Large-scale structure orientation in a compressible turbulent shear layer

Author(s):  
S. PETULLO ◽  
D. DOLLING

Organized structures in turbulent shear flow have been observed both in the laboratory and in the atmosphere and ocean. Recent work on modelling such structures in a temporally developing, horizontally homogeneous turbulent free shear layer (Liu & Merkine 19766) has been extended to the spatially developing mixing layer, there being no available rational transformation between the two nonlinear problems. We consider the kinetic energy development of the mean flow, large-scale structure and finegrained turbulence with a conditional average, supplementing the usual time average, to separate the non-random from the random part of the fluctuations. The integrated form of the energy equations and the accompanying shape assumptions are used to derive ‘ amplitude ’ equations for the mean flow, characterized by the shear layer thickness, the non-random and the random components of flow (which are characterized by their respective energy densities). The closure problem was overcome by the shape assumptions which entered into the interaction integrals: the instability-wavelike large-scale structure was taken to be two-dimensional and the local vertical distribution function was obtained by solving the Rayleigh equation for various local frequencies; the vertical shape of the mean stresses of the fine-grained turbulence was estimated by making use of experimental results; the vertical shapes of the wave-induced stresses were calculated locally from their corresponding equations.


2021 ◽  
Vol 927 ◽  
Author(s):  
Tomoaki Watanabe ◽  
Koji Nagata

Implicit large eddy simulation is performed to investigate large-scale characteristics of a temporally evolving, stably stratified turbulent shear layer arising from the Kelvin–Helmholtz instability. The shear layer at late time has two energy-containing length scales: the scale of the shear layer thickness, which characterizes large-scale motions (LSM) of the shear layer; and the larger streamwise scale of elongated large-scale structures (ELSS), which increases with time. The ELSS forms in the middle of the shear layer when the Richardson number is sufficiently large. The contribution of the ELSS to velocity and density variances becomes relatively important with time although the LSM dominate the momentum and density transport. The ELSS have a highly anisotropic Reynolds stress, to a degree similar to the near-wall region of turbulent boundary layers, while the Reynolds stress of the LSM is as anisotropic as in the outer region. Peaks in the spectral energy density associated with the ELSS emerge because of the slow decay of turbulence at very large scales. A forward interscale energy transfer from large to small scales occurs even at a small buoyancy Reynolds number. However, an inverse transfer also occurs for the energy of spanwise velocity. Negative production of streamwise velocity and density spectra, i.e. counter-gradient transport of momentum and density, is found at small scales. These behaviours are consistent with channel flows, indicating similar flow dynamics in the stratified shear layer and wall-bounded shear flows. The structure function exhibits a logarithmic law at large scales, implying a $k^{-1}$ scaling of energy spectra.


1985 ◽  
Vol 152 ◽  
pp. 83-111 ◽  
Author(s):  
K. B. M. Q. Zaman

The phenomena of excitation-induced suppression and amplification of broadband jet noise have been experimentally investigated in an effort to understand the mechanisms, especially in relation to the near flow-field large-scale structure dynamics. Suppression is found to occur only in jets at low speeds with laminar exit boundary layers, the optimum occurring for excitation at Stθ ≈ 0.017, where Stθ is the Strouhal number based on the initial shear-layer momentum thickness. The suppression mechanism is linked to an initial-condition effect on the large-scale structure dynamics. The interaction and evolution of laminar-like structures at low jet speeds produce more (normalized) noise and turbulence, compared to asymptotically lower levels at high speeds when the initial shear layer is no longer laminar. The effect of initial condition has been demonstrated by tripped versus untripped jet data. The excitation at Stθ ≈ 0.017 results in a quick roll-up and transition of the laminar shear-layer vortices, yielding coherent structures which are similar to those at high speeds. Thus, the broadband noise and turbulence are suppressed, but at the most to the asymptotically lower levels. When at the asymptotic level, the broadband jet noise can only be amplified by the excitation; the amplification is found to be maximum for excitation in the StD range of 0.65–0.85, StD being the Strouhal number based on the jet diameter. Excitation in this StD range also produces strongest vortexpairing activity. From spectral analysis of the flow-field and the near sound-pressure field, it is inferred that the pairing process induced by the excitation is at the origin of the broadband noise amplification.


1978 ◽  
Vol 84 (4) ◽  
pp. 673-694 ◽  
Author(s):  
J. E. Ffowcs Williams ◽  
A. J. Kempton

In this paper we assess the importance as a noise source of the well-ordered large-scale structure of a jet. We propose two simple models of the structure: the first emphasizes those features in common with waves that initially grow on an unstable shear layer but eventually saturate and decay, while the second regards the abrupt pairing of eddies as the most significant event in the jet's development. Our models demonstrate the possibility that forcing at one frequency could increase the broad-band noise of a jet, though, for jets with supersonic eddy convection velocities, the sound propagating in the direction of the Mach angle retains the spectrum of the excitation field. These features are consistent with the available experimental data, and strongly support the view that the large-scale structure of jet turbulence provides the dominant contribution to jet noise.


2010 ◽  
Vol 656 ◽  
pp. 51-81 ◽  
Author(s):  
B. VUKASINOVIC ◽  
Z. RUSAK ◽  
A. GLEZER

The effects of small-scale dissipative fluidic actuation on the evolution of large- and small-scale motions in a turbulent shear layer downstream of a backward-facing step are investigated experimentally. Actuation is applied by modulation of the vorticity flux into the shear layer at frequencies that are substantially higher than the frequencies that are typically amplified in the near field, and has a profound effect on the evolution of the vortical structures within the layer. Specifically, there is a strong broadband increase in the energy of the small-scale motions and a nearly uniform decrease in the energy of the large-scale motions which correspond to the most amplified unstable modes of the base flow. The near field of the forced shear layer has three distinct domains. The first domain (x/θ0 < 50) is dominated by significant concomitant increases in the production and dissipation of turbulent kinetic energy and in the shear layer cross-stream width. In the second domain (50 < x/θ0 < 300), the streamwise rates of change of these quantities become similar to the corresponding rates in the unforced flow although their magnitudes are substantially different. Finally, in the third domain (x/θ0 > 350) the inviscid instability of the shear layer re-emerges in what might be described as a ‘new’ baseline flow.


1995 ◽  
Vol 302 ◽  
pp. 149-178 ◽  
Author(s):  
Kenneth T. Kiger ◽  
Juan C. Lasheras

The transport of heavy, polydispersed particles and the inter-phase transfer of kinetic energy due to the viscous drag forces is measured experimentally in a turbulent shear layer. To study the effect of the large-scale vortex pairing event, the shear layer is forced simultaneously with a fundarmental and subharmonic perturbation. It is shown that vortex pairing plays a homogenizing role on the particulate field, but hte amount of homogenization is strongly dependent upon the particle's viscous relaxtion time, the eddy turnover time, as well as the time the particles interact with each scale prior to a pairing event. Thus, even though the smaller size particles become well-mixed across the large eddies, the larger sizes are still dispersed in an inhormogeneous fashion. It is also found that the kinetic energy transfer between the phases occurs inhomogeneously with energy being exchanged predominantly in a sublayer just outside the region of maximum turbulence intensity. The kinetic energy transfer is shown to exhibit notable positive and negative peaks located beneath the cores and stagnation points of the large-scale eddy field, and these peaks are shown to result from the irrotational velocity perturbations created by the vortices. This energy exchange mechanism remains a prominent process as long as the Stokes number of the particles relative to the vortices is of order unity.


Sign in / Sign up

Export Citation Format

Share Document