The Dynamics of Three-Dimensional Perturbations a Solid-Body Rotation Flow in a Circular Pipe

2016 ◽  
Author(s):  
Rui Gong ◽  
Shixiao Wang ◽  
Zvi Rusak
Keyword(s):  
Solid Body ◽  
Three Dimensional ◽  
Circular Pipe ◽  
Body Rotation ◽  
Solid Body Rotation

Wall-separation and vortex-breakdown zones in a solid-body rotation flow in a rotating finite-length straight circular pipe

2014 ◽  
Vol 759 ◽  
pp. 321-359 ◽  
Author(s):  
Zvi Rusak ◽  
Shixiao Wang
Keyword(s):  
Steady State ◽  
Numerical Simulations ◽  
Solid Body ◽  
Finite Length ◽  
Vortex Breakdown ◽  
Swirling Flows ◽  
Flow Dynamics ◽  
Circular Pipe ◽  
Body Rotation ◽  
Solid Body Rotation

AbstractThe incompressible, inviscid and axisymmetric dynamics of perturbations on a solid-body rotation flow with a uniform axial velocity in a rotating, finite-length, straight, circular pipe are studied via global analysis techniques and numerical simulations. The investigation establishes the coexistence of both axisymmetric wall-separation and vortex-breakdown zones above a critical swirl level, ${\it\omega}_{1}$. We first describe the bifurcation diagram of steady-state solutions of the flow problem as a function of the swirl ratio ${\it\omega}$. We prove that the base columnar flow is a unique steady-state solution when ${\it\omega}$ is below ${\it\omega}_{1}$. This state is asymptotically stable and a global attractor of the flow dynamics. However, when ${\it\omega}>{\it\omega}_{1}$, we reveal, in addition to the base columnar flow, the coexistence of states that describe swirling flows around either centreline stagnant breakdown zones or wall quasi-stagnant zones, where both the axial and radial velocities vanish. We demonstrate that when ${\it\omega}>{\it\omega}_{1}$, the base columnar flow is a min–max point of an energy functional that governs the problem, while the swirling flows around the quasi-stagnant and stagnant zones are global and local minimizer states and become attractors of the flow dynamics. We also find additional min–max states that are transient attractors of the flow dynamics. Numerical simulations describe the evolution of perturbations on above-critical columnar states to either the breakdown or the wall-separation states. The growth of perturbations in both cases is composed of a linear stage of the evolution, with growth rates accurately predicted by the analysis of Wang & Rusak (Phys. Fluids, vol. 8, 1996a, pp. 1007–1016), followed by a stage of saturation to either one of the separation zone states. The wall-separation states have the same chance of appearing as that of vortex-breakdown states and there is no hysteresis loop between them. This is strikingly different from the dynamics of vortices with medium or narrow vortical core size in a pipe.

Rotating free-shear flows. Part 2. Numerical simulations

1995 ◽  
Vol 293 ◽  
pp. 47-80 ◽  
Author(s):  
Olivier Métais ◽  
Carlos Flores ◽  
Shinichiro Yanase ◽  
James J. Riley ◽  
Marcel Lesieur
Keyword(s):  
Solid Body ◽  
Mixing Layer ◽  
Three Dimensional ◽  
Rossby Number ◽  
Two Dimensional ◽  
Body Rotation ◽  
Mean Flow ◽  
Hairpin Vortices ◽  
Solid Body Rotation ◽  
Rotation Rates

The three-dimensional dynamics of the coherent vortices in periodic planar mixing layers and in wakes subjected to solid-body rotation of axis parallel to the basic vorticity are investigated through direct (DNS) and large-eddy simulations (LES). Initially, the flow is forced by a weak random perturbation superposed on the basic shear, the perturbation being either quasi-two-dimensional (forced transition) or three-dimensional (natural transition). For an initial Rossby number Ro(i), based on the vorticity at the inflexion point, of small modulus, the effect of rotation is to always make the flow more two-dimensional, whatever the sense of rotation (cyclonic or anticyclonic). This is in agreement with the Taylor–Proudman theorem. In this case, the longitudinal vortices found in forced transition without rotation are suppressed.It is shown that, in a cyclonic mixing layer, rotation inhibits the growth of three-dimensional perturbations, whatever the value of the Rossby number. This inhibition exists also in the anticyclonic case for |Ro(i)| ≤ 1. At moderate anticyclonic rotation rates (Ro(i) < −1), the flow is strongly destabilized. Maximum destabilization is achieved for |Ro(i) ≈ 2.5, in good agreement with the linear-stability analysis performed by Yanase et al. (1993). The layer is then composed of strong longitudinal alternate absolute vortex tubes which are stretched by the flow and slightly inclined with respect to the streamwise direction. The vorticity thus generated is larger than in the nonrotating case. The Kelvin–Helmholtz vortices have been suppressed. The background velocity profile exhibits a long range of nearly constant shear whose vorticity exactly compensates the solid-body rotation vorticity. This is in agreement with the phenomenological theory proposed by Lesieur, Yanase & Métais (1991). As expected, the stretching is more efficient in the LES than in the DNS.A rotating wake has one side cyclonic and the other anticyclonic. For |Ro(i)| ≤ 1, the effect of rotation is to make the wake more two-dimensional. At moderate rotation rates (|Ro(i)| > 1), the cyclonic side is composed of Kármán vortices without longitudinal hairpin vortices. Karman vortices have disappeared from the anticyclonic side, which behaves like the mixing layer, with intense longitudinal absolute hairpin vortices. Thus, a moderate rotation has produced a dramatic symmetry breaking in the wake topology. Maximum destabilization is still observed for |Ro(i)| ≈ 2.5, as in the linear theory.The paper also analyses the effect of rotation on the energy transfers between the mean flow and the two-dimensional and three-dimensional components of the field.

On triadic resonance as an instability mechanism in precessing cylinder flow

2018 ◽  
Vol 841 ◽  
Author(s):  
Thomas Albrecht ◽  
Hugh M. Blackburn ◽  
Juan M. Lopez ◽  
Richard Manasseh ◽  
Patrice Meunier
Keyword(s):  
Solid Body ◽  
Three Dimensional ◽  
Frame Of Reference ◽  
Dynamic Mode Decomposition ◽  
Dynamic Mode ◽  
Instability Mechanism ◽  
Body Rotation ◽  
Solid Body Rotation ◽  
Successful Model ◽  
Basic States

Contained rotating flows subject to precessional forcing are well known to exhibit rapid and energetic transitions to disorder. Triadic resonance of inertial modes has been previously proposed as an instability mechanism in such flows, and that idea was developed into a successful model for predicting instability in a cylindrical container when departures from solid-body rotation are sufficiently small. Using direct numerical simulation and dynamic mode decomposition, we analyse instabilities of precessing cylinder flows whose three-dimensional basic states, steady in the gimbal frame of reference, may depart substantially from solid-body rotation. In the gimbal frame, the instability can be interpreted as resulting from a supercritical Hopf bifurcation that results in a limit-cycle flow. In the cylinder frame of reference, the basic state is a rotating wave with azimuthal wavenumber $m=1$, and the instability satisfies triadic-resonance conditions with the instability mode maintaining a fixed orientation with respect to the basic state. Thus, we are able to demonstrate the existence of two alternative but congruent explanations for the instability. Additionally, we show that basic states may depart substantially from solid-body rotation even with modest cylinder tilt angles, and growth rates for instabilities may be sufficiently large that nonlinear saturation to disordered states can occur within approximately ten cylinder revolutions, in agreement with experimental observations.

Three-dimensional instabilities and inertial waves in a rapidly rotating split-cylinder flow

2016 ◽  
Vol 800 ◽  
pp. 666-687 ◽  
Author(s):  
Juan M. Lopez ◽  
Paloma Gutierrez-Castillo
Keyword(s):  
Solid Body ◽  
Differential Rotation ◽  
Three Dimensional ◽  
Side Wall ◽  
Wall Layer ◽  
Bulk Flow ◽  
Body Rotation ◽  
Rotating Waves ◽  
Solid Body Rotation ◽  
Inertial Wave

The nonlinear dynamics of the flow in a differentially rotating split cylinder is investigated numerically. The differential rotation, with the top half of the cylinder rotating faster than the bottom half, establishes a basic state consisting of a bulk flow that is essentially in solid-body rotation at the mean rotation rate of the cylinder and boundary layers where the bulk flow adjusts to the differential rotation of the cylinder halves, which drives a strong meridional flow. There are Ekman-like layers on the top and bottom end walls, and a Stewartson-like side wall layer with a strong downward axial flow component. The complicated bottom corner region, where the downward flow in the side wall layer decelerates and negotiates the corner, is the epicentre of a variety of instabilities associated with the local shear and curvature of the flow, both of which are very non-uniform. Families of both high and low azimuthal wavenumber rotating waves bifurcate from the basic state in Eckhaus bands, but the most prominent states found near onset are quasiperiodic states corresponding to mixed modes of the high and low azimuthal wavenumber rotating waves. The frequencies associated with most of these unsteady three-dimensional states are such that spiral inertial wave beams are emitted from the bottom corner region into the bulk, along cones at angles that are well predicted by the inertial wave dispersion relation, driving the bulk flow away from solid-body rotation.

Oval Flow Mode Between Two Corotating Disks With Stationary Shroud

2014 ◽  
Vol 137 (3) ◽  
Author(s):  
Ching Min Hsu ◽  
Jia-Kun Chen ◽  
Min Kai Hsieh ◽  
Rong Fung Huang
Keyword(s):  
Flow Structure ◽  
Solid Body ◽  
Circumferential Velocity ◽  
Body Rotation ◽  
Flow Core ◽  
Core Flow ◽  
Node Point ◽  
Solid Body Rotation ◽  
Characteristic Flow ◽  
Buffer Region

The characteristic flow behavior, time-averaged velocity distributions, phase-resolved ensemble-averaged velocity profiles, and turbulence properties of the flow in the interdisk midplane between shrouded two corotating disks at the interdisk spacing to disk radius aspect ratio 0.2 and rotation Reynolds number 3.01 × 105 were experimentally studied by flow visualization method and particle image velocimetry (PIV). An oval core flow structure rotating at a frequency 60% of the disks rotating frequency was observed. Based on the analysis of relative velocities, the flow in the region outside the oval core flow structure consisted of two large vortex rings, which move circumferentially with the rotation motion of the oval flow core. Four characteristic flow regions—solid-body-rotation-like region, buffer region, vortex region, and shroud-influenced region—were identified in the flow field. The solid-body-rotation-like region, which was featured by its linear distribution of circumferential velocity and negligibly small radial velocity, was located within the inscribing radius of the oval flow core. The vortex region was located outside the circumscribing radius of the oval flow core. The buffer region existed between the solid-body-rotation-like region and the vortex region. In the buffer region, there existed a “node” point that the propagating circumferential velocity waves diminished. The circumferential random fluctuation intensity presented minimum values at the node point and high values in the solid-body-rotation-like region and shroud-influenced region due to the shear effect induced by the wall.

scholarly journals On a possible corrugation of the galactic plane

1970 ◽  
Vol 38 ◽  
pp. 147-150 ◽  
Author(s):  
C. M. Varsavsky ◽  
R. J. Quiroga
Keyword(s):  
Brightness Temperature ◽  
Solid Body ◽  
Rotation Curve ◽  
Galactic Plane ◽  
Maximum Temperature ◽  
Body Rotation ◽  
Maximum Brightness ◽  
Solid Body Rotation ◽  
The Galaxy ◽  
Sinusoidal Pattern

We have studied the rotation curve of the Galaxy at different heights below and above the equator. In the course of this work we noticed that the maximum brightness temperature of hydrogen oscillates around the galactic plane following a fairly sinusoidal pattern. It is further noticed that the maximum temperature of hydrogen occurs right on the plane in the regions where the rotation curve has a form indicating solid body rotation. A rotation curve based on points of maximum hydrogen temperature does not differ appreciably from a rotation curve measured on the galactic plane.

Fragmentation of elongated cylindrical clouds. IV - Clouds with solid-body rotation about an arbitrary axis

1992 ◽  
Vol 400 ◽  
pp. 579 ◽  
Author(s):  
Ian Bonnell ◽  
Jean-Pierre Arcoragi ◽  
Hugo Martel ◽  
Pierre Bastien
Keyword(s):  
Solid Body ◽  
Body Rotation ◽  
Solid Body Rotation ◽  
Arbitrary Axis

scholarly journals Observations of an Inertial Peak in the Intrinsic Wind Spectrum Shifted by Rotation in the Antarctic Vortex

2012 ◽  
Vol 69 (12) ◽  
pp. 3800-3811 ◽  
Author(s):  
L. J. Gelinas ◽  
R. L. Walterscheid ◽  
C. R. Mechoso ◽  
G. Schubert
Keyword(s):  
Solid Body ◽  
Wave Spectrum ◽  
Polar Vortex ◽  
Relative Vorticity ◽  
Body Rotation ◽  
Background Flow ◽  
Absolute Vorticity ◽  
Solid Body Rotation ◽  
The Absolute ◽  
The Antarctic

Abstract Spectral analyses of time series of zonal winds derived from locations of balloons drifting in the Southern Hemisphere polar vortex during the Vorcore campaign of the Stratéole program reveal a peak with a frequency near 0.10 h−1, more than 25% higher than the inertial frequency at locations along the trajectories. Using balloon data and values of relative vorticity evaluated from the Modern Era Retrospective-Analyses for Research and Applications (MERRA), the authors find that the spectral peak near 0.10 h−1 can be interpreted as being due to inertial waves propagating inside the Antarctic polar vortex. In support of this claim, the authors examine the way in which the low-frequency part of the gravity wave spectrum sampled by the balloons is shifted because of effects of the background flow vorticity. Locally, the background flow can be expressed as the sum of solid-body rotation and shear. This study demonstrates that while pure solid-body rotation gives an effective inertial frequency equal to the absolute vorticity, the latter gives an effective inertial frequency that varies, depending on the direction of wave propagation, between limits defined by the absolute vorticity plus or minus half of the background relative vorticity.

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