Modelling the nonlinear forcing is critical for linear models based on resolvent or input–output analyses. For compressible wall-bounded turbulence, little is known on what the real forcing looks like due to limited data, so the prediction agrees more qualitatively than quantitatively with direct numerical simulations (DNSs). Here, we present detailed forcing statistics of stochastic linear models, derived from elaborate DNS datasets for channel flows with bulk Mach number reaching 3. These statistics directly explain the success and failure of current models and provide guidance for further improvements. The benchmark linearised Navier–Stokes (LNS) and eLNS models are considered; the latter is assisted by eddy-viscosity-related terms. First, we prove the self-consistency of the models by using DNS-computed forcing as the input. Second, we present the spectral distributions of the forcing and its components. Third, we quantify the acoustic components, absent in incompressible cases, within the linear models. We reveal that the LNS forcing can exhibit relatively high coherence and low rank, very different from the modelled diagonal full-rank forcing. The eddy-viscosity-related term is not partial modelling of the LNS forcing; contrarily, the former is much larger than the latter, serving to disrupt the low-rank feature, enhance diagonal dominance and increase robustness across scales. The scales narrow in either horizontal direction are most susceptible to acoustic modes, while the others are little affected (${\lt}2\,\%$ in energy). Furthermore, the extended strong Reynolds analogy is assessed in predicting the density and temperature components.

The NutriLight system presents a novel dietary approach designed to enhance health communication, promote sustainable eating habits, and address limitations in existing dietary patterns. Using a traffic light scoring system, it simplifies dietary recommendations, making them more accessible and adaptable across diverse populations. Unlike rigid diets, NutriLight categorises foods into green, yellow, and red groups, encouraging balance rather than restriction. This flexibility allows for cultural adaptations, ensuring relevance in different dietary contexts while supporting planetary health. Additionally, NutriLight mitigates the risk of nutrient deficiencies by emphasising whole, minimally processed foods and reducing overconsumption of unhealthy options. While promising, its effectiveness depends on proper implementation, localised adaptation, and long-term evaluation to confirm its health benefits. By bridging the gap between nutritional science and practical application, NutriLight has the potential to serve as an effective tool in public health nutrition, fostering healthier and more sustainable dietary choices worldwide.

The skin-friction coefficient is a dimensionless quantity defined by the wall shear stress exerted on an object moving in a fluid, and it decreases as the Reynolds number increases for wall-bounded turbulent flows over a flat plate. In this work, a novel transformation, based on physical and asymptotic analyses, is proposed to map the skin-friction relation of high-speed turbulent boundary layers (TBLs) for air described by the ideal gas law to the incompressible skin-friction relation. Through this proposed approach, it has been confirmed theoretically that the transformed skin-friction coefficient $C_{f,i}$, and the transformed momentum-thickness Reynolds number $Re_{\theta ,i}$ for compressible TBLs with and without heat transfer, follow a general scaling law that aligns precisely with the incompressible skin-friction scaling law, expressed as $ (2/C_{f,i} )^{1/2}\propto \ln Re_{\theta ,i}$. Furthermore, the reliability of the skin-friction scaling law is validated by compressible TBLs with free-stream Mach number ranging from $0.5$ to $14$, friction Reynolds number ranging from $100$ to $2400$, and the wall-to-recovery temperature ratio ranging from $0.15$ to $1.9$. In all of these data, $ (2/C_{f,i} )^{1/2}$ and $\ln Re_{\theta ,i}$ based on the present theory collapse to the incompressible relation, with a squared Pearson correlation coefficient reaching an impressive value $0.99$, significantly exceeding $0.85$ and $0.86$ based on the established van Driest II and the Spalding–Chi transformations, respectively.

The well-known quadratic temperature–velocity (TV) relation is significant for physical understanding and modelling of compressible wall-bounded turbulence. Meanwhile, there is an increasing interest in employing the TV relation for laminar modelling. In this work, we revisit the TV relation for both laminar and turbulent flows, aiming to explain the success of the TV relation where it works, improve its accuracy where it deviates and relax its limitation as a wall model for accurate temperature prediction. We show that the general recovery factor defined by Zhang et al. (J. Fluid. Mech., vol. 739, 2014, pp. 392–440) is not a wall-normal constant in most laminar and turbulent cases. The effective Prandtl number $Pr_e$ is more critical in determining the shape of temperature profiles. The quadratic TV relation systematically deviates for laminar boundary layers irrespective of Mach number and wall boundary conditions. We find a universal distribution of $Pr_e$, based on which the TV relation can be notably improved, especially for cold-wall cases. For turbulent flows, the TV relation as the wall model can effectively improve the near-wall temperature prediction for cold-wall boundary layer cases, but it involves boundary-layer-edge quantities used in the Reynolds analogy scaling, which hinders the application of the wall model in complex flows. We propose a transformation-based temperature wall model by solving inversely the newly developed temperature transformation of Cheng and Fu (Phy. Rev. Fluids, vol. 9, 2024, no. 054610). The dependence on edge quantities is thus removed in the new model and the high accuracy in turbulent temperature prediction is maintained for boundary layer flows.

Mamyshev oscillators (MOs) demonstrate extraordinarily superior performance compared with fiber laser counterparts. However, the realization of a fully fiberized, monolithic laser system without pulse degradation remains a key challenge. Here we present a high-energy MO using large mode area Yb-doped fiber and fiber-integrable interferometric super-Gaussian spectral filters that directly generates a nearly diffraction-limited beam with approximately 9.84 W average power and 533 nJ pulse energy. By implementing pre-chirp management with anti-resonant hollow-core fiber (AR-HCF), the adverse effects of super-Gaussian filtering on pulse quality are effectively mitigated, enabling pulse compression to 1.23 times the transform limit. Furthermore, AR-HCF is employed to provide negative dispersion to compensate for the positive chirp of output pulses, resulting in approximately 37 fs de-chirped pulses with approximately 10 MW peak power. This approach represents a significant step toward the development of monolithic fiber lasers capable of generating and flexible delivery of sub-50-fs pulses with tens of megawatts peak power.

The eddy-viscosity model, as initially used to model the mean Reynolds stress, has been widely used in the linear analysis of turbulence recently by direct extension. In this study, the mechanism of the eddy viscosity in improving the prediction of fluctuation structures with linear analysis is clarified by investigating the statistical properties of forcing, eddy-viscosity term and their correlations. From the direct numerical simulation (DNS) results of turbulent channel flows with $Re_{\tau }=186$–$2003$, the spatial correlation of forcing is partially cancelled due to its interaction with eddy-viscosity terms. The stochastic forcing after excluding the eddy-viscosity term is nearly uncorrelated spatially, which better matches the condition where the resolvent modes are consistent with the spectral proper orthogonal decomposition (SPOD) modes from DNS. With the above findings, an optimisation framework is developed by minimising the spatial correlations of the stochastic forcing. The optimised eddy-viscosity profiles nearly overlap with the mean-quantity-based model in the near-wall region, but have different maximum values. Compared with the mean-quantity-based model, the optimised results enhance the consistency between the resolvent and DNS results significantly. Based on the optimised results, a new modelling framework is further abstracted, leaving only one to-be-modelled parameter of the maximum value of the eddy-viscosity profile. This parameter follows distinctive rules with spanwise flow scales, based on which a simplified predictive model is constructed. The resolvent modes predicted by the new model exhibit high consistency with SPOD modes, which are essentially comparable to the optimised results for wide ranges of streamwise and spanwise scales.

We study the melting process of a solid under microgravity, driven solely by lateral vibrations that are perpendicular to the applied temperature gradient due to the absence of gravity-induced convection. Using direct numerical simulations with the phase-field method, we examine two-dimensional vibration-induced melting in a square cavity over four orders of magnitude of vibrational Rayleigh numbers, $10^5\le Ra_{{vib}}\le 10^9$. Our results show that as melting progresses, the flow structure transitions from a periodic-circulation regime with diffusion-dominated heat transfer to a columnar regime with vibroconvection. The mean height of the liquid–solid interface follows a power-law dependency with time, $\bar {\xi } \sim \tilde t^{1/(2-2\alpha )}$, where $\alpha = 0$ in the periodic-circulation regime and $\alpha = 1/2$ in the columnar regime. We further observe that within the columnar regime, the morphological evolution of the liquid–solid interface is influenced by the interaction of columnar thermal plumes in the central regions and the peripheral flow near the sidewalls. Specifically, we offer a comprehensive analysis of the plume merging behaviour, which is governed by the aspect ratio ($\bar {\xi }$) of the liquid layer and the intensity of vibration, quantified by the effective vibrational Rayleigh number $Ra_{vib}^{eff}$. We identify the relationship between the number of columnar plumes $K_m$ and $Ra_{vib}^{eff}$, finding that $K_m \sim \bar {\xi }^{-1} (Ra_{vib}^{eff})^{\gamma }$ with the fitting scaling exponent $\gamma = 0.150 \pm 0.025$. We subsequently quantify the characteristics of the interface roughness amplitude evolution in microgravity vibroconvection. Our results indicate that the roughness amplitude exhibits a power-law dependence on the mean height of the liquid layer. Drawing from the Stefan boundary condition, we theoretically deduce this dependence under the assumption of a non-uniform heat flux distribution at the interface, where the theory is corroborated by our numerical simulations.

A high-energy pulsed vacuum ultraviolet (VUV) solid-state laser at 177 nm with high peak power by the sixth harmonic of a neodymium-doped yttrium aluminum garnet (Nd:YAG) amplifier in a KBe2BO3F2 prism-coupled device was demonstrated. The ultraviolet (UV) pump laser is a 352 ps pulsed, spatial top-hat super-Gaussian beam at 355 nm. A high energy of a 7.12 mJ VUV laser at 177 nm is obtained with a pulse width of 255 ps, indicating a peak power of 28 MW, and the conversion efficiency is 9.42% from 355 to 177 nm. The measured results fitted well with the theoretical prediction. It is the highest pulse energy and highest peak power ever reported in the VUV range for any solid-state lasers. The high-energy, high-peak-power, and high-spatial-uniformity VUV laser is of great interest for ultra-fine machining and particle-size measurements using UV in-line Fraunhofer holography diagnostics.

In the present study, we propose a Reynolds analogy model for compressible wall turbulence. This model is demonstrated to be able to alleviate the defects of the generalized Reynolds analogy model (GRA) (Zhang et al., J. Fluid Mech., vol. 739, 2014, pp. 392–420), and maintains its success in describing the mean velocity–temperature relation. Furthermore, the present model is superior to the GRA in depicting the relationship between their fluctuating fields and also bridges the gap between the phenomenological model and the mathematical representation of the Reynolds analogy. The key points of the present model are validated by analysing the data of compressible wall-bounded turbulence with different Mach numbers, Reynolds numbers and wall thermal conditions.

In this study, the resolvent-based estimation (RBE) is further generalised to cases with arbitrarily sampled measurements in time, where the generalised RBE is denoted as GRBE in this study. Different from the RBE that constructs the transfer function at each frequency, the GRBE minimises the estimation error energy in the physical temporal domain by considering the forcing and noise statistics. The GRBE is validated by estimating the complex Ginzburg–Landau equation and turbulent channel flows with the friction Reynolds number $Re_{\tau }=186$, 547 and 934, where the results from the RBE are also included. When the measurements are temporally resolved, the estimation results of the two approaches are equivalent to each other, and both match well with the reference numerical results. For the temporally unresolved cases, the estimation errors from the GRBE are obviously lower than those from the RBE. After validation, the GRBE is applied to investigate the impacts of the abundance of the measured information, including the temporal information and sensor types, on the estimation accuracy. Compared with the mean square error (MSE) in the estimation with temporally resolved measurements, that with measurements at only one snapshot, i.e. without any temporal information, increases by approximately $15\,\%$. On the other hand, it can effectively improve the estimation accuracy by increasing the number of sensor types. With temporally resolved measurements, the relative MSE decreases by $12.3\,\%$ when the sensor types increase from $\lbrace \tau _u \rbrace$ to $\lbrace \tau _u,\tau _w,p \rbrace$, where $\tau_u$, $\tau_w$ and p are the streamwise shear stress, spanwise shear stress and pressure at the wall. Finally, several existing forcing models are incorporated into the GRBE to investigate their performance in the linear estimation of flow state. The wall-distance-dependent model (W-model) results match well with the optimal linear estimations when the measurements are temporally unresolved. Meanwhile, with the increase of temporal information of the measurement, the estimation errors from the tested W-model and the scale-dependent model ($\lambda$-model) both increase, which contradicts the tendency observed in the optimal linear GRBE estimation results. Such a phenomenon highlights the importance of proper modelling of the forcing in the temporal domain for the accuracy of flow state estimation.

We report the unified constitutive law of vibroconvective turbulence in microgravity, i.e. $Nu \sim a^{-1} Re_{os}^\beta$ where the Nusselt number $Nu$ measures the global heat transport, $a$ is the dimensionless vibration amplitude, $Re_{os}$ is the oscillational Reynolds number and $\beta$ is the universal exponent. We find that the dynamics of boundary layers plays an essential role in vibroconvective heat transport and the $Nu$-scaling exponent $\beta$ is determined by the competition between the thermal boundary layer (TBL) and vibration-induced oscillating boundary layer (OBL). Then a physical model is proposed to explain the change of scaling exponent from $\beta =2$ in the TBL-dominant regime to $\beta = 4/3$ in the OBL-dominant regime. Our finding elucidates the emergence of universal constitutive laws in vibroconvective turbulence, and opens up a new avenue for generating a controllable effective heat transport under microgravity or even microfluidic environment in which the gravity effect is nearly absent.

In this work, we employ well-established relations for compressible turbulent mean flows, including the velocity transformation and algebraic temperature–velocity (TV) relation, to systematically improve the algebraic Baldwin–Lomax (BL) wall model for high-speed zero-pressure-gradient air boundary layers. Any new functions or coefficients fitted by ourselves are avoided. Twelve published direct numerical simulation (DNS) datasets are employed for a priori inspiration and a posteriori examination, with Mach numbers up to 14 under adiabatic, cold and heated walls. The baseline BL model is the widely used one with semilocal scalings. Three targeted modifications are made. First, we employ a total-stress-based transformation (Griffin et al., Proc. Natl Acad. Sci. USA, vol. 118, issue 34, 2021, e2111144118) to the inner-layer eddy viscosity for improved scaling up to the logarithmic region. Second, we utilize the van Driest transformation in the outer layer based on the compressible defect velocity scaling. Third, considering the difficulty in modelling the rapidly varying and singular turbulent Prandtl number near the temperature peak in cold-wall cases, we design a two-layer strategy and use the TV relation to formulate the inner-layer temperature. Numerical results prove that the modifications take effect as designed. The prediction accuracy for mean streamwise velocity is notably improved for diabatic cases, especially in the logarithmic region. Moreover, a significant improvement in mean temperature is realized for both adiabatic and diabatic cases. The mean relative errors of temperature to DNS for all cases are down to 0.4 % in the logarithmic wall-normal coordinate and 3.4 % in the outer coordinate, around one-third of those in the baseline model.

It is generally believed that the velocity and passive scalar fields share many similarities and differences in wall-bounded turbulence. In the present study, we conduct a series of direct numerical simulations of compressible channel flows with passive scalars and employ the two-dimensional spectral linear stochastic estimation and the correlation function as diagnostic tools to shed light on these aspects. Particular attention is paid to the relevant multiphysics couplings in the spectral domain, i.e. the velocity–temperature ($u-T$), scalar–temperature ($g-T$) and velocity–scalar ($u-g$) couplings. These couplings are found to be utterly different at a given wall-normal position in the logarithmic and outer regions. Specifically, in the logarithmic region, the $u-T$ and $u-g$ couplings are tight at the scales that correspond to the attached eddies and the very large-scale motions (VLSMs), whereas the $g-T$ coupling is robust in the whole spectral domain. In the outer region, $u-T$ and $u-g$ couplings are only active at the scales corresponding to the VLSMs, whereas the $g-T$ coupling is diminished but still strong at all scales. Further analysis indicates that although the temperature field in the vast majority of zones in a channel can be roughly treated as a passive scalar, its physical properties gradually deviate from those of a pure passive scalar as the wall-normal height increases due to the enhancement of the acoustic mode. Furthermore, the deep involvement of the pressure field in the self-sustaining process of energy-containing motions also drives the streamwise velocity fluctuation away from a passive scalar. The current work is an extension of our previous study (Cheng & Fu, J. Fluid Mech., vol. 964, 2023, A15), and further uncovers the details of the multiphysics couplings in compressible wall turbulence.