Nonlinear transient growth in a vortex column

2011 ◽  
Vol 682 ◽  
pp. 304-331 ◽  
Author(s):  
FAZLE HUSSAIN ◽  
DHOORJATY S. PRADEEP ◽  
ERIC STOUT
Keyword(s):  
Critical Radius ◽  
Nonlinear Regime ◽  
Transient Growth ◽  
Clear Trend ◽  
The Core ◽  
Growth Modes ◽  
Resonant Forcing ◽  
Initial Vorticity ◽  
Nonlinear Transient ◽  
Scale Turbulence

Growth of optimal transient perturbations to an Oseen vortex column into the nonlinear regime is studied via direct numerical simulation (DNS) for Reynolds number, Re (≡ circulation/viscosity), up to 10000. An optimal bending-wave transient mode is obtained from linear analysis and used as the initial condition. (DNS of a vortex column embedded in finer-scale turbulence reveals that optimal modes are preferentially excited during vortex–turbulence interaction.) Tilting of the optimal mode's radial vorticity perturbation into the azimuthal direction and its concomitant stretching by the column's strain field produces positive Reynolds stress, hence kinetic energy growth. Modes experiencing the largest growth are those with initial vorticity localized at a ‘critical radius’ outside the core, such that this perturbation vorticity resonantly induces core waves. Resonant forcing leads to growth of perturbation energy concentrated within the core. Moderate-amplitude (~5%) perturbations cause significant distortion of the core and generate secondary filament-like spiral structures (‘threads’) outside the core. As the mode evolves into the nonlinear regime, radially outward self-advection of thread dipoles accelerates growth arrest by removing the perturbation from the critical radius and disrupting resonant forcing. With increasing Re, the evolving vorticity patterns become more chaotic, more turbulent-like (finer scaled, contorted vorticity), and persist longer. This suggests that at typical Re (~106), nonlinear transient growth may indeed be able to break up, hence induce rapid decay of, column vortices – highly relevant for addressing the aircraft wake hazard crisis and the looming air traffic capacity crisis. In addition, we discover a regenerative transient growth scenario in which threads induce secondary perturbations closer to the vortex column. A parent–offspring regenerative mechanism is postulated and verified by DNS. There is a clear trend towards stronger regenerative growth with increasing Re. These results, showing an important role of transient growth in turbulent vortex decay, are highly relevant to the prediction and control of vortex-dominated flows.

Disturbing vortices

2001 ◽  
Vol 426 ◽  
pp. 95-133 ◽  
Author(s):  
N. J. BALMFORTH ◽  
STEFAN G. LLEWELLYN SMITH ◽  
W. R. YOUNG
Keyword(s):  
Critical Radius ◽  
Nonlinear Effects ◽  
Rotation Frequency ◽  
Finite Amplitude ◽  
Matched Asymptotic Expansion ◽  
Critical Amplitude ◽  
Subsequent Evolution ◽  
Weakly Nonlinear ◽  
Vorticity Distribution ◽  
The Core

Inviscid spatially compact vortices (such as the Rankine vortex) have discrete Kelvin modes. For these modes, the critical radius, at which the rotation frequency of the wave matches the angular velocity of the fluid, lies outside the vortex core. When such a vortex is not perfectly compact, but has a weak vorticity distribution beyond the core, these Kelvin disturbances are singular at the critical radius and become ‘quasi-modes’. These are not true eigenmodes but have streamfunction perturbations that decay exponentially with time while the associated vorticity wraps up into a tight spiral without decay. We use a matched asymptotic expansion to derive a simplified description of weakly nonlinear, externally forced quasi-modes.We consider the excitation and subsequent evolution of finite-amplitude quasi- modes excited with azimuthal wavenumber 2. Provided the forcing amplitude is below a certain critical amplitude, the quasi-mode decays and the disturbed vortex returns to axisymmetry. If the amplitude of the forcing is above critical, then nonlinear effects arrest the decay and cat's eye patterns form. Thus the vortex is permanently deformed into a tripolar structure.

Strong echo effect and nonlinear transient growth in shear flows

1998 ◽  
Vol 10 (6) ◽  
pp. 1398-1404 ◽  
Author(s):  
J. Vanneste ◽  
P. J. Morrison ◽  
T. Warn
Keyword(s):  
Shear Flows ◽  
Transient Growth ◽  
Nonlinear Transient ◽  
Echo Effect

scholarly journals Optimal transient growth on a vortex ring and its transition via cascade of ringlets

2017 ◽  
Vol 832 ◽  
pp. 269-286 ◽  
Author(s):  
X. Mao ◽  
F. Hussain
Keyword(s):  
Vortex Ring ◽  
Random Disturbance ◽  
Transient Growth ◽  
Time Intervals ◽  
Main Ring ◽  
Dynamics And Control ◽  
Ring Structures ◽  
Nonlinear Transient ◽  
Short Time ◽  
And Control

Linear and nonlinear transient growths of perturbations on a vortex ring up to Reynolds number ($\equiv$ circulation/viscosity) $Re=27\,000$ are studied. For short time intervals, perturbations around the ring axis undergo the strongest linear transient growth and lead to secondary structures in the form of ringlets, owing to the Orr mechanism and an inviscid vorticity-amplification mechanism: in contrast to the well-reported instabilities and lobe structures along the vortex ring core. These secondary ringlet structures induce a tertiary group of ringlets through similar transient perturbation growth. This cascade of ringlets lead to the breakup of the main ring even before activation of the vortex-core instabilities. Such a cascade scenario is also observed in the development of a vortex ring perturbed by random disturbance in the axis region. These new modes and mechanisms for the generation and breakup of vortex ring structures bring insights into the dynamics and control of vortex ring flows.

What face familiarity feelings say about the lateralization of specific entities within the core system

2019 ◽  
Vol 42 ◽  
Author(s):  
Guido Gainotti
Keyword(s):  
Temporal Lobe ◽  
Memory System ◽  
Core System ◽  
The Core ◽  
Memory Traces ◽  
Specific Memory ◽  
Target Article ◽  
Temporal Structures ◽  
The Right

Abstract The target article carefully describes the memory system, centered on the temporal lobe that builds specific memory traces. It does not, however, mention the laterality effects that exist within this system. This commentary briefly surveys evidence showing that clear asymmetries exist within the temporal lobe structures subserving the core system and that the right temporal structures mainly underpin face familiarity feelings.

A scanning electron microscopic study on dissolving process of cholesterol gallstones by chenodeoxycholic acid (CDCA)

1978 ◽  
Vol 36 (2) ◽  
pp. 522-523
Author(s):  
T. Kanetaka ◽  
M. Cho ◽  
S. Kawamura ◽  
T. Sado ◽  
K. Hara
Keyword(s):  
Electron Microscope ◽  
Chenodeoxycholic Acid ◽  
Outer Surface ◽  
Electron Microscopic ◽  
Cholesterol Gallstones ◽  
The Core ◽  
Scanning Electron Microscopic Study ◽  
Scanning Electron Microscopic ◽  
Acceleration Voltage ◽  
Scanning Electron

The authors have investigated the dissolution process of human cholesterol gallstones using a scanning electron microscope(SEM). This study was carried out by comparing control gallstones incubated in beagle bile with gallstones obtained from patients who were treated with chenodeoxycholic acid(CDCA).The cholesterol gallstones for this study were obtained from 14 patients. Three control patients were treated without CDCA and eleven patients were treated with CDCA 300-600 mg/day for periods ranging from four to twenty five months. It was confirmed through chemical analysis that these gallstones contained more than 80% cholesterol in both the outer surface and the core.The specimen were obtained from the outer surface and the core of the gallstones. Each specimen was attached to alminum sheet and coated with carbon to 100Å thickness. The SEM observation was made by Hitachi S-550 with 20 kV acceleration voltage and with 60-20, 000X magnification.

The Structure and Development of Microbodies in the Fat Body and other Tissues of an Insect (Calpodes Ethlius)

1970 ◽  
Vol 28 ◽  
pp. 148-149
Author(s):  
M. Locke ◽  
J. T. McMahon
Keyword(s):  
Electron Microscopy ◽  
Liquid Crystals ◽  
Fat Body ◽  
Competitive Inhibitor ◽  
Dense Core ◽  
Urate Oxidase ◽  
Blood Proteins ◽  
Free Base ◽  
The Core ◽  
The Matrix

The fat body of insects has always been compared functionally to the liver of vertebrates. Both synthesize and store glycogen and lipid and are concerned with the formation of blood proteins. The comparison becomes even more apt with the discovery of microbodies and the localization of urate oxidase and catalase in insect fat body.The microbodies are oval to spherical bodies about 1μ across with a depression and dense core on one side. The core is made of coiled tubules together with dense material close to the depressed membrane. The tubules may appear loose or densely packed but always intertwined like liquid crystals, never straight as in solid crystals (Fig. 1). When fat body is reacted with diaminobenzidine free base and H2O2 at pH 9.0 to determine the distribution of catalase, electron microscopy shows the enzyme in the matrix of the microbodies (Fig. 2). The reaction is abolished by 3-amino-1, 2, 4-triazole, a competitive inhibitor of catalase. The fat body is the only tissue which consistantly reacts positively for urate oxidase. The reaction product is sharply localized in granules of about the same size and distribution as the microbodies. The reaction is inhibited by 2, 6, 8-trichloropurine, a competitive inhibitor of urate oxidase.

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