have destabilizing effect on the system in the presence of rotation while in the absence of rotation it always has stabilizing effect. The medium permeability has destabilizing effect on the system in the absence of rotation while in the presence of rotation it may have stabilizing effect. The suspended particles and compressibility always have destabilizing effect. Due to vanishing of visco-elastic parameter, the compressible visco-elastic fluid behaves like Newtonian fluid. Graphs have also been plotted to depict the stability characteristics. The viscoelasticity, magnetic field and rotation are found to introduce oscillatory modes into the system which were non-existent in their absence.

Surface instability of a dielectric fluid in an electric field

1968 ◽  
Vol 64 (4) ◽  
pp. 1203-1207 ◽  
Author(s):  
D. H. Michael
Keyword(s):  
Free Surface ◽  
Dispersion Relation ◽  
Gravity Waves ◽  
Normal Mode Analysis ◽  
Horizontal Layer ◽  
Mode Analysis ◽  
Dielectric Fluid ◽  
Inviscid Fluid ◽  
Static Displacement ◽  
The Stability

This paper is a sequel to a recent paper (1) in which the author discussed gravity waves on a horizontal layer of conducting fluid with a normal electrostatic field at the free surface. In this work results are given for waves in an incompressible dielectric fluid, in a similar configuration. Treating the dielectric as an inviscid fluid the stability of the system is first described in terms of the changes in potential energy in a small static displacement. The result so obtained is then confirmed by a normal mode analysis in which a dispersion relation is obtained for the inviscid model. The paper gives finally a discussion of the results for a viscous dielectric fluid, the main point of which is that, as in (1), in the transition from stable to unstable disturbances viscosity plays no part, and that the stability characteristics are the same as those for an inviscid dielectric fluid.

Baroclinic instability in an eccentric annulus

1976 ◽  
Vol 77 (4) ◽  
pp. 769-788 ◽  
Author(s):  
P. R. Gent ◽  
H. Leach
Keyword(s):  
Normal Mode Analysis ◽  
Baroclinic Instability ◽  
Analytical Investigation ◽  
Mode Analysis ◽  
Slow Rotation ◽  
Rotating Fluid ◽  
Mixed Flow ◽  
Eccentric Annulus ◽  
Baroclinic Waves ◽  
The Stability

A study has been made of baroclinic instability in a differentially heated, rotating fluid annulus whose channel width varies azimuthally. Both laboratory experiments and an a.nalytica1 model employing a linear normal-mode analysis have been used. The experiments show three types of flow. For slow rotation the flow is 'symmetric’, whereas at high rotation speeds baroclinic waves occur at all azimuths. At intermediate rotation speeds it is possible to have a mixed flow which is ‘symmetric’ in the narrow part but has baroclinic waves in the wide part of the annulus. This result suggested the analytical investigation of the stability of a barocIinic flow whose meridional scale varies downstream. It was found that this model also permits three possible types of flow: everywhere stable, everywhere unstable, and also a mixed flow which is locally unstable where the meridional scale is largest but locally stable where the scale is smallest.

scholarly journals Rayleigh-Bénard convection in an elastico-viscous Walters’ (model B’) nanofluid layer

2015 ◽  
Vol 63 (1) ◽  
pp. 235-244 ◽  
Author(s):  
G.C. Rana ◽  
R. Chand
Keyword(s):  
Fluid Model ◽  
Normal Mode Analysis ◽  
Sufficient Conditions ◽  
Lewis Number ◽  
Horizontal Layer ◽  
Linear Stability Theory ◽  
Mode Analysis ◽  
Physical Parameters ◽  
Onset Of Convection ◽  
The Stability

Abstract In this study, the onset of convection in an elastico-viscous Walters’ (model B’) nanofluid horizontal layer heated from below is considered. The Walters’ (model B’) fluid model is employed to describe the rheological behavior of the nanofluid. By applying the linear stability theory and a normal mode analysis method, the dispersion relation has been derived. For the case of stationary convection, it is observed that the Walters’ (model B’) elastico-viscous nanofluid behaves like an ordinary Newtonian nanofluid. The effects of the various physical parameters of the system, namely, the concentration Rayleigh number, Prandtl number, capacity ratio, Lewis number and kinematics visco-elasticity coefficient on the stability of the system has been numerically investigated. In addition, sufficient conditions for the non-existence of oscillatory convection are also derived.

Perturbed normal-mode analysis of induction times, relaxation times, and reaction rates in unimolecular reactions

1979 ◽  
Vol 57 (13) ◽  
pp. 1723-1730 ◽  
Author(s):  
Andrew W. Yau ◽  
Huw O. Pritchard
Keyword(s):  
Normal Mode ◽  
Transition Probabilities ◽  
Normal Mode Analysis ◽  
Relaxation Times ◽  
Normal Modes ◽  
Reaction Rates ◽  
Mode Analysis ◽  
Decomposition Reactions ◽  
Induction Times ◽  
Network Relationship

A perturbed normal-mode analysis is presented of the induction (or incubation) time, the relaxation rate, and the reaction rate of a diluted unimolecular system. At high temperature, the unimolecular rate approaches the Lindemann behaviour and the low-pressure rate is related to the normal modes of relaxation of the reactive states in a simple manner. In a step-ladder model system, the network relationship between the normal modes and the microscopic transition probabilities leads to explicit theoretical correlations between the respective experimental quantities. Illustrative calculations of such correlations are presented for the decomposition reactions of N2O and CO2 diluted in Ar at shock wave temperatures, and are compared with experiment.

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