On the Application of Wavelet Transform in Jet Aeroacoustics

Wavelet transform has become a common tool for processing non-stationary signals in many different fields. The present paper reports a review of some applications of wavelet in aeroacoustics with a special emphasis on the analysis of experimental data taken in compressible jets. The focus is on three classes of wavelet-based signal processing procedures: (i) conditional statistics; (ii) acoustic and hydrodynamic pressure separation; (iii) stochastic modeling. The three approaches are applied to an experimental database consisting of pressure time series measured in the near field of a turbulent jet. Future developments and possible generalization to other applications, e.g., airframe or propeller noise, are also discussed.

Effects of Aspect Ratio on Higher-Order Moments, Conditional Statistics, TKE Budget and Anisotropy in Narrow Open Channel Flow

The paper investigates the influence of aspect ratio on the higher-order statistics of velocity fluctuations in hydraulically rough narrow OCF. In the experiments, the aspect ratios were varied between 2.5 and 4. Velocities were measured with ADV. The third-order moments were found to be sensitive to the aspect ratio in the outer region. The contributions of all quadrant events are approximately equal in lower aspect ratio flows, whereas ejections and sweeps are the dominant as the aspect ratio increases. The upward transfer of TKE flux increases in the outer layer with increase in aspect ratio. The TKE production and dissipation are found to be dependent on the aspect ratio. The analysis of Reynolds stress AIM reveals that for low aspect ratio flows turbulence tends to attain rod like axisymmetric turbulence only in the intermediate layer whereas for higher aspect ratio, turbulence attains rod like axisymmetric turbulence throughout the depth.

Aging haloes: implications of the magnitude gap on conditional statistics of stellar and gas properties of massive haloes

ABSTRACT Cold dark matter model predicts that the large-scale structure grows hierarchically. Small dark matter haloes form first. Then, they grow gradually via continuous merger and accretion. These haloes host the majority of baryonic matter in the Universe in the form of hot gas and cold stellar phase. Determining how baryons are partitioned into these phases requires detailed modelling of galaxy formation and their assembly history. It is speculated that formation time of the same mass haloes might be correlated with their baryonic content. To evaluate this hypothesis, we employ haloes of mass above $10^{14}\, \mathrm{M}_{\odot }$ realized by TNG300 solution of the IllustrisTNG project. Formation time is not directly observable. Hence, we rely on the magnitude gap between the brightest and the fourth brightest halo galaxy member, which is shown that traces formation time of the host halo. We compute the conditional statistics of the stellar and gas content of haloes conditioned on their total mass and magnitude gap. We find a strong correlation between magnitude gap and gas mass, BCG stellar mass, and satellite galaxies stellar mass, but not the total stellar mass of halo. Conditioning on the magnitude gap can reduce the scatter about halo property–halo mass relation and has a significant impact on the conditional covariance. Reduction in the scatter can be as significant as 30 per cent, which implies more accurate halo mass prediction. Incorporating the magnitude gap has a potential to improve cosmological constraints using halo abundance and allows us to gain insight into the baryon evolution within these systems.

Conditional statistics and flow structures in turbulent boundary layers buffeted by free-stream disturbances

Direct numerical simulations are performed to study zero-pressure-gradient turbulent boundary layers beneath quiescent and vortical free streams. The inflow boundary layer is computed in a precursor simulation of laminar-to-turbulence transition, and the free-stream vortical forcing is obtained from direct numerical simulations of homogeneous isotropic turbulence. A level-set approach is employed in order to objectively distinguish the boundary-layer and free-stream fluids, and to accurately evaluate their respective contributions to flow statistics. When free-stream turbulence is present, the skin friction coefficient is elevated relative to its value in the canonical boundary-layer configuration. An explanation is provided in terms of an increase in the power input into production of boundary-layer turbulence kinetic energy. This increase takes place deeper than the extent of penetration of the external perturbations towards the wall, and also despite the free-stream perturbations being void of any Reynolds shear stress. Conditional statistics demonstrate that the free-stream turbulence has two effects on the boundary layer: one direct and the other indirect. The low-frequency components of the free-stream turbulence penetrate the logarithmic layer. The associated wall-normal Reynolds stress acts against the mean shear to enhance the shear stress, which in turn enhances turbulence production. This effect directly enlarges the scale and enhances the energy of outer large-scale motions in the boundary layer. The second, indirect effect is the influence of these newly formed large-scale structures. They modulate the near-wall shear stress and, as a result, increase the turbulence kinetic energy production in the buffer layer, which is deeper than the extent of penetration of free-stream turbulence towards the wall.

Comments on “The Gulf Stream Convergence Zone in the Time-Mean Winds”

In a recent study, O’Neill et al. analyzed the divergence of surface winds above the northwest Atlantic. In the time mean, a band of convergence is found, overlying the southern flank of the Gulf Stream. To quantify the impact of synoptic storms, the authors proposed to compare the time-mean divergence with the divergence averaged in the absence of rain. In the resulting conditional-average field, divergence was found to be positive nearly everywhere. O'Neill et al. concluded that this absence of convergence precludes the Ekman-balanced mass adjustment to be responsible for the atmospheric response above the Gulf Stream. Using a simplistic toy model as well as a numerical simulation representative of a storm track, we show that the absence of negative divergence values purely results from the correlation between rain and convergence: the conditional average based on the absence of rain necessarily implies a shift toward positive divergence values. In consequence, we argue that conditional statistics (based on the absence of rain or removing extreme values in the divergence field), as produced by O’Neill et al., do not allow conclusions on the mechanisms underlying the atmospheric response to the Gulf Stream. They nevertheless highlight the essential role of synoptic storms in shaping the divergence field in instantaneous fields.