On generation of sound in wall-bounded shear flows: source identificaion, mean-flow refraction, back action of sound and global acoustic coupling

2011 ◽  
Author(s):  
Xuesong Wu
Keyword(s):  
Shear Flows ◽  
Mean Flow ◽  
Acoustic Coupling ◽  
Back Action

On generation of sound in wall-bounded shear flows: back action of sound and global acoustic coupling

2011 ◽  
Vol 689 ◽  
pp. 279-316 ◽  
Author(s):  
Xuesong Wu
Keyword(s):  
Acoustic Field ◽  
Acoustic Radiation ◽  
Leading Order ◽  
Mean Flow ◽  
S Wave ◽  
Acoustic Coupling ◽  
Hydrodynamic Motion ◽  
Roughness Elements ◽  
Supersonic Regime ◽  
Back Action

AbstractIn two previous papers (Wu, J. Fluid Mech., vol. 453, 2002, p. 289, and Wu & Hogg, J. Fluid Mech., vol. 550, 2006, p. 307), a formal asymptotic procedure was developed to calculate the sound radiated by unsteady boundary-layer flows that are described by the triple-deck theory. That approach requires lengthy calculations, and so is now improved to construct a simpler composite theory, which retains the capacity of systematically identifying and approximating the relevant sources, but also naturally includes the effect of mean-flow refraction and more importantly the back action of the emitted sound on the source itself. The combined effect of refraction and back action is represented by an ‘impedance coefficient’, and the present analysis yields an analytical expression for this parameter, which was usually introduced on a semi-empirical basis. The expression indicates that for Mach number $M= O(1)$, the mean-flow refraction and back action of the sound have a leading-order effect on the acoustic field within the shallow angles to the streamwise directions. A parametric study suggests that the back effect of sound is actually appreciable in a sizeable portion of the acoustic field for $M\gt 0. 5$, becomes more pronounced, and eventually influences the entire acoustic field in the transonic limit. In the supersonic regime, the acoustic field is characterized by distinctive Mach-wave beams, which exert a leading-order influence on the source. The analysis also indicates that acoustic radiation in the subsonic and supersonic regimes is fundamentally different. In the subsonic regime, the sound is produced by small-wavenumber components of the hydrodynamic motion, and can be characterized by acoustic multipoles, whereas in the supersonic regime, broadband finite-wavenumber components of the hydrodynamic motion contribute and the concept of a multipolar source becomes untenable. The global acoustic feedback loop is investigated using a model consisting of two well-separated roughness elements, in which the sound wave emitted due to the scattering of a Tollmien–Schlichting (T–S) wave by the downstream roughness propagates upstream and impinges on the upstream roughness to regenerate the T–S wave. Numerical calculations suggest that at high Reynolds numbers and for moderate roughness heights, the long-range acoustic coupling may lead to global instability, which is characterized by self-sustained oscillations at discrete frequencies. The dominant peak frequency may jump from one value to another as the Reynolds number or the distance between the roughness elements is varied gradually.

scholarly journals Ageostrophic instability in rotating, stratified interior vertical shear flows

2014 ◽  
Vol 755 ◽  
pp. 397-428 ◽  
Author(s):  
Peng Wang ◽  
James C. McWilliams ◽  
Claire Ménesguen
Keyword(s):  
Energy Source ◽  
Kinetic Energy ◽  
Potential Energy ◽  
Gravity Waves ◽  
Shear Flows ◽  
Vertical Shear ◽  
Mean Flow ◽  
Efficient Energy Transfer ◽  
The Mean ◽  
Inertia Gravity Waves

AbstractThe linear instability of several rotating, stably stratified, interior vertical shear flows $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\overline{U}(z)$ is calculated in Boussinesq equations. Two types of baroclinic, ageostrophic instability, AI1 and AI2, are found in odd-symmetric $\overline{U}(z)$ for intermediate Rossby number ($\mathit{Ro}$). AI1 has zero frequency; it appears in a continuous transformation of the unstable mode properties between classic baroclinic instability (BCI) and centrifugal instability (CI). It begins to occur at intermediate $\mathit{Ro}$ values and horizontal wavenumbers ($k,l$) that are far from $l= 0$ or $k = 0$, where the growth rate of BCI or CI is the strongest. AI1 grows by drawing kinetic energy from the mean flow, and the perturbation converts kinetic energy to potential energy. The instability AI2 has inertia critical layers (ICL); hence it is associated with inertia-gravity waves. For an unstable AI2 mode, the coupling is either between an interior balanced shear wave and an inertia-gravity wave (BG), or between two inertia-gravity waves (GG). The main energy source for an unstable BG mode is the mean kinetic energy, while the main energy source for an unstable GG mode is the mean available potential energy. AI1 and BG type AI2 occur in the neighbourhood of $A-S= 0$ (a sign change in the difference between absolute vertical vorticity and horizontal strain rate in isentropic coordinates; see McWilliams et al., Phys. Fluids, vol. 10, 1998, pp. 3178–3184), while GG type AI2 arises beyond this condition. Both AI1 and AI2 are unbalanced instabilities; they serve as an initiation of a possible local route for the loss of balance in 3D interior flows, leading to an efficient energy transfer to small scales.

On the Propagation of Sound in a High-Speed Non-Isothermal Shear Flow

2009 ◽  
Vol 8 (3) ◽  
pp. 199-230 ◽  
Author(s):  
L.M.B.C. Campos ◽  
M.H. Kobayashi
Keyword(s):  
Wave Equation ◽  
Shear Flow ◽  
Acoustic Wave ◽  
Sound Speed ◽  
High Speed ◽  
Shear Flows ◽  
Critical Layer ◽  
Acoustic Wave Equation ◽  
Mean Flow ◽  
Flow Vorticity

The propagation of sound in shear flows is relevant to the acoustics of wall and duct boundary layers, and to jet shear layers. The acoustic wave equation in a shear flow has been solved exactly only for a plane unidirectional homentropic mean shear flow, in the case of three velocity profiles: linear, exponential and hyperbolic tangent. The assumption of homentropic mean flow restricts application to isothermal shear flows. In the present paper the wave equation in an plane unidirectional shear flow with a linear velocity profile is solved in an isentropic non-homentropic case, which allows for the presence of transverse temperature gradients associated with the ***non-uniform sound speed. The sound speed profile is specified by the condition of constant enthalpy, i.e. homenergetic shear flow. In this case the acoustic wave equation has three singularities at finite distance (besides the point at infinity), viz. the critical layer where the Doppler shifted frequency vanishes, and the critical flow points where the sound speed vanishes. By matching pairs of solutions around the singular and regular points, the amplitude and phase of the acoustic pressure in calculated and plotted for several combinations of wavelength and wave frequency, mean flow vorticity and sound speed, demonstrating, among others, some cases of sound suppression at the critical layer.

The evolution of a localized vortex disturbance in external shear flows. Part 2. Comparison with experiments in rotating shear flows

1999 ◽  
Vol 379 ◽  
pp. 351-380 ◽  
Author(s):  
EDWIN MALKIEL ◽  
VLADIMIR LEVINSKI ◽  
JACOB COHEN
Keyword(s):  
Theoretical Model ◽  
Shear Flows ◽  
Laser Doppler Anemometry ◽  
Finite Amplitude ◽  
Base Flow ◽  
Mean Flow ◽  
Hairpin Vortices ◽  
Flow Parameters ◽  
Angular Velocities ◽  
Rotating Shear Flows

The evolution of artificially generated localized disturbances in the shape of hairpin vortices, in laminar axisymmetric rotating shear flows, is investigated experimentally. The results are compared with the predictions of a theoretical model (Levinski & Cohen 1995) with respect to the growth of such disturbances. Hairpin vortices were generated at the surface of the inner cylinder of an axisymmetric Couette apparatus, employing an injection–suction technique. The flow field was analysed from flow visualization using top and side views and by measurements of the mean and instantaneous velocity fields, carried out using laser Doppler anemometry and particle image velocimetry. An instability domain, within the range of base flow parameters where the flow is known to be linearly stable, was found. The marginal ratio between the angular velocities of the inner and outer cylinders beyond which the flow is stable to finite-amplitude localized disturbances agrees with the theoretical prediction based on the measured mean flow in the region of the disturbance. The dependence of the hairpin's inclination angle on the ratio between the two angular velocities is fairly well predicted by the theoretical model.

Diffusion in free turbulent shear flows

1957 ◽  
Vol 3 (1) ◽  
pp. 67-80 ◽  
Author(s):  
G. K. Batchelor
Keyword(s):  
Time Scales ◽  
Particle Velocity ◽  
Random Function ◽  
Shear Flows ◽  
Fluid Particle ◽  
Turbulent Shear ◽  
Mean Flow ◽  
Turbulent Shear Flows ◽  
The Mean ◽  
Stationary Random Function

This paper is concerned with some statistical properties of the displacement of a marked fluid particle released from a given position in a turbulent shear flow, and in particular with the dispersion about the mean position after a long time. It is known that the dispersion takes a simple asymptotic form when the particle velocity is a stationary random function of time, and that analogous results are obtainable when the particle velocity can be transformed to a stationary random function by suitable stretching of the velocity and time scales. The basic hypothesis of the paper is that, in steady free turbulent shear flows which are generated at a point and have a similar structure at different stations downstream, the velocity of a fluid particle exhibits a corresponding Lagrangian similarity and can be so transformed to a stationary random function.The velocity and time scales characterizing the motion of a fluid particle at time t after release at the origin are determined in terms of the powers with which the Eulerian length and velocity scales of the turbulence vary with distance x from the origin. The time scale has the same dependence on t for all jets, wakes and mixing layers (and also for decaying homogeneous turbulence) possessing the usual kind of Eulerian similarity. The dispersion of a particle in the longitudinal or mean-flow direction (and likewise that in the lateral direction in cases of two-dimensional mean flow) is found to vary with t in such a way as to be proportional to the thickness of the shear layer at the mean position of the particle. The way in which the maximum value of the mean concentration of marked fluid falls off with t (for release of a single particle) or with x (for continuous release) is also found.

Nonlinear temporal-spatial modulation of near-planar Rayleigh waves in shear flows: formation of streamwise vortices

1993 ◽  
Vol 256 ◽  
pp. 685-719 ◽  
Author(s):  
Xuesong Wu
Keyword(s):  
Shear Flows ◽  
Numerical Solutions ◽  
Broad Class ◽  
Nonlinear Effects ◽  
Amplitude Equation ◽  
Spatial Modulation ◽  
Linear Growth Rate ◽  
Instability Wave ◽  
Streamwise Vortices ◽  
Mean Flow

The nonlinear temporal-spatial modulation of a near-planar Rayleigh instability wave is studied. The amplitude of the wave is allowed to be a slowly varying function of spanwise position as well as of time (or streamwise variable in the spatial evolution case). It is shown that the development of the disturbance is controlled by critical-layer nonlinear effects when the linear growth rate decreases to O(ε⅖), where ε is the magnitude of the disturbance. Nonlinear interactions influence the evolution by producing spanwise dependent mean-flow distortions. The evolution is governed by an integro-partial-differential equation containing history-dependent nonlinear terms of Hickernell (1984) type. A notable feature of the amplitude equation is that the highest derivative with respect to spanwise position appears in the nonlinear terms. These terms are associated with three-dimensionality. The possible properties of the amplitude equation are discussed. Numerical solutions show that a disturbance initially centred at a spanwise position can propagate laterally to form concentrated, quasi-periodic streamwise vortices. This qualitatively captures the phenomena observed in experiments. The focusing of vorticity may be associated with a localized singularity which can occur at a finite distance downstream or within a finite time. It is noted that the amplitude equation is rather generic and applies to a broad class of shear flows which is inviscidly unstable.

Turbulent gravity-stratified shear flows

1984 ◽  
Vol 138 ◽  
pp. 353-378 ◽  
Author(s):  
Vincent H. Chu ◽  
Raouf E. Baddour
Keyword(s):  
Shear Flows ◽  
Saline Water ◽  
Mixing Layer ◽  
Stable State ◽  
Longitudinal Direction ◽  
Stable Stratification ◽  
Turbulent Shear ◽  
Mean Flow ◽  
Initial Development ◽  
Surface Jet

Two simple turbulent shear flows, namely a surface jet and a mixing layer, under the influence of stable gravity stratification, were investigated experimentally. The shear flows were generated in the laboratory by letting fresh water flow over saline water in a two-dimensional channel. Velocity and salinity measurements were made using a hot-film probe and a single-electrode conductivity probe. The experimental results for the two flows were correlated each using a different set of length and velocity scales. The initial development of the flows was relatively unaffected by the stable stratification. As the shear flows grew in thickness, they were observed to have a tendency to approach a ‘neutrally stable state’ in which the turbulent motion neither extracted energy from nor lost energy to the mean flow. The gradient Richardson number in this neutrally stable state was found to have the critical value predicted by linear inviscid stability theory. The decay of turbulent intensity in the longitudinal direction was observed to follow a power-law relationship similar to the one obtained by Comte-Bellot & Corrsin (1966) for the decay of grid-generated turbulence.

scholarly journals First-principle description of acoustic radiation of shear flows

2019 ◽  
Vol 377 (2159) ◽  
pp. 20190077 ◽  
Author(s):  
Xuesong Wu ◽  
Zhongyu Zhang
Keyword(s):  
Acoustic Waves ◽  
Shear Flows ◽  
Acoustic Radiation ◽  
Higher Order ◽  
Far Field ◽  
Sound Waves ◽  
Leading Order ◽  
Mean Flow ◽  
Asymptotic Approach ◽  
Flow Distortion

As a methodology complementary to acoustic analogy, the asymptotic approach to aeroacoustics seeks to predict aerodynamical noise on the basis of first principles by probing into the physical processes of acoustic radiation. The present paper highlights the principal ideas and recent developments of this approach, which have shed light on some of the fundamental issues in sound generation in shear flows. The theoretical work on sound wave emission by nonlinearly modulated wavepackets of supersonic and subsonic instability modes in free shear flows identifies the respective physical sources or emitters. A wavepacket of supersonic modes is itself an efficient emitter, radiating directly intensive sound in the form of a Mach wave beam, the frequencies of which are in the same band as those of the modes in the packet. By contrast, a wavepacket of subsonic modes radiates very weak sound directly. However, the nonlinear self-interaction of such a wavepacket generates a slowly modulated mean-flow distortion, which then emits sound waves with low frequencies and long wavelengths on the scale of the wavepacket envelope. In both cases, the acoustic waves emitted to the far field are explicitly expressed in terms of the amplitude function of the wavepacket. The asymptotic approach has also been applied to analyse generation of sound waves in wall-bounded shear flows on the triple-deck scale. Several subtleties have been found. The near-field approximation has to be worked out to a sufficiently higher order in order just to calculate the far-field sound at leading order. The back action of the radiated sound on the flow in the viscous sublayer and the main shear layer is accounted for by an impedance coefficient. This effect is of higher order in the subsonic regime, but becomes a leading order in the transonic and supersonic regimes. This article is part of the theme issue ‘Frontiers of aeroacoustics research: theory, computation and experiment’.

Upper bounds on general dissipation functionals in turbulent shear flows: revisiting the ‘efficiency’ functional

2002 ◽  
Vol 461 ◽  
pp. 239-275 ◽  
Author(s):  
R. R. KERSWELL
Keyword(s):  
Shear Flows ◽  
Momentum Balance ◽  
Total Power ◽  
Function Technique ◽  
Turbulent Shear ◽  
Mean Flow ◽  
Special Cases ◽  
Turbulent Shear Flows ◽  
Long Time ◽  
The Mean

We show how the variational formulation introduced by Doering & Constantin to rigorously bound the long-time-averaged total dissipation rate [ ] in turbulent shear flows can be extended to treat other long-time-averaged functionals lim supT→∞(1/T)×∫0Tf(D, Dm, Dv)dt of the total dissipation D, dissipation in the mean field Dm and dissipation in the fluctuation field Dv. Attention is focused upon the suite of functionals f = D(Dv/Dm)n and f = Dm(Dv/Dm)n (n [ges ] 0) which include the ‘efficiency’ functional f = D(Dv/Dm) (Malkus & Smith 1989; Smith 1991) and the dissipation in the mean flow f = Dm (Malkus 1996) as special cases. Complementary lower estimates of the rigorous bounds are produced by generalizing Busse's multiple-boundary-layer trial function technique to the appropriate Howard–Busse variational problems built upon the usual assumption of statistical stationarity and constraints of total power balance, mean momentum balance, incompressibility and boundary conditions. The velocity field that optimizes the ‘efficiency’ functional is found not to capture the asymptotic structure of the observed mean flow in either plane Couette flow or plane Poiseuille flow. However, there is evidence to suppose that it is ‘close’ to a neighbouring functional that may.

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