scholarly journals Acoustic–vorticity coupling in linearly varying shear flows using the WKB method

2013 ◽  
Vol 469 (2153) ◽  
pp. 20120708 ◽  
Author(s):  
Gael Favraud ◽  
Vincent Pagneux
Keyword(s):  
Acoustic Mode ◽  
Rigid Rotation ◽  
Wkb Method ◽  
Plane Couette Flow ◽  
First Order ◽  
Acoustic Modes ◽  
Hyperbolic Flow ◽  
Linear Flows ◽  
Flow Plane ◽  
Typical Frequency

The evolution of acoustic and vorticity perturbations in a two-dimensional incompressible linear flow is investigated. A weighted decomposition of the flow into a hyperbolic part and a rotation part allows continuous spanning of all linear flows such as hyperbolic flow, plane Couette flow and rigid rotation for instance. Using the Kelvin non-modal approach, the equations governing the time evolution of plane wave perturbations are reduced into a system of three first-order ordinary differential equations. This system is analysed using a WKB method where the small parameter ε is the ratio of the shear rate of the flow over the typical frequency of the perturbations. With this method, a basis of three modes naturally appears: two acoustic modes and one vorticity mode. At finite but small ε , couplings between the modes appear when the length of the wavenumber is minimal. For hyperbolic flow, incident vorticity mode generates the two acoustic modes, and an incident acoustic mode generates the other acoustic mode. More generally, for all flows, the hyperbolic part of the flow is responsible of the coupling between acoustic and vorticity modes, but also of the coupling between the two acoustic modes. These phenomena are illustrated by displaying wavepacket evolutions.

scholarly journals Patterns in Wall-Bounded Shear Flows

2020 ◽  
Vol 52 (1) ◽  
pp. 343-367 ◽  
Author(s):  
Laurette S. Tuckerman ◽  
Matthew Chantry ◽  
Dwight Barkley
Keyword(s):  
Numerical Simulations ◽  
Couette Flow ◽  
Poiseuille Flow ◽  
Pipe Flow ◽  
Shear Flows ◽  
Plane Couette Flow ◽  
Plane Poiseuille Flow ◽  
Flow Focusing ◽  
Annular Pipe ◽  
Flow Plane

Experiments and numerical simulations have shown that turbulence in transitional wall-bounded shear flows frequently takes the form of long oblique bands if the domains are sufficiently large to accommodate them. These turbulent bands have been observed in plane Couette flow, plane Poiseuille flow, counter-rotating Taylor–Couette flow, torsional Couette flow, and annular pipe flow. At their upper Reynolds number threshold, laminar regions carve out gaps in otherwise uniform turbulence, ultimately forming regular turbulent–laminar patterns with a large spatial wavelength. At the lower threshold, isolated turbulent bands sparsely populate otherwise laminar domains, and complete laminarization takes place via their disappearance. We review results for plane Couette flow, plane Poiseuille flow, and free-slip Waleffe flow, focusing on thresholds, wavelengths, and mean flows, with many of the results coming from numerical simulations in tilted rectangular domains that form the minimal flow unit for the turbulent–laminar bands.

Azimuthal Behaviour of Self-Excited Diametral Modes of Internal Cavities

2009 ◽  
Author(s):  
K. Aly ◽  
S. Ziada
Keyword(s):  
Acoustic Mode ◽  
Free Shear Layer ◽  
Complex Flow ◽  
Complex Behaviour ◽  
Pressure Transducers ◽  
Acoustic Modes ◽  
Mode Amplitude ◽  
Temporal Phase ◽  
Internal Cavities ◽  
Shallow Cavities

The aerodynamic excitation of ducted cavity diametral modes, which are inherently antisymmetric acoustic modes, by the oscillation of the axisymmetric free shear layer gives rise to complex flow-sound interaction mechanisms, in which the acoustic diametral modes do not possess a preferred azimuthal orientation. The azimuthal behaviour of this self-excitation mechanism is investigated experimentally. The study is performed for axisymmetric shallow cavities in a duct for a range of cavity length to depth ratio of L/d = 1 to 4, and for Mach numbers up to 0.4. Three pressure transducers flush mounted to the cavity floor are used to determine the acoustic mode amplitude and orientation. The excited acoustic modes are classified into spinning, partially spinning and stationary diametral modes. An analytical model based on the superposition of two orthogonal modes with 90° temporal phase shift is developed to reproduce the spinning and the partially spinning diametral modes. The developed model clarifies the observed complex behaviour of the azimuthal modes.

Finite-wavelength scattering of incident vorticity and acoustic waves at a shrouded-jet exit

2008 ◽  
Vol 612 ◽  
pp. 407-438 ◽  
Author(s):  
ARNAB SAMANTA ◽  
JONATHAN B. FREUND
Keyword(s):  
Mach Number ◽  
Acoustic Waves ◽  
Vortex Sheet ◽  
Acoustic Mode ◽  
Uniform Flow ◽  
Sharp Edge ◽  
Potential Mechanism ◽  
Ambient Flow ◽  
Acoustic Modes ◽  
Cylindrical Vortex

As the vortical disturbances of a shrouded jet pass the sharp edge of the shroud exit some of the energy is scattered into acoustic waves. Scattering into upstream-propagating acoustic modes is a potential mechanism for closing the resonance loop in the ‘howling’ resonances that have been observed in various shrouded jet configurations over the years. A model is developed for this interaction at the shroud exit. The jet is represented as a uniform flow separated by a cylindrical vortex sheet from a concentric co-flow within the cylindrical shroud. A second vortex sheet separates the co-flow from an ambient flow outside the shroud, downstream of its exit. The Wiener–Hopf technique is used to compute reflectivities at the shroud exit. For some conditions it appears that the reflection of finite-wavelength hydrodynamic vorticity modes on the vortex sheet defining the jet could be sufficient to reinforce the shroud acoustic modes to facilitate resonance. The analysis also gives the reflectivities for the shroud acoustic modes, which would also be important in establishing resonance conditions. Interestingly, it is also predicted that the shroud exit can be ‘transparent’ for ranges of Mach numbers, with no reflection into any upstream-propagating acoustic mode. This is phenomenologically consistent with observations that indicate a peculiar sensitivity of resonances of this kind to, say, jet Mach number.

Excitation of geodesic acoustic mode continuum by drift wave turbulence

2012 ◽  
Vol 78 (6) ◽  
pp. 651-655 ◽  
Author(s):  
JUN YU ◽  
J. Q. DONG ◽  
X. X. LI ◽  
D. DU ◽  
X. Y. GONG
Keyword(s):  
Growth Rate ◽  
Acoustic Mode ◽  
Kinetic Approach ◽  
Wave Turbulence ◽  
Ion Temperature ◽  
Drift Wave Turbulence ◽  
Acoustic Modes ◽  
Drift Wave ◽  
Radial Structure ◽  
Geodesic Acoustic Mode

AbstractExcitation of the geodesic acoustic mode continuum by drift wave turbulence is studied using the wave kinetic approach. For a model profile of weak non-uniform ion temperature, the forms of growth rate and radial structure of geodesic acoustic modes are obtained analytically. The growth rate is analyzed for several conditions for present-day tokamaks and compared with that for uniform ion temperature, as well as that given by the coherent mode approach for non-uniform ion temperature.

Modelling a Structural-Acoustic Coupled System with an Equivalent Lumped Parameter Mechanical System

1999 ◽  
Vol 121 (4) ◽  
pp. 453-459 ◽  
Author(s):  
S. M. Kim ◽  
M. J. Brennan
Keyword(s):  
Coupled System ◽  
Acoustic Mode ◽  
Physical Parameters ◽  
Acoustic System ◽  
Acoustic Modes ◽  
Lumped Parameter ◽  
Resonance Frequencies ◽  
Mechanical Models ◽  
Equivalent Mass ◽  
Physical Insight

This paper describes the way in which a structural acoustic coupled system can be modelled using an equivalent lumped parameter mechanical model. The impedance-mobility approach is first used to model the system, and by relating the physical parameters to equivalent mass and stiffness, lumped parameter models can be derived provided that damping in the acoustic system is neglected in all modes, but the first (zero order) mode. A limitation of this approach, however, is that these simple mechanical models formulated in terms of the uncoupled structural and acoustic modes are only possible for either a single structural mode coupled to many acoustic modes, or a single acoustic mode coupled to many structural modes. These models facilitate physical insight into the dynamic behavior of a lightly-damped structural-acoustic system at frequencies close to the resonance frequencies of the coupled system.

HOW THIN IS A THIN BED?

Geophysics ◽  
1973 ◽  
Vol 38 (6) ◽  
pp. 1176-1180 ◽  
Author(s):  
M. B. Widess
Keyword(s):  
Order Of Approximation ◽  
First Order ◽  
Reflective Power ◽  
Typical Frequency

Based on reflective properties, a thin bed may be conveniently defined as one whose thickness is less than about [Formula: see text] where [Formula: see text] is the (predominant) wavelength computed using the velocity of the bed. The amplitude of a reflection from a thin bed is to the first order of approximation equal to [Formula: see text] where b is the thickness of the bed and A is the amplitude of the reflection if the bed were to be very thick. The equation shows that a bed as thin as 10 ft has, for typical frequency and velocity, considerably more reflective power than is usually attributed to it.

Resonance of Trapped Acoustic Modes of a Ducted Rectangular Cavity

2015 ◽  
Author(s):  
Michael Bolduc ◽  
Samir Ziada ◽  
Philippe Lafon
Keyword(s):  
Shear Layer ◽  
Particle Velocity ◽  
Acoustic Mode ◽  
Velocity Fields ◽  
Mode Shapes ◽  
Test Results ◽  
Trapped Modes ◽  
Cross Sectional ◽  
Acoustic Modes ◽  
Axisymmetric Cavities

Flow over ducted cavities can lead to strong resonances of the trapped acoustic modes due to the presence of the cavity within the duct. Aly & Ziada [1–3] investigated the excitation mechanism of acoustic trapped modes in axisymmetric cavities. These trapped modes in axisymmetric cavities tend to spin because they do not have preferred orientation. The present paper investigates rectangular cross-sectional cavities as this cavity geometry introduces an orientation preference to the excited acoustic mode. Three cavities are investigated, one of which is square while the other two are rectangular. In each case, numerical simulations are performed to characterize the acoustic mode shapes and the associated acoustic particle velocity fields. The test results show the existence of stationary modes, being excited either consecutively or simultaneously, and a particular spinning mode for the cavity with square cross-section. The computed acoustic pressure and particle velocity fields of the excited modes suggest complex oscillation patterns of the cavity shear layer because it is excited, at the upstream corner, by periodic distributions of the particle velocity along the shear layer circumference.

scholarly journals Isotropic polarization of compressible flows

2015 ◽  
Vol 787 ◽  
pp. 440-448 ◽  
Author(s):  
Jian-Zhou Zhu
Keyword(s):  
Compressible Flows ◽  
Large Scale ◽  
Negative Temperature ◽  
Acoustic Mode ◽  
Positive Definite ◽  
Helmholtz Decomposition ◽  
Adiabatic Flow ◽  
Acoustic Modes

The helical absolute equilibrium of a compressible adiabatic flow presents not only polarization between two purely helical modes of opposite chiralities but also that between vortical and acoustic modes, deviating from the equipartition predicted by Kraichnan (J. Acoust. Soc. Am., vol. 27, 1955, pp. 438–441). Owing to the existence of the acoustic mode, even if all the Fourier modes of one chiral sector in the sharpened Helmholtz decomposition (Moses, SIAM J. Appl. Maths, vol. 21, 1971, pp. 114–130) are thoroughly truncated, leaving the system with positive-definite helicity and energy, negative temperature and the corresponding large-scale concentration of vortical modes are not allowed, unlike in the incompressible case.

scholarly journals The damping of terahertz acoustic modes in aqueous nanoparticle suspensions

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Alessio De Francesco ◽  
Luisa Scaccia ◽  
Ferdinando Formisano ◽  
Eleonora Guarini ◽  
Ubaldo Bafile ◽  
...  
Keyword(s):  
Bayesian Analysis ◽  
Relative Concentration ◽  
Acoustic Mode ◽  
Acoustic Damping ◽  
Longitudinal Acoustic ◽  
X Ray ◽  
Acoustic Modes ◽  
X Ray Scattering ◽  
Nanoparticle Suspensions ◽  
Shed Light

AbstractIn this work, we investigate the possibility of controlling the acoustic damping in a liquid when nanoparticles are suspended in it. To shed light on this topic, we performed Inelastic X-Ray Scattering (IXS) measurements of the terahertz collective dynamics of aqueous suspensions of nanospheres of various materials, size, and relative concentration, either charged or neutral. A Bayesian analysis of measured spectra indicates that the damping of the two acoustic modes of water increases upon nanoparticle immersion. This effect seems particularly pronounced for the longitudinal acoustic mode, which, whenever visible at all, rapidly damps off when increasing the exchanged wavevector. Results also indicate that the observed effect strongly depends on the material the immersed nanoparticles are made of.

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