Natural Surface Oscillations of Rotating Fluid Along Radial Baffles of Rotor

2016 ◽  
Vol 138 (6) ◽  
Author(s):  
A. Nikiforov
Keyword(s):  
Dynamic Equilibrium ◽  
Fluid Motion ◽  
Plane Motion ◽  
Rotating Fluid ◽  
Cylindrical Chamber ◽  
Centrifugal Effect ◽  
Unperturbed Motion ◽  
Resonant Frequencies ◽  
Axial Coordinate ◽  
Lateral Deflections

This paper determines natural and resonant frequencies of radial–circular oscillations (waves) on the nonviscous, incompressible fluid partially and evenly filling similar compartments in a rotor that has the cylindrical chamber, solid radial baffles, and constant angular velocity. It is assumed as follows: influence of the gravity and surface tension is negligibly small as compared to the centrifugal effect; configuration of dynamic equilibrium (unperturbed motion) of fluid is an annular rigid body rotation; and the fluid motion perturbed by small lateral deflections of the rotor does not depend on the axial coordinate (plane motion).

On the spin-up and spin-down of a rotating fluid. Part 2. Measurements and stability

1976 ◽  
Vol 77 (4) ◽  
pp. 709-735 ◽  
Author(s):  
Patrick D. Weidman
Keyword(s):  
Stability Boundary ◽  
Fluid Motion ◽  
Azimuthal Velocity ◽  
Laser Doppler Velocimeter ◽  
Rotating Fluid ◽  
Constant Acceleration ◽  
Centrifugal Instability ◽  
The Stability ◽  
Theoretical Results

Measurements of the azimuthal velocity inside a cylinder which spins up or spins down at constant acceleration were obtained with a laser-Doppler velocimeter and compared with the theoretical results presented in part 1. Velocity profiles near the wave front in spin-up indicate that the velocity discontinuity given by the inviscid Wedemeyer model is smoothed out in a shear layer whose thickness varies with radius and time but scales with hE1/4Ω. The spin-down profiles are always in excellent agreement with theory when the flow is stable. Visualization studies with aluminium tracers have made possible the determination of the stability boundary for Ekman spiral waves (principally type II waves) observed on the cylinder end walls during spin-up. For spin-down to rest the flow always experienced a centrifugal instability which ultimately disrupted the interior fluid motion.

A new integral property of inertial waves in rotating fluid spheres

2008 ◽  
Vol 465 (2104) ◽  
pp. 1075-1091 ◽  
Author(s):  
Xinhao Liao ◽  
Keke Zhang
Keyword(s):  
Recurrence Relations ◽  
Mathematical Proof ◽  
Fluid Motion ◽  
Complex Conjugate ◽  
Inviscid Fluid ◽  
Rotating Fluid ◽  
Hyperbolic Partial Differential Equation ◽  
Inertial Waves ◽  
Integral Property ◽  
Poincaré Polynomial

The problem of fluid motion in the form of inertial waves in an incompressible inviscid fluid contained in a rotating sphere is governed by the Poincaré equation, a second-order hyperbolic partial differential equation. Its explicit general analytical solution in terms of a double Poincaré polynomial was found by Zhang et al . ( Zhang et al . 2001 J. Fluid Mech . 437 , 103–119), describing the pressure p mnK and the velocity u mnK of spherical inertial waves, where the triple indices ( mnK ) are indicative of the azimuthal, vertical and radial structures, respectively. On the basis of the general explicit solution, we reveal a new intriguing integral property of the spherical inertial waves for all possible values of m , l and n , where M and K are related to the degree of the double Poincaré polynomial and denotes the complex conjugate of u mlM . A mathematical proof of the vanishing of the integral involving the construction of two auxiliary recurrence relations is presented. Furthermore, a comparison with the corresponding integral for rotating cylinders is made, showing a fundamental difference between the two systems.

On the spatial oscillations of a horizontally heated rotating fluid

1977 ◽  
Vol 81 (2) ◽  
pp. 325-349 ◽  
Author(s):  
P. G. Daniels ◽  
K. Stewartson
Keyword(s):  
Multiple Scales ◽  
Fluid Motion ◽  
Lower Surface ◽  
Laboratory Model ◽  
Rotating Fluid ◽  
Oscillatory Solutions ◽  
Convective Parameter ◽  
Spatial Oscillations ◽  
Side Walls ◽  
Discrete Values

SummaryA laboratory model simulating aspects of oceanic or atmospheric circulationconsists of a rotating fluid annulus which is subject to a temperature gradient on the lower surface and is insulated on the inner and outer curved walls and on the top surface. A theoretical study of the resulting steady axi-symmetric fluid motion in the limit of small Ekman number, E, by Daniels (2) indicated that if an appropriate convective parameter is sufficiently large, oscillatory solutions are generated in the layer which is located on the hotter of the two side-walls, which do not decay into the geostrophic interior. The present paper resolves this difficulty by using the method of multiple scales to trace the development of the oscillatory solutions in the interior of the fluid. This leads to a consistent overall flow pattern throughout the annulus, except at an infinite set of discrete values of the convective parameter at which resonance is predicted.

scholarly journals Inverse centrifugal effect induced by collective motion of vortices in rotating turbulent convection

2020 ◽  
Author(s):  
Shan-Shan Ding ◽  
Kai Leong Chong ◽  
Jun-Qiang Shi ◽  
Guang-Yu Ding ◽  
Hao-Yuan Lu ◽  
...  
Keyword(s):  
Collective Motion ◽  
Fluid Motion ◽  
Vortex Motion ◽  
Turbulent Convection ◽  
Fluid System ◽  
Centrifugal Effect ◽  
Scale Free ◽  
Range Correlation ◽  
Outward Motion ◽  
Cluster Length

Abstract When a fluid system is subject to strong rotation, centrifugal fluid motion is expected, i.e., denser (lighter) fluid moves outward (inward) from (toward) the axis of rotation. Here we demonstrate, both experimentally and numerically, the existence of an unexpected outward motion of warm and lighter vortices in rotating turbulent convection. This anomalous vortex motion occurs under rapid rotations when the centrifugal buoyancy is sufficiently strong to induce a symmetry-breaking in the vorticity field, i.e., the vorticity of the cold anticyclones overrides that of the warm cyclones. We show that through hydrodynamic interactions the densely populated vortices can self-aggregate into coherent clusters and exhibit collective motion in this flow regime. Interestingly, the correlation of the vortex velocity fluctuations within a cluster is scale-free, with the correlation length being about 30% of the cluster length. Such long-range correlation leads to the collective outward motion of cyclones. Our study provides new understanding of vortex dynamics that are widely present in nature.

scholarly journals Inverse centrifugal effect induced by collective motion of vortices in rotating thermal convection

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Shan-Shan Ding ◽  
Kai Leong Chong ◽  
Jun-Qiang Shi ◽  
Guang-Yu Ding ◽  
Hao-Yuan Lu ◽  
...  
Keyword(s):  
Thermal Convection ◽  
Collective Motion ◽  
Fluid Motion ◽  
Vortex Motion ◽  
Fluid System ◽  
Centrifugal Effect ◽  
Scale Free ◽  
Range Correlation ◽  
Outward Motion ◽  
Cluster Length

AbstractWhen a fluid system is subject to strong rotation, centrifugal fluid motion is expected, i.e., denser (lighter) fluid moves outward (inward) from (toward) the axis of rotation. Here we demonstrate, both experimentally and numerically, the existence of an unexpected outward motion of warm and lighter vortices in rotating thermal convection. This anomalous vortex motion occurs under rapid rotations when the centrifugal buoyancy is sufficiently strong to induce a symmetry-breaking in the vorticity field, i.e., the vorticity of the cold anticyclones overrides that of the warm cyclones. We show that through hydrodynamic interactions the densely distributed vortices can self-aggregate into coherent clusters and exhibit collective motion in this flow regime. Interestingly, the correlation of the vortex velocity fluctuations within a cluster is scale-free, with the correlation length being proportional ( ≈ 30%) to the cluster length. Such long-range correlation leads to the counterintuitive collective outward motion of warm vortices. Our study brings insights into the vortex dynamics that are widely present in nature.

Microtubule nucleation sequence studied by time-resolved x-ray scattering and electron microscopy

1983 ◽  
Vol 41 ◽  
pp. 766-767
Author(s):  
Eva-Maria Mandelkow ◽  
Eckhard Mandelkow ◽  
Joan Bordas
Keyword(s):  
Electron Microscopy ◽  
Dynamic Equilibrium ◽  
Time Resolved ◽  
X Ray ◽  
Additional Information ◽  
X Ray Scattering ◽  
Low Concentrations ◽  
Microtubule Growth ◽  
Ray Patterns ◽  
Ray Scattering

When a solution of microtubule protein is changed from non-polymerising to polymerising conditions (e.g. by temperature jump or mixing with GTP) there is a series of structural transitions preceding microtubule growth. These have been detected by time-resolved X-ray scattering using synchrotron radiation, and they may be classified into pre-nucleation and nucleation events. X-ray patterns are good indicators for the average behavior of the particles in solution, but they are difficult to interpret unless additional information on their structure is available. We therefore studied the assembly process by electron microscopy under conditions approaching those of the X-ray experiment. There are two difficulties in the EM approach: One is that the particles important for assembly are usually small and not very regular and therefore tend to be overlooked. Secondly EM specimens require low concentrations which favor disassembly of the particles one wants to observe since there is a dynamic equilibrium between polymers and subunits.

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