The significant impacts of pressure-flow scour have emerged as a critical concern in recent decades, largely due to the severe environmental effects of climate change. Earlier research primarily concentrated on estimating the maximum pressure-flow scour depth around cylindrical bridge piers through dimensional analysis and theoretical approaches. However, the reliability of some previous equations for predicting the scour depth has been questioned. This paper introduces two new theoretical methods to enhance the predictive accuracy of pressure-flow scour depth around cylindrical piers. Using the existing equations for maximum scour depth along the vertical jet centerlines, the first method adapts these principles to develop an equation for the pressure-flow scour around cylindrical bridge piers. The second method is grounded in phenomenological turbulence theory. It employs two distinct equations for calculating the angle and velocity of the combined jet, as well as the effective depth under the bridge deck. The equations formulated in this research have been calibrated using datasets that span sufficiently long-time intervals. The results indicate that both methods can accurately predict the maximum pressure-flow scour depth at equilibrium time. Notably, statistical indicators suggest that the second method offers significantly better results compared to the first and previous equations.

Abstract The effect of a square-mesh wire grid on the compressible flow of an organic vapor was investigated, utilizing a closed-loop wind tunnel facility working with the fluid Novec 649 in the dilute gas regime. Due to its thermodynamic properties, this working fluid enabled hot-wire anemometry investigations while avoiding typical issues related to calibration and data reduction as usually observed in compressible flows. Due to the low speed of sound, the mean velocity level could be kept low, which was helpful regarding frequency resolution issues. The results of the experiments conducted under essentially incompressible flow conditions agreed well with the predictions of the turbulence theory, and a good level of isotropy was achieved downstream of the grid. With increasing flow Mach number, the anisotropy of the turbulence increased, and the isotropy was practically lost at flow Mach numbers in the range of the grid choking Mach number. The flow Mach number normalized by the grid choking Mach number was identified as a useful, primary variable for presenting the experimental data.

Recent research has indicated the existence of slow diffusion phenomena in pulsar wind nebulae (PWNe), where the diffusion coefficient of particles is significantly smaller than the value considered to be the average in the Galaxy. We aim to explore the particle slow diffusion mechanism in the frame of a time-dependent model with particle advection and diffusion. Based on the turbulence theories, the gyroresonant interactions between the particles and turbulent waves are considered, which enables us to determine the diffusion coefficients of particles within nebulae via the turbulence injection scale and magnetic field components (ordered magnetic field and turbulent magnetic field). Meanwhile, by considering injection, advection, adiabatic loss and radiative loss of particles, the multiband nonthermal emission from a PWN is produced by the relativistic leptons through synchrotron radiation and inverse Compton process. The diffusion coefficient increases with injection scale, whereas it decreases with the turbulent-to-ordered magnetic field strength ratio. Meanwhile, effects of turbulent injection scale and magnetic field components on spectral energy distributions (SEDs) are analyzed. This model is applied to HESS J1420-607, and the observed spectral energy distribution of photon emission is reproduced well. The results suggest that (1) the particle cooling processes are dominated by adiabatic loss in lower-energy bands and IC scattering losses dominate for the higher-energy particles; (2) the advection is the most prominent process to particle transport within this nebula, and the diffusion only plays a role in the high-energy band. More importantly, our model estimates the current diffusion coefficient at an electron energy of 1 TeV 2.6 times 10^ cm^2s^-1, and the slow diffusion mechanism may be caused by the small-scale turbulent injection and relatively ordered magnetic field distribution within HESS J1420-607.

ABSTRACT The first issue of the Journal of Family Communication was published in 2001, the same year as the publication of the inaugural study investigating processes of relational turbulence. To mark the 25th anniversary of both events, we consider the applicability of relational turbulence theory beyond its original focus on romantic relationships to family relationships. We trace research on relational turbulence from dating relationships to marital relationships to non-marital dyads in the family, theorize about the relevance of the theory’s key constructs in family contexts, and delineate implications for both research and practice. Our synthesis emphasizes points of both convergence and divergence in relational turbulence processes within romantic dyads versus family systems. Along the way, we identify opportunities for future research to usher in a new era of scholarship on relational turbulence and family communication.

We report the numerical observation of a far-from-equilibrium equation of state (EOS) in the Gross-Pitaevskii (GP) model. We first show that the momentum distribution of the turbulent cascade is well described by wave-turbulent kinetic theory in the appropriate limits. Calculating the energy and particle fluxes Π ϵ ( k ) and Π N ( k ) , we show that the turbulent state possesses the hallmarks of a direct energy cascade. Building on this, we show that the GP model encodes a universal EOS in the form of a relationship between the turbulent cascade’s momentum distribution amplitude n 0 and the energy flux ε in the steady state. We find that in our regime of “mixed” turbulence—where both vortices and waves play a significant role— n 0 ∝ ε 0.67 ( 2 ) , a result that is not captured by any existing theory of turbulence but that agrees with a recent experimental measurement for large energy fluxes. Finally, we find that the concept of quasi-static thermodynamic processes between equilibrium states extends to far-from-equilibrium steady states.

Kinetic theory offers a promising alternative to conventional turbulence modelling by providing a mesoscopic perspective that naturally captures non-equilibrium physics such as non-Newtonian effects. In this work, we present an extension and theoretical analysis of the kinetic model for incompressible turbulent flows developed by Chen et al. ( Atmosphere , 2023, vol. 14(7), p. 1109), constructed for unbounded flows. The first extension is to reselect a relaxation time such that the turbulent transport coefficients are obtained consistently and better align with well-established turbulence theory. The Chapman–Enskog (CE) analysis of the kinetic model reproduces the linear eddy-viscosity and gradient diffusion models for Reynolds stress and turbulent kinetic energy flux at the first order, and yields nonlinear eddy-viscosity and closure models at the second order. In particular, a previously unreported CE solution for turbulent kinetic energy flux is obtained. The second extension is to enable the model for wall-bounded turbulent flows with preserved near-wall asymptotic behaviours. This involves developing a low-Reynolds-number model incorporating wall damping effects and viscous diffusion, with boundary conditions enabling both viscous sublayer resolution and wall function application. Comprehensive validation against experimental and direct numerical simulation data for turbulent Couette flow demonstrates excellent agreement in predicting mean velocity profiles, skin friction coefficients and Reynolds shear-stress distributions, although the near-wall-normal stress anisotropy is underestimated. The results show that averaged turbulent flow behaves similarly to rarefied-gas flow at finite Knudsen number, capturing non-Newtonian effects beyond linear eddy-viscosity models. This kinetic model provides a physics-based foundation for turbulence modelling with reduced empirical dependence.

Bed shear stress is a key parameter governing sediment transport and fluxes at the sediment–water interface. In vegetated channels, predicting bed shear stress, especially for rough beds, remains a challenge. This study developed a unified theoretical model for bed shear stress that smoothly spans conditions from bare bed to vegetated bed for both smooth and rough beds. Building on phenomenological turbulence theory, the model relates bed shear stress to the characteristic velocities of the larger energy-containing eddies and the smaller, near-bed eddies, with the new assumption that the bottom boundary layer (BBL) thickness controls the larger, energy-containing eddy length scale. The BBL was defined as the region within which the bed shear stress contributed significantly, compared to vegetation drag, and a force balance predicted that the BBL thickness scales with the ratio of bed shear stress to vegetation drag. In the limit of zero vegetation density, the BBL thickness equals the water depth, and the bed shear stress model reduces to the classical bare bed formulation. With increasing vegetation density (drag), the thickness of the boundary layer decreases, and the bed friction coefficient increases, which is consistent with previous observations. For rough beds, the bed friction coefficient increases with bed roughness, but is not dependent on the mean velocity. In contrast, for smooth beds, the bed friction coefficient decreases with increasing mean velocity. The coupled models for bed shear stress and BBL thickness were compared against 114 physical and numerical experiments from multiple previous studies.

Recent advances in turbulent transport theory in magnetized plasmas point to applicability across a wide range of physical systems, including fluids and optical media. These findings highlight the central role of nonlinear processes and motivate generalized modeling

In spring 2020, school boards across the country were suddenly confronted with a public health crisis that threatened an unknown impact on children as young as five years old. They had to make sense of constantly shifting information and data about the virus and subsequently create or adapt policies related to school closures, adjustments to online learning platforms, mandating masks and other COVID-mitigating strategies. We pose two questions: 1) How did the turbulence of the COVID-19 pandemic experience affect the two districts? and 2) What influenced the severity of the turbulence that the school boards experienced? This paper uses a comparative case study research design to understand how school board members in two districts experienced and navigated pandemic-related turbulence. We apply turbulence theory and its three drivers, positionality, cascading, and stability. The findings illustrate that one district faced higher turbulence due to its greater instability. The other district avoided extreme turbulence through diverse board representation and strong collegiality which enabled the board to maintain a unified voice through challenges. The other district, however, benefited from long-term board members and internally hiring their superintendent, ensuring leadership continuity. The two districts experienced different levels of turbulence, yet both were able to maintain relative stability through strong collaboration or sustained leadership practices.

Context. Switchbacks–transient, large-angle deflections of the interplanetary magnetic field–pervade the solar wind, yet their origin remains disputed. Current ex situ theories, notably coronal jets and interchange reconnection, are typically tested on day-scale intervals. Aims. We aim to establish a connection between switchbacks and ex situ theories on solar-cycle timescales. Methods. We exploited 27 years of continuous in situ measurements from ACE, Wind, and STEREO-A/B at 1 au, complemented by synoptic remote-sensing data from SDO, to examine the solar-cycle modulation of switchback occurrence and to test whether ex situ scenarios (coronal jets and interchange reconnection) play a dominant role in such long-term modulation. Results. The switchback occurrence rate correlates strongly with Alfvénicity ( cc = 0.70 ± 0.04) and shows no solar-maximum preference (independent of the sunspot number, cc = 0.13 ± 0.05). Coronal jets affect switchbacks only indirectly via modulation of the solar wind speed. Multi-spacecraft consensus confirms that a stable, Alfvénicity-dependent process governs switchback variability, rather than episodic surface drivers. In addition, these results are robust to the deflection threshold of switchbacks. These findings impose quantitative constraints on theories of solar-wind turbulence and the transport of magnetic energy from the Sun to interplanetary space.

We discussed a variant of a new theory of local similarity (NTLS) that uses, as basic parameters, the “spectral” Prandtl mixing length and the second moment of the vertical velocity. This approach allows turbulent exchange coefficients, the dissipation of turbulent kinetic energy, and mixed moments of buoyancy and vertical velocity to be expressed solely through two independent basic parameters of local similarity. Comparison of the local similarity approximations with experimental data supports the proposed relations and demonstrates the high effectiveness of NTLS. The results of the new theory of local similarity are compared with well known semi-empirical turbulence theories. It is shown that, throughout the atmospheric convective boundary layer, the local similarity approximations for the turbulent exchange coefficient and the dissipation of kinetic energy are fully consistent with the relations of the semi-empirical theories of Prandtl, Richardson–Onsager, and Hanna. Under weak wind conditions, partial consistency with Taylor's semi-empirical theory is demonstrated. For the semi-empirical theories of von Kármán and Prandtl–Kolmogorov, partial consistency with local similarity is established. Above the surface convective layer, the relations of these theories differ from the NTLS approximations, while within the convective surface layer their relations are identical to the local similarity approximations. In the surface layer, the NTLS approximations are also compared with the classical Monin–Obukhov similarity theory (MOST). It is established that, in windless conditions, the surface asymptotics of NTLS are identical to the free convection limits of MOST.

A dataset of high-resolution snapshots of the viscous sublayer from direct numerical simulation of a turbulent boundary layer up to Re θ=2400.

PFAS contamination represents a slow, invisible chronic technological disaster with documented long-term psychosocial impacts on affected communities. However, existing research has predominantly focused on toxicological and biomedical outcomes, leaving the lived experiences and narrative dimensions of contamination underexplored. This study investigates how residents of PFAS-contaminated communities experience and narrate environmental contamination by applying Edelstein's Theory of Environmental Turbulence (TET) and integrating a bottom-up stage-based model of psychosocial reaction with narrative epidemiology. Twenty-five personal narratives were selected from the digital archive Living With PFAS and analyzed through thematic analysis. Three main themes emerged, corresponding to the TET dimensions of lifescape, lifestyle, and lifestrain, articulated across twelve subthemes: inversion of health, self, home community and place, environment, livelihood, trust, environmental stigma, shock and fear, chronic concern, anger, parental guilt and relation strain. The findings demonstrate that PFAS contamination produces multidimensional disruptions that extend beyond toxic exposure to encompass identity, social relationships, institutional trust, and collective memory. Integrating TET with Psycho-Social Impact Assessment (PSIA) offers a theoretically grounded and exploratory transdisciplinary framework for identifying hidden suffering and informing more responsive environmental health policies and community interventions.

Relational turbulence theory explains the mechanisms whereby relationship parameters influence partners’ emotion, cognition, and communication during specific episodes. Using dyadic, collaborative interactions, this study tested three understudied claims proposed by the theory to shed light on the antecedents and consequences of emotion during everyday conversations between romantic partners. Seventy-one couples completed a pre-test survey that included measures of relationship parameters, were video-taped participating in two planning discussions (randomly ordered), and completed post-tests after each discussion. The conversations were then evaluated for communication engagement and valence by outside observers. Results point to relationship uncertainty as a predictor of emotion during communication and add nuance to our understanding of how happiness and annoyance associate with communicative valence and engagement during everyday interactions.

To improve the accuracy of turbulence identification in low-altitude flight safety monitoring, a turbulence intensity modeling and optimization method based on Turbulent Kinetic Energy theory and the XGBoost model is proposed. Firstly, atmospheric stability is determined using the Richardson number. Subsequently, turbulence intensity is calculated by combining different stability conditions and Turbulent Kinetic Energy theory. The data for constructing physical model a originates from observations obtained by wind profile radar and microwave radiometer. Considering that temperature and humidity detection equipment like microwave radiometers are not always available in real-world scenarios, and in observation scenarios relying solely on wind profile radar, a Gradient Boosting Decision Tree algorithm is further introduced to construct a turbulence inversion model based exclusively on wind profile radar data. This model fully exploits the nonlinear relationships between multi-dimensional observational features such as radial velocity, velocity spectrum width, and signal-to-noise ratio of the radar and turbulence intensity. It is trained using the output of the benchmark model. Experimental results indicate that after optimizing the turbulence intensity calculation model b (based solely on wind profile radar) with model a, the model’s MSE decreases by 0.11, MAE decreases by 0.13, and the R² value increases by 0.28. This optimization process reduces reliance on auxiliary temperature and humidity data and effectively addresses the challenge of turbulence identification under limited observational information.

We theoretically and experimentally investigate spontaneous self-organization in a conservative (Hamiltonian) turbulent wave system, operating far from thermodynamic equilibrium. Our system is governed by two coherently coupled nonlinear Schrödinger equations, describing the polarization evolution of light in a dispersive nonlinear optical fiber. The analysis reveals the emergence of two fundamentally distinct turbulent regimes. In a first regime, the waves undergo a slow, irreversible thermalization process, which is accurately described by the wave turbulence kinetic equation and the associated H theorem of entropy growth. In stark contrast with this expected irreversible process, we identify a second different regime, where strong phase correlations spontaneously emerge, giving rise to a fast reversible oscillatory dynamics of the normal correlator and anomalous phase correlator. Experimental observations confirm the occurrence of both irreversible thermalization and reversible dynamics mediated by the anomalous correlated fluctuations.

Recent Parker Solar Probe (PSP) measurements have revealed that solar wind (SW) turbulence transits from a subsonic to a transonic regime near the Sun, while remaining sub-Alfvénic. These observations call for a revision of the existing SW models, where turbulence is considered to be both subsonic and sub-Alfvénic. In this work, we introduce a new magnetohydrodynamic (MHD) model of transonic sub-Alfvénic turbulence (TsAT). We used 3D MHD simulations initialized with parameters measured by PSP to investigate the properties of the new near-Sun SW transonic turbulent regime. We then derived a reduced set of MHD equations in the transonic sub-Alfvénic limit to interpret our numerical results. Our TsAT model shows that turbulence is effectively nearly incompressible (NI) and has a 2D + slab (quasi-2D) geometry not only in the subsonic limit, but also in the transonic regime, as long as it remains sub-Alfvénic, a condition essentially enforced everywhere in the heliosphere by the strong local magnetic field. These predictions are consistent with 3D MHD simulations, showing that transonic turbulence is dominated by low-frequency quasi-2D incompressible structures, while compressible fluctuations are a minor component corresponding to low-frequency slow modes and high-frequency fast modes. Our new TsAT model extends existing NI theories of turbulence, and is potentially relevant for the theoretical and numerical modeling of space and astrophysical plasmas, including the near-Sun SW, the solar corona, and the interstellar medium.

This article examines the features and regularities in the amplitude-frequency response of the hydrodynamic sound of liquid turbulent flow in a pipeline. The objective of the study is to develop a theoretical foundation for the creation of a high-precision in-line diagnostic device based on the analysis of acoustic signals. This requires identifying the features and regularities of the amplitude-frequency response of the hydrodynamic sound of liquid turbulent flow and developing a mathematical model of its origin during flow around various elements of a pipeline system. This paper analyzes the theoretical foundations of hydrodynamic noise generation in liquid turbulent flow in accordance with A. N. Kolmogorov's theory of turbulence. Numerical modeling using the COMSOL Multiphysics software package was used to test the hypothesis regarding the formation of characteristic stationary vortices on geometric inhomogeneities and defects. Numerical modeling yielded velocity distributions within the internal cavity of the studied objects, as well as the parameters (size and frequency) of stationary vortices generated in the areas of through faults and tee branches. The feasibility of identifying the location through faults and pipeline fittings based on the parameters of the stationary vortices they generate was theoretically substantiated and confirmed by numerical modeling. The obtained results form the basis for developing algorithms for analyzing diagnostic data from acoustic in-line devices, which will improve the accuracy and efficiency of leak and unauthorized tie-in detection.

In this work we consider the problem of constructing initial conditions for a flow model such that the resulting flow evolution leads to a self-similar energy cascade consistent with Kolmogorov's statistical theory of turbulence. As a first step in this direction, we focus on the one-dimensional viscous Burgers equation as a toy model. Its solutions exhibiting self-similar behavior, in a precisely defined sense, are found by framing this problem in terms of partial differential equation (PDE)-constrained optimization. The main physical parameters are the time window over which self-similar behavior is sought (equal to approximately one eddy turnover time), viscosity (inversely proportional to the “Reynolds number”), and an integer parameter characterizing the distance in the Fourier space over which self-similar interactions occur. Local solutions to this nonconvex PDE optimization problem are obtained with a state-of-the-art adjoint-based gradient method. Two distinct families of solutions, termed and , are identified and are distinguished primarily by the behavior of enstrophy which, respectively, uniformly decays and grows in the two cases. The physically meaningful and appropriately self-similar inertial solutions are found only when a sufficiently small viscosity is considered. These flows achieve the self-similar behavior by a uniform steepening of the wave fronts present in the solutions. The results obtained demonstrate that the proposed methodology may be used to search for self-similar behavior in more complex flow models, including shell models, two-dimensional turbulence, and, ultimately, three-dimensional turbulence.

The elliptic approximation (EA) – rooted in Taylor’s frozen flow hypothesis, Kolmogorov’s theory of small-scale turbulence, and the Kraichnan–Tennekes random sweeping hypothesis – remains a foundational framework for modelling spatiotemporal velocity correlations in incompressible wall-bounded turbulence. This study revisits the model’s theoretical basis, and extends its applicability to velocity and temperature fluctuations in supersonic channel flows. First, we identify non-elliptic distortions in the viscous sublayer, and introduce a shear-induced acceleration that captures the observed deviation from the assumed constant convection velocity at large time separations. Next, we show that the inertial-range scalings underpinning the EA are not valid in regions where the model remains accurate; instead, its validity is supported by extended self-similarity between spatial and temporal structure functions. Finally, we conduct high-fidelity direct numerical simulations of compressible channel flows with fluctuating Mach numbers up to 0.8; our data confirm the robustness of the EA under supersonic conditions, and its effectiveness in characterising both velocity and temperature correlations. Together, these findings provide new theoretical insights into the spatiotemporal structure of wall-bounded turbulence, and broaden the operational envelope of the EA.