Short-wavelength stability analysis of a helical vortex tube

2009 ◽  
Vol 21 (1) ◽  
pp. 014104 ◽  
Author(s):  
Y. Hattori ◽  
Y. Fukumoto
Keyword(s):  
Stability Analysis ◽  
Short Wavelength ◽  
Vortex Tube ◽  
Helical Vortex

Modal stability analysis of a helical vortex tube with axial flow

2013 ◽  
Vol 738 ◽  
pp. 222-249 ◽  
Author(s):  
Yuji Hattori ◽  
Yasuhide Fukumoto
Keyword(s):  
Boundary Condition ◽  
Growth Rate ◽  
Stability Analysis ◽  
Vortex Tube ◽  
Axial Flow ◽  
Short Wave ◽  
Combined Effects ◽  
Leading Order ◽  
Helical Vortex ◽  
Wave Limit

AbstractThe linear stability of a helical vortex tube with axial flow, which is a model of helical vortices emanating from rotating wings, is studied by modal stability analysis. At the leading order the base flow is set to the Rankine vortex with uniform velocity along the helical tube whose centreline is a helix of constant curvature and torsion. The helical vortex tube in an infinite domain, in which the free boundary condition is imposed at the surface of the tube, is our major target although the case of the rigid boundary condition is also considered in order to elucidate the effects of torsion and the combined effects of torsion and axial flow. The analysis is based on the linearized incompressible Euler equations expanded in $\epsilon $ which is the ratio of the core to curvature radius of the tube. The unstable growth rate can be evaluated using the leading-order neutral modes called the Kelvin waves with the expanded equations. At $O(\epsilon )$ the instability is a linear combination of the curvature instability due to the curvature of the tube and the precessional instability due to the axial flow, both parametric instabilities appearing at the same resonance condition. At the next order $O({\epsilon }^{2} )$ not only the effects of torsion but also the combined effects of torsion and axial flow appear, a fact which has been shown only for the short-wave limit. The maximum growth rate increases for the right-handed/left-handed helix with positive/negative helicity, in which the torsion makes the period of particle motion increase. All results converge to the previous local stability results in the short-wave limit. The differences between the two cases of different boundary conditions are due to the isolated mode of the free boundary case, whose dispersion curve depends strongly on the axial flow.

scholarly journals Kelvin waves on helical vortex tube in swirling flow

2018 ◽  
Vol 980 ◽  
pp. 012003
Author(s):  
M A Tsoy ◽  
S G Skripkin ◽  
P A Kuibin ◽  
S I Shtork ◽  
S V Alekseenko
Keyword(s):  
Vortex Tube ◽  
Swirling Flow ◽  
Kelvin Waves ◽  
Helical Vortex

scholarly journals The velocity field induced by a helical vortex tube

2005 ◽  
Vol 17 (10) ◽  
pp. 107101 ◽  
Author(s):  
Y. Fukumoto ◽  
V. L. Okulov
Keyword(s):  
Velocity Field ◽  
Vortex Tube ◽  
Helical Vortex

Short-wavelength stability analysis of thin vortex rings

2003 ◽  
Vol 15 (10) ◽  
pp. 3151 ◽  
Author(s):  
Y. Hattori ◽  
Y. Fukumoto
Keyword(s):  
Stability Analysis ◽  
Short Wavelength ◽  
Vortex Rings

Effects of axial flow on the stability of a helical vortex tube

2012 ◽  
Vol 24 (5) ◽  
pp. 054102 ◽  
Author(s):  
Y. Hattori ◽  
Y. Fukumoto
Keyword(s):  
Vortex Tube ◽  
Axial Flow ◽  
Helical Vortex ◽  
The Stability

Short-wavelength stability analysis of Hill’s vortex with/without swirl

2010 ◽  
Vol 22 (7) ◽  
pp. 074104 ◽  
Author(s):  
Y. Hattori ◽  
K. Hijiya
Keyword(s):  
Stability Analysis ◽  
Short Wavelength

Evolution of localized disturbances in the elliptic instability

2014 ◽  
Vol 755 ◽  
pp. 603-627 ◽  
Author(s):  
Yuji Hattori ◽  
Mohd Syafiq bin Marzuki
Keyword(s):  
Growth Rate ◽  
Stability Analysis ◽  
Energy Spectrum ◽  
Short Wavelength ◽  
Isotropic Turbulence ◽  
Inertial Range ◽  
Mean Flow ◽  
Weakly Nonlinear ◽  
Elliptical Flow ◽  
The Mean

AbstractThe time evolution of localized disturbances in an elliptical flow confined in an elliptical cylinder is studied by direct numerical simulation (DNS). The base flow is subject to the elliptic instability. The unstable growth of localized disturbances predicted by the short-wavelength stability analysis is captured. The time evolution can be divided into four stages: linear, weakly nonlinear, nonlinear and turbulent. In the linear stage a single wavepacket grows exponentially without changing its shape. The exponential growth is accompanied by large oscillations which have time period half that of the fluid particles in the elliptical flow. An averaged wavepacket, which is a train of bending waves that has a finite spatial extent, also grows exponentially, while the oscillations of the growth rate are small. The averaged growth rate increases as the kinematic viscosity decreases; the inviscid limit is close to the value predicted by the short-wavelength stability analysis. In the weakly nonlinear stage the energy stops growing. The vortical structure of the initial disturbances is deformed into wavy patterns. The energy spectrum loses the peak at the initial wavenumber, developing a broad spectrum, and the flow goes into the next stage. In the nonlinear stage weak vorticity is scattered in the whole domain although strong vorticity is still localized. The probability density functions (p.d.f.) of a velocity component and its longitudinal derivative are similar to those of isotropic turbulence; however, the energy spectrum does not have an inertial range showing the Kolmogorov spectrum. Finally in the turbulent stage fine-scale structures appear in the vorticity field. The p.d.f. of the longitudinal derivative of velocity shows the strong intermittency known for isotropic turbulence. The energy spectrum attains an inertial range showing the Kolmogorov spectrum. The turbulence is not symmetric because of rotation and strain; the component of vorticity in the compressing direction is smaller than the other two components. The energy of the mean flow as well as the total energy decreases. The ratio of the lost energy to the initial energy of the mean flow is large in the core region.

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