scholarly journals The resonant drag instability of dust streaming in turbulent protoplanetary disc

2020 ◽  
Vol 494 (1) ◽  
pp. 1395-1410 ◽  
Author(s):  
V V Zhuravlev
Keyword(s):  
Effective Viscosity ◽  
Schmidt Number ◽  
Equations Of Motion ◽  
Local Approach ◽  
Additional Increase ◽  
Standard Case ◽  
Viscous Instability ◽  
Dust Fraction ◽  
Inertial Wave ◽  
Small Dust

ABSTRACT Damping of the previously discovered resonant drag instability (RDI) of dust streaming in the protoplanetary disc is studied using the local approach to dynamics of gas–dust perturbations in the limit of the small dust fraction. Turbulence in a disc is represented by the effective viscosity and diffusivity in equations of motion for gas and dust, respectively. In the standard case of the Schmidt number (ratio of the effective viscosity to diffusivity) Sc = 1, the reduced description of RDI in terms of the inertial wave (IW) and the streaming dust wave (SDW) falling in resonance with each other reveals that damping solution differs from the inviscid solution simply by adding the characteristic damping frequency to its growth rate. RDI is fully suppressed at the threshold viscosity, which is estimated analytically, first, for radial drift, next, for vertical settling of dust, and at last, in the case of settling combined with a radial drift of the dust. In the last case, RDI survives up to the highest threshold viscosity, with a greater excess for smaller solids. Once Sc ≠ 1, a new instability specific for dissipative perturbations on the dust settling background emerges. This instability of the quasi-resonant nature is referred to as settling viscous instability (SVI). The mode akin to SDW (IW) becomes growing in a region of long waves provided that Sc > 1 (Sc < 1). SVI leads to an additional increase in the threshold viscosity.

scholarly journals The Dynamics of Meteoroid Streams

1992 ◽  
Vol 152 ◽  
pp. 299-313
Author(s):  
I. P. Wiliams
Keyword(s):  
Chaotic Behavior ◽  
Equations Of Motion ◽  
Meteoroid Streams ◽  
Meteor Streams ◽  
High Order Resonance ◽  
Large Numbers ◽  
The Mean ◽  
Heliocentric Orbits ◽  
Basic Level ◽  
Small Dust

Meteor showers are seen at regular and frequent intervals on Earth. They are caused by meteoroids (that is small dust grains) in a coherent stream, all moving on similar heliocentric orbits, burning up on encountering the atmosphere of the Earth. Such streams contain 1012 or more meteoroids, with the mass of the visible meteoroids ranging up to about 1 g. The main evolutionary effect on such streams is gravitational perturbations by the planets. Though grain-grain collision may be catastrophic for the two grains involved, it has no effect on the remainder of the stream, other than the fact that there are now two less grains in it. Solar radiation has some effect, but this can be included in the equations of motion. Because of the large numbers of particles involved, meteoroid streams represent a laboratory where many of our dynamical concepts can be tested.At a basic level, meteoroid streams represent a collective dynamical phenomenon in which all members display roughly the same behavior. One of the fundamental questions which can be investigated is whether the behavior of the mean orbit of the whole stream represents the mean behavior of the stream members. Within the boundaries of some meteor streams lie regions where the orbits are in high order resonance with Jupiter. This also represents a phenomenon of interest. Finally, the possibility exists that some streams are in chaotic regions and it is interesting to investigate whether or not meteoroids in such regions do display chaotic behavior.

Laser Measurements of Fly Ash Rebound Parameters for Use in Trajectory Calculations

1987 ◽  
Vol 109 (4) ◽  
pp. 535-540 ◽  
Author(s):  
W. Tabakoff ◽  
M. F. Malak
Keyword(s):  
Gas Flow ◽  
Initial Conditions ◽  
Incidence Angle ◽  
Equations Of Motion ◽  
Solid Particles ◽  
Dust Particles ◽  
Laser Doppler Velocimeter ◽  
Laser Measurements ◽  
Flow Through ◽  
Small Dust

This paper describes an experimental method used to find particle restitution coefficients. The equations that govern the motion of solid particles suspended by a compressible gas flow through a turbomachine depend on the restitution coefficients. Analysis of the data obtained by a laser-Doppler velocimeter (LDV) system of the collision phenomenon gives the restitution ratios as a function of the incidence angle. From these ratios, the particle velocity components after collision are computed and used as the initial conditions to the solution of the governing equations of motion for particle trajectories. The erosion of metals impacted by small dust particles can be calculated by knowing the restitution coefficients. The alloy used in this investigation was 410 stainless steel.

Idealized Numerical Modelling of Internal Waves Through Density Staircases

2021 ◽  
Author(s):  
Mikhail Schee ◽  
Nicolas Grisouard
Keyword(s):  
Internal Waves ◽  
Laboratory Experiments ◽  
Equations Of Motion ◽  
Vertical Mixing ◽  
Boussinesq Equations ◽  
The Arctic ◽  
Inertial Wave ◽  
Ice Floes ◽  
Mixed Layers ◽  
Transmission And Reflection

<p>The Arctic Ocean contains a warm layer originating from the Atlantic Ocean below the pycnocline which has a thermohaline staircase structure that inhibits vertical mixing. If this heat were to rise to the surface, the rate of sea ice loss would increase dramatically. Wind stress and ice floes generate internal waves which can cause vertical mixing. As the ice cover in the Arctic continues to decline, it will be important to predict how these changing internal waves propagate through such stratification profiles. Here, we investigate how density staircases enhance or limit downward near-inertial wave propagation. We use direct numerical simulations to solve the Boussinesq equations of motion using spectral methods. We simulate the propagation of internal waves through a vertically stratified fluid which includes one or more steps (i.e., mixed layers). We find that we reproduce the results of laboratory experiments showing transmission and reflection of internal waves from one or two mixed layers. We then extend our parameter regime to simulate the propagation of internal waves through a more realistic stratification profile tending toward that of the Arctic pycnocline.</p>

scholarly journals Jeffrey Fluid Flow through Porous Medium in the Presence of Magnetic Field in Narrow Tubes

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Santhosh Nallapu ◽  
G. Radhakrishnamacharya
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Fluid Flow ◽  
Effective Viscosity ◽  
Equations Of Motion ◽  
Flow Characteristics ◽  
Darcy Number ◽  
Jeffrey Fluid ◽  
Tube Radius ◽  
The Core

Jeffrey fluid flow in the presence of magnetic field through porous medium in tubes of small diameters is studied. It is assumed that the core region consists of a Jeffrey fluid and the peripheral region of a Newtonian fluid. Making the assumptions as in the work of Chaturani and Upadhya, the linearised equations of motion have been solved and analytical solution has been obtained. The influence of various pertinent parameters on the flow characteristics such as effective viscosity, core hematocrit, and mean hematocrit has been studied and discussed through graphs. It is found that the effective viscosity and mean hematocrit decrease with Jeffrey parameter and Darcy number but increase with tube hematocrit and tube radius. Also, the core hematocrit decreases with Jeffrey parameter, Darcy number, tube hematocrit, and tube radius. Further, it is noticed that the flow exhibits the anomalous Fahraeus-Lindquist effect.

Laser Measurements of Fly Ash Rebound Parameters for Use in Trajectory Calculations

1985 ◽  
Author(s):  
W. Tabakoff ◽  
M. F. Malak
Keyword(s):  
Gas Flow ◽  
Initial Conditions ◽  
Incidence Angle ◽  
Equations Of Motion ◽  
Solid Particles ◽  
Dust Particles ◽  
Laser Doppler Velocimeter ◽  
Laser Measurements ◽  
Flow Through ◽  
Small Dust

This paper describes an experimental method used to find the particles restitution coefficients. The equations that govern the motion of solid particles suspended by a compressible gas flow through a turbomachine depend on the restitution coefficients. Analysis of the data obtained by Laser Doppler Velocimeter (LDV) System of the collision phenomenon gives the restitution ratios as a function of the incidence angle. From these ratios, the particle velocity components after collision are computed and used as the initial conditions to the solution of the governing equations of motion for the particles trajectory. The erosion of metals impacted by small dust particles can be calculated by knowing the restitution coefficients. The alloy used in this investigation was 410 stainless steel.

Hamiltonian theory of guiding-centre motion in an electric field with strong gradient

1998 ◽  
Vol 59 (2) ◽  
pp. 211-242 ◽  
Author(s):  
M. DIRICKX ◽  
B. WEYSSOW
Keyword(s):  
Magnetic Field ◽  
Electric Field ◽  
Equations Of Motion ◽  
Standard Case ◽  
Hamiltonian Theory ◽  
Strong Gradient ◽  
Particles In Electromagnetic Fields ◽  
Dynamics Of Particles ◽  
The Magnetic Field ◽  
Drift Parameter

The guiding-centre equations of motion of a classical charged particle in a strong magnetic field and a strongly sheared electric field are derived. They can be used to analyse the dynamics of particles in electromagnetic fields whose spatial profiles are similar to those observed during the H mode in the DIII-D tokamak, for instance. The derivation of the equations of motion is performed up to second order in the drift parameter by applying a Hamiltonian pseudocanonical transformation that removes the gyrophase induced by the magnetic field. The main difference with the standard case of a slowly varying electric field relates to the variation of the new gyrophase and to the expression for the magnetic moment: mv2⊥/2B must be replaced byformula hereThe latter case is also reconsidered – mainly to reveal the consequences of the removal of a hidden divergence for small parallel velocities resulting from the usual averaging transformation.

The motion of a lunar orbiter

1966 ◽  
Vol 25 ◽  
pp. 373
Author(s):  
Y. Kozai
Keyword(s):  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Artificial Satellite ◽  
Equations Of Motion ◽  
Triaxial Ellipsoid ◽  
The Moon ◽  
Secular Motion ◽  
The Earth ◽  
Close Satellite ◽  
The Mean

The motion of an artificial satellite around the Moon is much more complicated than that around the Earth, since the shape of the Moon is a triaxial ellipsoid and the effect of the Earth on the motion is very important even for a very close satellite.The differential equations of motion of the satellite are written in canonical form of three degrees of freedom with time depending Hamiltonian. By eliminating short-periodic terms depending on the mean longitude of the satellite and by assuming that the Earth is moving on the lunar equator, however, the equations are reduced to those of two degrees of freedom with an energy integral.Since the mean motion of the Earth around the Moon is more rapid than the secular motion of the argument of pericentre of the satellite by a factor of one order, the terms depending on the longitude of the Earth can be eliminated, and the degree of freedom is reduced to one.Then the motion can be discussed by drawing equi-energy curves in two-dimensional space. According to these figures satellites with high inclination have large possibilities of falling down to the lunar surface even if the initial eccentricities are very small.The principal properties of the motion are not changed even if plausible values ofJ3andJ4of the Moon are included.This paper has been published in Publ. astr. Soc.Japan15, 301, 1963.

On the motion of comet P/d’Arrest

1974 ◽  
Vol 22 ◽  
pp. 145-148
Author(s):  
W. J. Klepczynski
Keyword(s):  
Equations Of Motion ◽  
Variational Equations ◽  
Partial Derivatives

AbstractThe differences between numerically approximated partial derivatives and partial derivatives obtained by integrating the variational equations are computed for Comet P/d’Arrest. The effect of errors in the IAU adopted system of masses, normally used in the integration of the equations of motion of comets of this type, is investigated. It is concluded that the resulting effects are negligible when compared with the observed discrepancies in the motion of this comet.

Longitudinal Changes in Individual BrainAGE in Healthy Aging, Mild Cognitive Impairment, and Alzheimer’s Disease

GeroPsych ◽  
2012 ◽  
Vol 25 (4) ◽  
pp. 235-245 ◽  
Author(s):  
Katja Franke ◽  
Christian Gaser
Keyword(s):  
Alzheimer’S Disease ◽  
Alzheimer's Disease ◽  
Healthy Aging ◽  
Brain Aging ◽  
Elderly Subjects ◽  
Additional Increase ◽  
Longitudinal Changes ◽  
Novel Method ◽  
The Brain

We recently proposed a novel method that aggregates the multidimensional aging pattern across the brain to a single value. This method proved to provide stable and reliable estimates of brain aging – even across different scanners. While investigating longitudinal changes in BrainAGE in about 400 elderly subjects, we discovered that patients with Alzheimer’s disease and subjects who had converted to AD within 3 years showed accelerated brain atrophy by +6 years at baseline. An additional increase in BrainAGE accumulated to a score of about +9 years during follow-up. Accelerated brain aging was related to prospective cognitive decline and disease severity. In conclusion, the BrainAGE framework indicates discrepancies in brain aging and could thus serve as an indicator for cognitive functioning in the future.

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