Uncoupled Wave Systems and Dispersion in an Infinite Solid Cylinder

1989 ◽  
Vol 56 (2) ◽  
pp. 347-355 ◽  
Author(s):  
Yoon Young Kim
Keyword(s):  
Cylindrical Surface ◽  
Wave Motion ◽  
Fourier Number ◽  
Large Wave ◽  
Surface Conditions ◽  
Asymptotic Nature ◽  
Wave Numbers ◽  
Complex Wave ◽  
Insight Into ◽  
Free Cylindrical Surface

In this study, it is shown that there exist uncoupled wave systems for general non-axisymmetric wave propagation in an infinite isotropic cylinder. Two cylindrical surface conditions corresponding to the uncoupled wave systems are discussed. The solutions of the uncoupled wave systems are shown to provide proper bounds of Pochhammer’s equation for a free cylindrical surface. The bounds, which are easy to construct for any Fourier number in the circumferential direction, can be used to trace the branches of Pochhammer’s equation. They also give insight into the modal composition of the branches of Pochhammer’s equation at and between the intersections of the bounds. More refined dispersion relations of Pochhammer’s equation are possible through an asymptotic analysis of the itersections of the branches of Pochhammer’s equation with one family of the bounds. The asymptotic nature of wave motion corresponding to large wave numbers, imaginary or complex, for Pochhammer’s equation is studied. The wave motion is asymptotically equivoluminal for large imaginary wave numbers, and is characterized by coupled dilatation and shear for large complex wave numbers.

scholarly journals COMPLEX WAVE NUMBERS IN THE VICINITY OF THE SCHWARZSCHILD EVENT HORIZON

2008 ◽  
Vol 23 (09) ◽  
pp. 1417-1433 ◽  
Author(s):  
M. SHARIF ◽  
UMBER SHEIKH
Keyword(s):  
Event Horizon ◽  
Plasma Wave ◽  
Cold Plasma ◽  
Dispersion Relations ◽  
Wave Numbers ◽  
Complex Wave ◽  
And Behavior ◽  
Wave Properties

This paper is devoted to investigate the cold plasma wave properties outside the event horizon of the Schwarzschild planar analogue. The dispersion relations are obtained from the corresponding Fourier analyzed equations for nonrotating and rotating, nonmagnetized and magnetized backgrounds. These dispersion relations provide complex wave numbers. The wave numbers are shown in graphs to discuss the nature and behavior of waves and the properties of plasma lying in the vicinity of the Schwarzschild event horizon.

STUDIES OF THE ENERGY SPECTRUM AND THE WAVE FUNCTION FOR LOW ENERGY EXCITED STATES IN LIQUID HELIUM II

2007 ◽  
Vol 21 (21) ◽  
pp. 1383-1390
Author(s):  
DE-HUA LIN ◽  
PING ZOU ◽  
ZHONG-WEI ZHANG ◽  
HONG-LEI WANG ◽  
JUN PAN ◽  
...  
Keyword(s):  
Experimental Data ◽  
Wave Function ◽  
Energy Spectrum ◽  
Liquid Helium ◽  
Excited States ◽  
Low Energy ◽  
Large Wave ◽  
Helium Ii ◽  
Wave Numbers ◽  
Specific Temperature

In this paper, we study the elementary excitations and energy spectrum proposed by L. D. Landau in liquid helium II. On the basis of the energy spectrum for the phonons and rotons, we put forward a uniform expression of energy spectrum in liquid helium II, which is limited in a specific temperature range. By using the wave function for low energy excited states proposed by R. P. Feynman or the modified one proposed by Feynman and Cohen, it can be found that the estimated energy spectrum is quite different from the experimental data, especially for the region with large wave numbers. By proposing an improved form for the wave function, we re-analyze the energy spectrum in liquid helium II, and our results show a better agreement with the experimental data.

scholarly journals Enstrophy Cascade and Smagorinsky Model of 2D Turbulent Flows

2001 ◽  
Vol 17 (3) ◽  
pp. 121-129
Author(s):  
Mei-Jiau Huang
Keyword(s):  
Reynolds Number ◽  
Large Eddy Simulation ◽  
Turbulent Flows ◽  
Smagorinsky Model ◽  
Large Wave ◽  
Eddy Simulation ◽  
Large Eddy ◽  
Wave Numbers ◽  
Enstrophy Cascade ◽  
Stretching Effect

ABSTRACTDirect numerical simulations of 2D turbulent flows, freely decaying as well as forced, are performed to examine the mechanism of the enstrophy cascade and serve as a template of developing LES models. The stretching effect on the 2D vorticity gradients is emphasized on the analogy of the stretching effect on 3D vorticity. The enstrophy cascade rate, the Reynolds stresses and the associated eddy viscosity for 2D turbulence are correspondingly derived and investigated. Proposed herein is that the enstrophy cascade rate to be modeled in a large-eddy simulation can be and should be calculated using the only available large-eddy information, especially when the Reynolds number is not very large or when the flow is not stationary.The simulation results suggest all Kolmogorov's, Kraichnan's, and Saffman's similarity spectra. The Kolmogorov's spectrum appears in front of forced wave numbers and creates a subrange of a zero enstrophy cascade rate and a constant energy cascade rate. The Saffman's spectrum is the dissipation spectrum at large wave numbers. Kraichnan's spectrum shows up at intermediate wave numbers when the Reynolds number is sufficiently high. When the Smagorinsky model is employed for a large eddy simulation, its inability of capturing the significant reverse cascade phenomenon as observed in the DNS data becomes a fatal defect. Nonetheless, if only the mean cascade rate is concerned, the required Smagorinsky constant is evaluated using the DNS data and compared with the theoretical prediction of the Kraichnan's spectrum.

Wave Propagation and Instability in a Circular Semi-Infinite Liquid Jet Harmonically Forced at the Nozzle

1978 ◽  
Vol 45 (3) ◽  
pp. 469-474 ◽  
Author(s):  
D. B. Bogy
Keyword(s):  
Wave Propagation ◽  
Radiation Condition ◽  
Liquid Jet ◽  
Propagation Characteristics ◽  
Frequency Spectra ◽  
One Dimensional ◽  
Wave Numbers ◽  
Complex Wave ◽  
The Stability ◽  
The Waves

The linearized form of the inviscid, one-dimensional Cosserat jet equations derived by Green [6] are used to study wave propagation in a circular jet with surface tension. The frequency spectra are shown for complex wave numbers for a complete range of Weber numbers. The propagation characteristics of the waves are studied in order to determine which branches of the frequency spectra to use in the semi-infinite jet problem with harmonic forcing at the nozzle. Two of the four branches are eliminated by a radiation condition that energy must be outgoing at infinity; the remaining two branches are used to satisfy the nozzle boundary conditions. The variation of the jet radius along its length is shown graphically for various Weber numbers and forcing frequencies. The stability or instability is explained in terms of the behavior of the two propagating phases.

Stability of fibers near a free cylindrical surface

1988 ◽  
Vol 24 (10) ◽  
pp. 939-944 ◽  
Author(s):  
A. N. Guz' ◽  
Yu. N. Lapusta
Keyword(s):  
Cylindrical Surface ◽  
Free Cylindrical Surface

Forced Wave Motion of Liquid Partially Filling a High-Speed Rotor

1985 ◽  
Vol 107 (4) ◽  
pp. 446-452
Author(s):  
J. Inoue ◽  
Y. Jinnouchi ◽  
Y. Araki
Keyword(s):  
High Speed ◽  
Wave Motion ◽  
Equations Of Motion ◽  
Governing Equations ◽  
Rotor Vibration ◽  
Liquid Motion ◽  
Large Wave ◽  
Main Emphasis ◽  
Two Dimensional Flow ◽  
Theoretical Results

Wave motion of a liquid in a partially filled hollow cylindrical rotor, which rotates at a high speed and is forced to vibrate, is theoretically and experimentally investigated. Main emphasis is placed on the analysis of a large wave motion in the liquid which may cause self-excited vibrations of the rotor. Assuming a thin liquid layer, simplified equations of motion are derived by integration of the governing equations for a two-dimensional flow. Nonlinearity and viscosity are taken into account in the analysis. A large wave motion with a broken wavecrest is analyzed by applying a theory of hydraulic jump. Illustrating typical examples of the theoretical results together with the experimental ones, the dynamic behavior of the liquid motion and the basic relations between the liquid force and the rotor vibration are discussed.

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