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A novel data-driven modal analysis method, reduced-order variational mode decomposition (RVMD), is proposed, inspired by the Hilbert–Huang transform and variational mode decomposition (VMD), to resolve transient or statistically non-stationary flow dynamics. First, the form of RVMD modes (referred to as an ‘elementary low-order dynamic process’, ELD) is constructed by combining low-order representation and the idea of intrinsic mode function, which enables the computed modes to characterize the non-stationary properties of space–time fluid flows. Then, the RVMD algorithm is designed based on VMD to achieve a low-redundant adaptive extraction of ELDs in flow data, with the modes computed by solving an elaborate optimization problem. Further, a combination of RVMD and Hilbert spectral analysis leads to a modal-based time-frequency analysis framework in the Hilbert view, providing a potentially powerful tool to discover, quantify and analyse the transient and non-stationary dynamics in complex flow problems. To provide a comprehensive evaluation, the computational cost and parameter dependence of RVMD are discussed, as well as the relations between RVMD and some classic modal decomposition methods. Finally, the virtues and utility of RVMD and the modal-based time-frequency analysis framework are well demonstrated via two canonical problems: the transient cylinder wake and the planar supersonic screeching jet.
The highly nonlinear evolution of the single-mode stratified compressible Rayleigh–Taylor instability (RTI) is investigated via direct numerical simulation over a range of Atwood numbers ($A_T=0.1$–$0.9$) and Mach numbers ($Ma=0.1$–$0.7$) for characterising the isothermal background stratification. After the potential stage, it is found that the bubble is accelerated to a velocity which is well above the saturation value predicted in the potential flow model. Unlike the bubble re-acceleration behaviour in quasi-incompressible RTI with uniform background density, the characteristics in the stratified compressible RTI are driven by not only vorticity accumulation inside the bubble but also flow compressibility resulting from the stratification. Specifically, in the case of strong stratification and high $A_T$, the flow compressibility dominates the bubble re-acceleration characters. To model the effect of flow compressibility, we propose a novel model to reliably describe the bubble re-acceleration behaviours in the stratified compressible RTI, via introducing the dilatation into the classical model that takes into account only vorticity accumulation.
Without rapid international action to curb greenhouse gas emissions, climate scientists have predicted catastrophic sea-level rise by 2100. Globally, archaeologists are documenting the effects of sea-level rise on coastal cultural heritage. Here, the authors model the impact of 1m, 2m and 5m sea-level rise on China's coastal archaeological sites using data from the Atlas of Chinese Cultural Relics and Shanghai City's Third National Survey of Cultural Relics. Although the resulting number of endangered sites is large, the authors argue that these represent only a fraction of those actually at risk, and they issue a call to mitigate the direct and indirect effects of rising sea levels.
We have demonstrated and studied polymeric solid-state dye lasers (SSDLs) fabricated by three-dimensional (3D) polystyrene colloidal crystals and tert-butyl roadamine B (t-Bu RhB) doped Poly (methyl methacrylate) (PMMA) films with different film thickness. The sandwich-typed resonator cavities with different active layer thickness display single-mode lasing oscillations in the reflection bandgap of the colloidal crystals. The lasing thresholds could be optimized by changing the thickness of t-Bu RhB doped PMMA films, which is as low as 7.43 W/cm2. Adjusting active layer thickness would provide an opportunity to accelerate the development of fabricating polymeric SSDLs with low threshold.
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