Weakly nonlinear saturation of short-wave instabilities in a strained Lamb–Oseen vortex

2000 ◽  
Vol 12 (7) ◽  
pp. 1715-1729 ◽  
Author(s):  
Denis Sipp
Keyword(s):  
Short Wave ◽  
Nonlinear Saturation ◽  
Weakly Nonlinear ◽  
Wave Instabilities ◽  
Oseen Vortex

scholarly journals Short-wave instabilities on a vortex pair of unequal strength circulation ratio

2011 ◽  
Vol 35 (4) ◽  
pp. 1581-1590 ◽  
Author(s):  
Joine So ◽  
Kris Ryan ◽  
Gregory J. Sheard
Keyword(s):  
Vortex Pair ◽  
Short Wave ◽  
Circulation Ratio ◽  
Wave Instabilities

Flow/Acoustic Mechanisms in Three-Dimensional Vortices Undergoing Sinusoidal-Wave Instabilities

2007 ◽  
Author(s):  
Wenhua Li ◽  
Z. C. Zheng ◽  
Ying Xu
Keyword(s):  
Flow Field ◽  
Three Dimensional ◽  
Vortex Pair ◽  
Particle Method ◽  
Acoustic Signals ◽  
Short Wave ◽  
Vortical Flow ◽  
Vortex Particle Method ◽  
Structure Changes ◽  
Wave Instabilities

It has been identified that vorticity in a vortex core directly relates to the frequency of a significant sound peak from an aircraft wake vortex pair where each of the vortices is modeled as an elliptic core Kirchhoff vortex. In three-dimensional vortices, sinusoidal instabilities at various length scales result in significant flow structure changes in these vortices, and thus influence their radiated acoustic signals. In this study, a three-dimensional vortex particle method is used to simulate the incompressible vortical flow. The flow field, in the form of vorticity, is employed as the source in the far-field acoustic calculation using a vortex sound formula that enables computation of acoustic signals radiated from an approximated incompressible flow field. Cases of vortex rings and a pair of counter-rotating vortices are studied when they are undergoing both long- and short-wave instabilities. Both inviscid and viscous interactions are considered and effects of turbulence are simulated using sub-grid-scale models.

scholarly journals Long- and short-wave instabilities in helical vortices

2014 ◽  
Vol 524 ◽  
pp. 012154 ◽  
Author(s):  
T Leweke ◽  
H U Quaranta ◽  
H Bolnot ◽  
F J Blanco-Rodríguez ◽  
S Le Dizès
Keyword(s):  
Short Wave ◽  
Helical Vortices ◽  
Wave Instabilities

A Visual Study of Vortex Instabilities in the Wake of a Rotor in Hover

2012 ◽  
Vol 57 (4) ◽  
pp. 1-8 ◽  
Author(s):  
Christopher V. Ohanian ◽  
Gregory J. McCauley ◽  
Ömer Savaş
Keyword(s):  
Growth Rate ◽  
Exponential Growth ◽  
Linear Growth ◽  
Short Wave ◽  
Linear Growth Rate ◽  
Water Tank ◽  
Vortex Filaments ◽  
Visual Study ◽  
Helical Vortex ◽  
Wave Instabilities

A visual study of the instability characteristics of the helical vortex filaments trailing from the tips of a three-bladed lifting rotor in a water tank is presented. The rotor diameter was 25.4 cm, and its rotation rate ranged from 4 to 12 revolutions per second. Soon after their formation, the vortex filaments developed long- and short-wave instabilities. In the long-wave instability mode, two of the three vortices coming off the rotor orbited around each other and merged in about 0.4 of the theoretical orbit time of equistrength two-dimensional vortices, after which the third vortex joined the merger to form a single, apparently turbulent helical vortex filament. The wavelengths of the short-wave instabilities were about 0.4 of the wake radius, about 17 cycles over the circumference. The short waves exhibited a linear growth rate during the first half of their orbital motion and an exponential growth prior to merging. The linear growth rate was about 0.0034 D/rad. The e-folding time for the exponential growth rate was about 0.52 rad.

Direct simulation of unsteady axisymmetric core–annular flow with high viscosity ratio

1999 ◽  
Vol 391 ◽  
pp. 123-149 ◽  
Author(s):  
JIE LI ◽  
YURIKO RENARDY
Keyword(s):  
Annular Flow ◽  
Travelling Waves ◽  
High Viscosity ◽  
Time Dependent ◽  
Nonlinear Saturation ◽  
Weakly Nonlinear ◽  
Pressure Fields ◽  
Linearized Stability ◽  
Spatially Periodic ◽  
Extremal Values

Axisymmetric pipeline transportation of oil and water is simulated numerically as an initial value problem. The simulations succeed in predicting the spatially periodic Stokes-like waves called bamboo waves, which have been documented in experiments of Bai, Chen & Joseph (1992) for up-flow. The numerical scheme is validated against linearized stability theory for perfect core–annular flow, and weakly nonlinear saturation to travelling waves. Far from onset conditions, the fully nonlinear saturation to steady bamboo waves is achieved. As the speed is increased, the bamboo waves shorten, and peaks become more pointed. A new time-dependent bamboo wave is discovered, in which the interfacial waveform is steady, but the accompanying velocity and pressure fields are time-dependent. The appearance of vortices and the locations of the extremal values of pressure are investigated for both up- and down-flows.

Nonlinear dynamics of vorticity waves in the coastal zone

1996 ◽  
Vol 326 ◽  
pp. 181-203 ◽  
Author(s):  
Victor I. Shrira ◽  
Vyacheslav V. Voronovich
Keyword(s):  
Evolution Equation ◽  
Potential Vorticity ◽  
Large Scale ◽  
Evolution Equations ◽  
Short Wave ◽  
Nonlinear Evolution Equations ◽  
Principal Mechanism ◽  
Weakly Nonlinear ◽  
The Mean ◽  
Wave Limit

Vorticity waves are wave-like motions occurring in various types of shear flows. We study the dynamics of these motions in alongshore shear currents in situations where it can be described within weakly nonlinear asymptotic theory. The principal mechanism of vorticity waves can be interpreted as potential vorticity conservation with the background vorticity gradient provided both by the mean current shear and the variation of depth. Under the assumption that the mean potential vorticity distibution is monotonic in the cross-shore direction, the nonlinear stage of the dynamics of weakly nonlinear vorticity waves, long in comparison with the current cross-shore scale, is found to be governed by an evolution equation of the generalized Benjamin–Ono type. The dispersive terms are given by an integro-differential operator with the kernel determined by the large-scale cross-shore depth and current dependence. The derived equations form a wide new class of nonlinear evolution equations. They all tend to the Benjamin–Ono equation in the short-wave limit, while in the long-wave limit their asymptotics depend on the specific form of the depth and current profiles. For a particular family of model bottom profiles the equations are ‘intermediate’ between Benjamin–Ono and Korteweg–de Vries equations, but are distinct from the Joseph intermediate equation. Solitary-wave solutions to the equations for these depth profiles are found to decay exponentially. Taking into account coastline inhomogeneity or/and alongshore depth variations adds a linear forcing term to the evolution equation, thus providing an effective generation mechanism for vorticity waves.

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