Longitudinal Waves in a Submerged Cylindrical Rod 1

2010 ◽  
Vol 78 (2) ◽  
Author(s):  
G. Iosilevskii
Keyword(s):  
Boundary Layer ◽  
Wave Number ◽  
Analytical Relation ◽  
Velocity Of Sound ◽  
Longitudinal Displacement ◽  
Wave Propagation Velocity ◽  
Longitudinal Waves ◽  
Short Waves ◽  
The Waves ◽  
Surrounding Fluid

This study is concerned with longitudinal displacement waves propagating in an elastic cylindrical rod submerged in a viscous fluid. Provided that the wave propagation velocity in the rod is small compared with the velocity of sound in the surrounding fluid and the wavelength is large compared with the thickness of the boundary layer around the rod, an analytical relation is obtained between the wave number and the frequency. The presence of the fluid makes the waves disperse—the short waves become faster than the long ones.

‘Inactive’ motion and pressure fluctuations in turbulent boundary layers

1967 ◽  
Vol 30 (2) ◽  
pp. 241-258 ◽  
Author(s):  
P. Bradshaw
Keyword(s):  
Boundary Layer ◽  
Outer Layer ◽  
Pressure Fluctuations ◽  
Turbulent Energy ◽  
Viscous Sublayer ◽  
Wave Number ◽  
Noticeable Effect ◽  
Frequency Spectra ◽  
Active Motion ◽  
Order Of Magnitude

Townsend's (1961) hypothesis that the turbulent motion in the inner region of a boundary layer consists of (i) an ‘active’ part which produces the shear stress τ and whose statistical properties are universal functions of τ and y, and (ii) an ‘inactive’ and effectively irrotational part determined by the turbulence in the outer layer, is supported in the present paper by measurements of frequency spectra in a strongly retarded boundary layer, in which the ‘inactive’ motion is particularly intense. The only noticeable effect of the inactive motion is an increased dissipation of kinetic energy into heat in the viscous sublayer, supplied by turbulent energy diffusion from the outer layer towards the surface. The required diffusion is of the right order of magnitude to explain the non-universal values of the triple products measured near the surface, which can therefore be reconciled with universality of the ‘active’ motion.Dimensional analysis shows that the contribution of the ‘active’ inner layer motion to the one-dimensional wave-number spectrum of the surface pressure fluctuations varies as τ2w/k1 up to a wave-number inversely proportional to the thickness of the viscous sublayer. This result is strongly supported by the recent measurements of Hodgson (1967), made with a much smaller ratio of microphone diameter to boundary-layer thickness than has been achieved previously. The disagreement of the result with most other measurements is attributed to inadequate transducer resolution in the other experiments.

Experimental Investigation of Boundary Layer Instabilities on the Free Surface of Non-Turbulent Jet

2012 ◽  
Author(s):  
Matthieu A. Andre ◽  
Philippe M. Bardet
Keyword(s):  
Boundary Layer ◽  
Free Surface ◽  
High Speed ◽  
Particle Tracking Velocimetry ◽  
Capillary Waves ◽  
Wave Growth ◽  
Image Velocimetry ◽  
Planar Laser ◽  
Surface Visualization ◽  
The Waves

Shear instabilities induced by the relaxation of laminar boundary layer at the free surface of a high speed liquid jet are investigated experimentally. Physical insights into these instabilities and the resulting capillary wave growth are gained by performing non-intrusive measurements of flow structure in the direct vicinity of the surface. The experimental results are a combination of surface visualization, planar laser induced fluorescence (PLIF), particle image velocimetry (PIV), and particle tracking velocimetry (PTV). They suggest that 2D spanwise vortices in the shear layer play a major role in these instabilities by triggering 2D waves on the free surface as predicted by linear stability analysis. These vortices, however, are found to travel at a different speed than the capillary waves they initially created resulting in interference with the waves and wave growth. A new experimental facility was built; it consists of a 20.3 × 146.mm rectangular water wall jet with Reynolds number based on channel depth between 3.13 × 104 to 1.65 × 105 and 115. to 264. based on boundary layer momentum thickness.

scholarly journals Simultaneous Measurements of Temperature and Viscosity for Viscous Fluids Using an Ultrasonic Waveguide

Sensors ◽  
2021 ◽  
Vol 21 (16) ◽  
pp. 5543
Author(s):  
Jinrui Huang ◽  
Frederic Cegla ◽  
Andy Wickenden ◽  
Mike Coomber
Keyword(s):  
Viscous Liquid ◽  
Viscous Fluids ◽  
Fluid Temperature ◽  
Wave Propagation Velocity ◽  
Temperature Detector ◽  
Elastic Shear ◽  
Surrounding Fluid ◽  
Commercial Resistance ◽  
Measurement Repeatability ◽  
Better Than

The characterisation and monitoring of viscous fluids have many important applications. This paper reports a refined ‘dipstick’ method for ultrasonic measurement of the properties of viscous fluids. The presented method is based on the comparison of measurements of the ultrasonic properties of a waveguide that is immersed in a viscous liquid with the properties when it is immersed in a reference liquid. We can simultaneously determine the temperature and viscosity of a fluid based on the changes in the velocity and attenuation of the elastic shear waves in the waveguide. Attenuation is mainly dependent on the viscosity of the fluid that the waveguide is immersed in and the speed of the wave mainly depends on the surrounding fluid temperature. However, there is a small interdependency since the mass of the entrained viscous liquid adds to the inertia of the system and slows down the wave. The presented measurements have unprecedented precision so that the change due to the added viscous fluid mass becomes important and we propose a method to model such a ‘viscous effect’ on the wave propagation velocity. Furthermore, an algorithm to correct the velocity measurements is presented. With the proposed correction algorithm, the experimental results for kinematic viscosity and temperature show excellent agreement with measurements from a highly precise in-lab viscometer and a commercial resistance temperature detector (RTD) respectively. The measurement repeatability of the presented method is better than 2.0% in viscosity and 0.5% in temperature in the range from 8 to 300 cSt viscosity and 40 to 90 °C temperature.

VELOCITY OF SOUND IN CYLINDRICAL RODS

1931 ◽  
Vol 5 (6) ◽  
pp. 619-624 ◽  
Author(s):  
Geo. S. Field
Keyword(s):  
Velocity Of Sound ◽  
Low Frequencies ◽  
Longitudinal Waves ◽  
Experimental Knowledge ◽  
Close Analogy ◽  
Theory And Experiment

The experimental knowledge so far available of the velocity of longitudinal waves in cylindrical rods is reviewed, and it is shown that a close analogy most probably exists between waves in cylinders of liquid and in solid rods. The theory for rods due to Pochhammer is considered with reference to a specific case for which experimental velocities have been determined, and it is shown that the agreement at low frequencies is good. At higher frequencies, however, theory and experiment differ widely.

LONGITUDINAL WAVES IN AN INHOMOGENEOUS MAGNETIC FIELD – PLASMA INTERFACE BASED ON THE WKB APPROXIMATION

1963 ◽  
Vol 41 (4) ◽  
pp. 569-580
Author(s):  
I. P. Shkarofsky
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Ion Beam ◽  
Inhomogeneous Magnetic Field ◽  
Wave Number ◽  
Plasma Region ◽  
Order Solution ◽  
Uniform Medium ◽  
Magnetic Field Region ◽  
Point To Point

Longitudinal perturbations are investigated which propagate in an inhomogeneous interface or transition boundary layer, from a plasma region where no magnetic field exists well within its interior, to a static magnetic field region from which the plasma is excluded. The inhomogeneity in this boundary layer is the prime inhomogeneity considered here. A WKB solution is obtained for waves whose wavelength is small compared with the equilibrium characteristic length. The component of the propagation wave number is assumed to vary in the direction in which the interface is inhomogeneous. From the zero-order solution it is shown that this wave number satisfies the same relation with the frequency of perturbation and velocities of the electron and ion beams, as that obtained in counter-streaming of an electron-plus-ion beam against another electron-plus-ion beam in a uniform medium. The first-order solution yields the manner in which the amplitude of the wave varies from point to point in the plasma interface. The physical significance of these modes and the time and space variation of these waves will be discussed. It is shown that the WKB solution is valid in the sheath up to quite small distances from the sheath boundary. Under certain conditions, a wave can exist which increases exponentially in time and whose amplitude increases towards the boundary. The problem of joining the WKB solution appropriately to a perturbed solution outside of the boundary is discussed.

scholarly journals On a nonlinear state of the electromagnetic ion/ion cyclotron instability

2000 ◽  
Vol 7 (3/4) ◽  
pp. 173-177
Author(s):  
M. Cremer ◽  
M. Scholer
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Plasma Sheet ◽  
Large Temperature ◽  
Plasma Sheet Boundary Layer ◽  
Temperature Anisotropy ◽  
Nonlinear Properties ◽  
Cyclotron Instability ◽  
Ion Cyclotron ◽  
The Waves

Abstract. We have investigated the nonlinear properties of the electromagnetic ion/ion cyclotron instability (EMIIC) by means of hybrid simulations (macroparticle ions, massless electron fluid). The instability is driven by the relative (super-Alfvénic) streaming of two field-aligned ion beams in a low beta plasma (ion thermal pressure to magnetic field pressure) and may be of importance in the plasma sheet boundary layer. As shown in previously reported simulations the waves propagate obliquely to the magnetic field and heat the ions in the perpendicular direction as the relative beam velocity decreases. By running the simulation to large times it can be shown that the large temperature anisotropy leads to the ion cyclotron instability (IC) with parallel propagating Alfvén ion cyclotron waves. This is confirmed by numerically solving the electromagnetic dispersion relation. An application of this property to the plasma sheet boundary layer is discussed.

scholarly journals Stern waves with vorticity

2002 ◽  
Vol 43 (3) ◽  
pp. 321-332 ◽  
Author(s):  
Y. Kang ◽  
J.-M. Vanden-Broeck
Keyword(s):  
Integral Equation ◽  
Numerical Solutions ◽  
Free Surface Flow ◽  
Integral Equation Method ◽  
Surface Flow ◽  
Boundary Integral ◽  
Analytical Relation ◽  
Far Field ◽  
Two Dimensional ◽  
The Waves

AbstractSteady two-dimensional free surface flow past a semi-infinite flat plate is considered. The vorticity in the flow is assumed to be constant. For large values of the Froude number F, an analytical relation between F, the vorticity parameter ω and the steepness s of the waves in the far field is derived. In addition numerical solutions are calculated by a boundary integral equation method.

scholarly journals THB INFLUENCE OF WAVES OH CURRENT PROFILES

1986 ◽  
Vol 1 (20) ◽  
pp. 7 ◽  
Author(s):  
Felicity C. Coffey ◽  
Peter Nielsen
Keyword(s):  
Boundary Layer ◽  
Friction Velocity ◽  
Dimensionless Parameter ◽  
Velocity Amplitude ◽  
Steady Current ◽  
Vertical Scale ◽  
Flow Components ◽  
Current Reduction ◽  
Wave Boundary ◽  
The Waves

A simple model is presented for steady current profiles in the presence of waves. The current reduction and apparent roughness increase caused by the waves are shown to depend mainly on one dimensionless parameter u*/u"*, i.e. the ratio between the friction velocity amplitude due to the waves and the time averaged friction velocity. The model recognises the need to apply different eddy viscosities to different flow components. Also, the thickness of the wave influenced layer near the bed is comceptually separated from the vertical scale of the wave boundary layer.

scholarly journals An asymptotic investigation of the stationary modes of instability of the boundary layer on a rotating disc

1986 ◽  
Vol 406 (1830) ◽  
pp. 93-106 ◽  
Keyword(s):  
Boundary Layer ◽  
Nonlinear Problems ◽  
Wave Number ◽  
Viscous Effects ◽  
Rotating Disc ◽  
Expansion Procedure ◽  
Asymptotic Investigation ◽  
Starting Point ◽  
Consistent Manner ◽  
High Reynolds

The paper investigates high-Reynolds-number stationary instabilities in the boundary layer on a rotating disc. The investigation demonstrates that, in addition to the inviscid mode found by Gregory, Stuart & Walker ( Phil. Trans. R. Soc. Lond. A 248, 155 (1955)) at high Reynolds numbers, there is a stationary short-wavelength mode. This mode has its structure fixed by a balance between viscous and Coriolis forces and cannot be described by an inviscid theory. The asymptotic structure of the wave-number and orientation of this mode is obtained, and a similar analysis is given for the inviscid mode. The expansion procedure provides the capacity of taking non-parallel effects into account in a self-consistent manner. The inviscid solution of Gregory et al . is modified to take account of viscous effects. The expansion procedure used is again capable of taking non-parallel effects into account. The results obtained suggest why the inviscid approach of Gregory et al . should give a good approximation to the experimentally measured orientation of the vortices. The results also explain partly why the inviscid analysis should not give such a good approximation to the wavenumber of the vortices. The asymptotic analysis of both modes provides a starting point for the corresponding nonlinear problems.

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