Spectral broadening and flow randomization in free shear layers

Wu, Xuesong; Tian, Feng

doi:10.1017/jfm.2012.262

Cited by 11 publications

(10 citation statements)

References 41 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…to describe the spatial and temporal modulation of the disturbance (Wu & Tian 2012). Forx = O(1), the CS corresponds to a nearly neutral instability mode (or more generally a wavetrain) residing on the turbulent mean flow.…”

Section: Asymptotic Scalingsmentioning

confidence: 99%

“…The procedure is similar to those in Goldstein & Hultgren (1988) and Wu & Tian (2012), but the main difference is that non-parallelism now appears at leading order in the critical layer. The reader who is interested primarily in physical aspects of the problem may skip the detail, and go directly to the final outcome of the analysis, which is the nonlinear evolution system consisting of the amplitude equation …”

Section: Asymptotic Scalingsmentioning

confidence: 99%

See 1 more Smart Citation

Nonlinear dynamics of large-scale coherent structures in turbulent free shear layers

Zhuang

2015

J. Fluid Mech.

Self Cite

View full text Add to dashboard Cite

Fully developed turbulent free shear layers exhibit a high degree of order, characterized by large-scale coherent structures in the form of spanwise vortex rollers. Extensive experimental investigations show that such organised motions bear remarkable resemblance to instability waves, and their main characteristics, including the length scales, propagation speeds and transverse structures, are reasonably well predicted by linear stability analysis of the mean flow. In this paper, we present a mathematical theory to describe the nonlinear dynamics of coherent structures. The formulation is based on the triple decomposition of the instantaneous flow into a mean field, coherent fluctuations and small-scale turbulence but with the mean-flow distortion induced by nonlinear interactions of coherent fluctuations being treated as part of the organised motion. The system is closed by employing gradient type of models for the time-and phase-averaged Reynolds stresses of fine-scale turbulence. In the high-Reynolds-number limit, the nonlinear non-equilibrium critical-layer theory for laminar-flow instabilities is adapted to turbulent shear layers by accounting for (a) the enhanced non-parallelism associated with fast spreading of the mean flow, and (b) the influence of small-scale turbulence on coherent structures. The combination of these factors with nonlinearity leads to an interesting evolution system, consisting of the coupled amplitude and vorticity equations, in which non-parallelism contributes the so-called translating critical-layer effect. Numerical solutions of the evolution system capture vortex roll-up, which is the hallmark of turbulent mixing layer, and the predicted amplitude development mimics the qualitative feature of oscillatory saturation that has been observed in a number of experiments. A fair degree of quantitative agreement is obtained with one set of experimental data.

show abstract

Section: Asymptotic Scalingsmentioning

confidence: 99%

Section: Asymptotic Scalingsmentioning

confidence: 99%

Nonlinear dynamics of large-scale coherent structures in turbulent free shear layers

Zhuang

2015

J. Fluid Mech.

Self Cite

View full text Add to dashboard Cite

show abstract

“…the components with L < 0, have larger growth rates than those of the upper-sideband modes with L > 0, in the linear region. Due to the nonlinear interactions, the amplitudes of lower sidebands would exceed those of the upper ones, displaying an energy back-scattering phenomenon; see also Wu & Tian (2012) and [I].…”

Section: Numerical Results Of Nonlinear Evolution-modulation Of Ring-...mentioning

confidence: 99%

Nonlinear evolution and low-frequency acoustic radiation of ring-mode coherent structures on subsonic turbulent circular jets

Zhang

2022

J. Fluid Mech.

Self Cite

View full text Add to dashboard Cite

By adapting the triple decomposition of an instantaneous turbulent flow into a time-averaged mean field, large-scale coherent motion and fine-scale random fluctuations, and treating the coherent motion as instability modes on the mean flow, a mathematical theory is developed to describe the nonlinear spatial–temporal modulation and acoustic radiation of a coherent structure (CS) on a circular jet in the form of a wavepacket consisting of an axisymmetric (ring) mode and its sideband components. The effect of fine-scale turbulence on the CS is characterised via a gradient closure model, and the non-parallelism due to the axial variation and radial velocity of the mean flow is taken into account. By employing the matched asymptotic expansion and multi-scale techniques, a strongly nonlinear system is derived, which governs the envelope of the CS and its vorticity and temperature in the critical layer. Numerical solutions to the evolution system show that the theory captures the nonlinear amplitude attenuation and vorticity roll-up as observed in experiments. The large-distance asymptotic properties of the CS allow us to describe and predict its acoustic radiation on the basis of first principles. The CS is trapped within the jet, but its self-interaction generates a temporally and axially modulated mean-flow distortion, which acts as the emitter to radiate low-frequency sound waves, with the Reynolds stresses driving this mean-flow distortion being identified unambiguously to be the physical source in the present context. An equivalent source in the Lighthill type of acoustic analogy is also identified. For the present ring-mode CS in the fully developed region of a circular jet, the equivalent source can be determined before the acoustic field is, and the intensity of the radiated sound waves is found to be $O(\epsilon ^3)$ , where $\epsilon$ measures the magnitude of the CS. The directivity and spectrum of the acoustic far field are calculated for representative parameters, and the predicted features resemble experimental measurements.

show abstract

“…Such spectral content arises because naturally present disturbances exciting the CS are unlikely to be purely monochromatic. When nonlinear effects come into play, the resulting energy transfer among different spectral components causes significant intermittency or jittering (Wu & Tian 2012), which is known to be important in the radiation of sound waves. Forx = O(1), the nonlinear effect as well as the effects of conductivities and viscosities all appear at leading order in the critical layer, if we choose the scalings as,…”

Section: Asymptotic Scalingsmentioning

confidence: 99%

“…The solutions for A, T and Q can be written as Fourier series (cf. Goldstein & Leib 1988;Wu & Tian 2012),…”

Section: Fourier Decompositions and Boundary Conditionsmentioning

confidence: 99%

Spectral broadening and flow randomization in free shear layers

Cited by 11 publications

References 41 publications

Nonlinear dynamics of large-scale coherent structures in turbulent free shear layers

Nonlinear dynamics of large-scale coherent structures in turbulent free shear layers

Nonlinear evolution and low-frequency acoustic radiation of ring-mode coherent structures on subsonic turbulent circular jets

Nonlinear evolution and acoustic radiation of coherent structures in subsonic turbulent free shear layers

Contact Info

Product

Resources

About