scholarly journals The conjugate locus for the Euler top I. The axisymmetric case

2007 ◽  
Vol 2 ◽  
pp. 2109-2139 ◽  
Author(s):  
L. Bates ◽  
F. Fasso
Keyword(s):  
Axisymmetric Case ◽  
Conjugate Locus ◽  
Euler Top

Nonholonomic deformation of coupled and supersymmetric KdV equations and Euler–Poincaré–Suslov method

2015 ◽  
Vol 27 (04) ◽  
pp. 1550011 ◽  
Author(s):  
Partha Guha
Keyword(s):  
Kdv Equation ◽  
Infinite Dimensional ◽  
Kdv Equations ◽  
Finite Dimensional ◽  
Euler Top ◽  
Two Component ◽  
Finite Dimensional Case ◽  
Coupled Kdv Equations ◽  
The Right ◽  
Supersymmetric Kdv Equation

Recently, Kupershmidt [38] presented a Lie algebraic derivation of a new sixth-order wave equation, which was proposed by Karasu-Kalkani et al. [31]. In this paper, we demonstrate that Kupershmidt's method can be interpreted as an infinite-dimensional analogue of the Euler–Poincaré–Suslov (EPS) formulation. In a finite-dimensional case, we modify Kupershmidt's deformation of the Euler top equation to obtain the standard EPS construction on SO(3). We extend Kupershmidt's infinite-dimensional construction to construct a nonholonomic deformation of a wide class of coupled KdV equations, where all these equations follow from the Euler–Poincaré–Suslov flows of the right invariant L2 metric on the semidirect product group [Formula: see text], where Diff (S1) is the group of orientation preserving diffeomorphisms on a circle. We generalize our construction to the two-component Camassa–Holm equation. We also give a derivation of a nonholonomic deformation of the N = 1 supersymmetric KdV equation, dubbed as sKdV6 equation and this method can be interpreted as an infinite-dimensional supersymmetric analogue of the Euler–Poincaré–Suslov (EPS) method.

Manifolds With Restricted Conjugate Locus: II

1964 ◽  
Vol 80 (2) ◽  
pp. 330 ◽  
Author(s):  
Wilhelm Klingenberg
Keyword(s):  
Conjugate Locus

A Comparison Between Experimental and Predicted Flow Profiles Beneath a Semi-Confined Axisymmetric Impinging Jet

2003 ◽  
Author(s):  
C. Y. Cheong ◽  
P. T. Ireland ◽  
S. Ashforth-Frost
Keyword(s):  
Viscous Flow ◽  
Flow Model ◽  
Three Dimensional ◽  
Impinging Jet ◽  
Theoretical Models ◽  
Velocity Profiles ◽  
Axisymmetric Case ◽  
Air Jet ◽  
Wall Flow ◽  
Near Wall

Theoretical predictions have been compared with experiment for a single semi-confined impinging jet. The turbulent air jet discharged at Re = 20 000 and impinged at nozzle-to-plate spacings (z/d) of 2 and 6.5. Experimental velocity profiles were obtained using hot-wire anemometry. Theoretical velocity profiles were derived using stagnation three-dimensional flow model and viscous flow model for an axisymmetric case. For z/d = 2, velocity profiles in the inviscid region of the near wall flow can be predicted accurately using the stagnation flow model. As the edge of the jet is approached, the flow becomes complex and, as expected, cannot be predicted using the model. Prediction of boundary layer profiles using the viscous flow solution for an axisymmetric case is also reasonable. For z/d = 6.5, the developing impinging jet is essentially turbulent on impact and consequently predictions of near wall flow field, using both the theoretical models, are inappropriate.

Integrability of the discretization of the controlled Euler Top

2010 ◽  
Vol 215 (12) ◽  
pp. 4185-4190
Author(s):  
Supriya Mukherjee ◽  
Sourav Dutta
Keyword(s):  
Euler Top

Self-Sustained Oscillations of High Speed Impinging Planar Jets

2010 ◽  
Author(s):  
David Arthurs ◽  
Samir Ziada
Keyword(s):  
Shear Layer ◽  
High Speed ◽  
Large Scale ◽  
Impinging Jets ◽  
Free Shear Layer ◽  
Planar Case ◽  
Axisymmetric Case ◽  
Choked Flow ◽  
Tone Generation ◽  
Flow Velocities

High speed impinging jets are frequently used in a variety of industrial applications including thermal and coating control processes. These flows are liable to the production of very intense narrow band acoustic tones, which are produced by a feedback mechanism between instabilities in the jet free shear layer which roll up to form large scale coherent structures, and pressure fluctuations produced by the impingement of these structures at the impingement surface. This paper examines tone generation of a high speed planar gas jet impinging normally on a flat, rigid surface. Experiments are performed over the complete range of subsonic and transonic jet flow velocities for which tones are generated, from U0 = 150m/s (M≈0.4) to choked flow (U0 = 343m/s, M = 1), and over the complete range of impingement distance for which tones occur. The effect of varying the jet thickness is also examined. The behavior of the planar impinging jet case is compared to that of the axisymmetric case, and found to be significantly different, with tones being excited at larger impingement distances, and at lower flow velocities. The Strouhal numbers associated with tone generation in the planar case are on average an order of magnitude lower than that of the axisymmetric case when using similar velocity and length scales. The frequency behavior of the resulting tones is predicted using a simple feedback model, which allows the identification of the various shear layer modes of the instabilities driving tone generation. Finally, a thorough dimensionless analysis is performed in order to quantify the system behavior in terms of the appropriate scales.

Sign in / Sign up

Export Citation Format

Share Document