The large-scale footprint in small-scale Rayleigh-B\'enard turbulence

Turbulent convection systems are known to give rise to prominent large scale circulation. At the same time, the `background' (or `small-scale') turbulence is also highly relevant and e.g. carries the majority of the heat transport in the bulk of the flow. Here, we investigate how the small-scale turbulence is interlinked with the large-scale flow organization of Rayleigh-B\'enard convection. Our results are based on a numerical simulation at Rayleigh number $Ra = 10^8$ in a large aspect ratio ($\Gamma=32$) cell to ensure a distinct scale separation. We extract local magnitudes and wavenumbers of small scale turbulence and find significant correlation of large scale variations in these quantities with the large-scale signal. Most notably, we find stronger temperature fluctuations and increased small scale transport (on the order of $10\%$ of the global Nusselt number $Nu$) in plume impacting regions and opposite trends in the plume emitting counterparts. This concerns wall distances up to $2\delta_\theta$ (thermal boundary layer thickness). Local wavenumbers are generally found to be higher on the plume emitting side compared to the impacting one. A second independent approach by means of conditional averages confirmed these findings and yields additional insight into the large-scale variation of small-scale properties. Our results have implications for modelling small-scale turbulence.Comment: 19 pages, 9 figures, accepted at the Journal of Fluid Mechanic

Acoustics from high-speed jets with crackle

textA scaling model based on an effective Gol'dberg number is proposed for predicting the presence of cumulative nonlinear distortions in the acoustic waveforms produced by high-speed jets. Two acoustic length scales, the shock formation distance and the absorption length are expressed in terms of jet exit parameters. This approach allows one to compute the degree of cumulative nonlinear distortion in a full-scale scenario, from laboratory-scale observations, or vice versa. Surveys of the acoustic pressure waveforms emitted by a laboratory-scale, shock-free and unheated Mach 3 jet are used to support the findings of the model. These acoustic waveforms are acquired on a planar grid in an acoustically treated and range-restricted environment. Various statistical metrics are employed to examine the degree of local and cumulative nonlinearity in the measured waveforms and their temporal derivatives. This includes skewness, kurtosis, the number of zero crossings in the waveform, a wave steepening factor, the Morfey-Howell nonlinearity indicator and an application of the generalized Burgers equation. It is advocated that in order for the Morfey-Howell indicator to be used as an investigative tool for the presence of cumulative nonlinear waveform distortion, that it be applied as a multi-point indicator. Based on findings of the model and the spatial topography of the metrics, it is concluded that cumulative nonlinear steepening effects are absent in the current data set. This implies that acoustic shock-structures in the waveforms are generated by local mechanisms in, or in close vicinity to, the jet's hydrodynamic region. Furthermore, these shock-structures induce the crackle noise component. The research aims to quantify crackle in a temporal and spectral fashion, and is motivated by the fact that (1) it is perceived as the most annoying component of jet noise, (2) no unique measures of crackle exist, and (3) significant reductions in jet noise will be achieved when crackle can be controlled. A unique detection algorithm is introduced which isolates the shock-structures in the temporal waveform that are responsible for crackle. Ensemble-averages of the identified waveform sections are employed to gain an in-depth understanding of the crackling structures. Moreover, PDF's of the temporal intermittence of these shocks reveal modal trends and show evidence that crackling shock-structures are present in groups of multiple shocks. A spectral measure of crackle is considered by using wavelet-based time-frequency analyses. The increase in sound energy is computed by considering the global pressure spectra of the waveforms and the ones that represent the spectral behavior during instances of crackle. This energy-based metric is postulated to be an appropriate metric for the level of crackle.Aerospace Engineerin