Hydrodynamic Fluctuations Research Articles

Hydrodynamic fluctuations near a Hopf bifurcation: Stochastic onset of vortex shedding behind a circular cylinder

Hydrodynamic fluctuations near a Hopf bifurcation: Stochastic onset of vortex shedding behind a circular cylinder

The impact of changes in water–sediment relationships at river confluences on the evolution of river bars

The confluence of tributaries and the main stream affects riverbed siltation and alters the upstream water–sediment relationships and flow structure of the main stream by adding additional flow. The relationship between these changes and the evolution of river bars, however, is yet to be fully understood. In this study, the areas of the river bars were extracted from Landsat image and analyzed using soft clustering to identify evolutionary patterns of the bars at the confluence of the Fen River (FR) and Yellow River (YR), and to analyze the hydrodynamic mechanism with hydrodynamic modeling. The results show that the spatial and temporal evolution of river bars in the study area over the past 50 years exhibits an evolutionary pattern, which exhibited evident clustering distributions and significant stage-based characteristics. This pertains to the water–sediment relationships as well as hydrodynamic fluctuations. At the confluence of FR and YR, the intensity of fluvial erosion experiences a mean increment of 9.67 %, while the incoming sediment coefficient witnesses a mean reduction of 5.74 %. The position of the confluence point exhibits a close association with the evolutionary characterized of spatial clustering and temporal phasing of the river bars. The river confluence area showcases a complex turbulence structure, wherein alterations in sediment transport capacity occur due to the influence of secondary flow and the topography of the confluence area. Consequently, this impacts the flushing of river sandbars and brings about modifications in siltation. Overall, this study provides the scientific basis for YR sediment management and channel modification in response to changing runoff and sediment conditions.

Strategizing internals’ geometry to improve resilience of marinized bubbling fluidized beds to roll-induced maldistribution

Marinized bubbling fluidized beds show potential for reducing ship exhaust emissions, but their performance is hampered by the unstable marine environment, which affects their hydrodynamic stability. This study addresses the challenge of roll-induced maldistribution by testing different geometric strategies of bed internals to improve operational resilience. Direct visualization techniques (including digital image analysis and particle image velocimetry) were used to investigate the hydrodynamics and stability of bubbling fluidized beds under various configurations in pseudo-2D vertical, inclined, and rolling conditions. Internal designs, such as rhombic and herringbone patterns, and vertical baffle arrays, significantly shield the beds from gas maldistribution and provide stable fluidization comparable to conventional aboveground setups. The rhombic internals achieved up to 93% of the stability of classical vertical configurations without internals, while the herringbone reached 60 % and the vertical baffles reached 55 %. These configurations mitigate hydrodynamic fluctuations due to oscillations, improving operational reliability to effectively reduce emissions in marine environments.

Floating active carpets drive transport and aggregation in aquatic ecosystems

Communities of swimming microorganisms often thrive near liquid–air interfaces. We study how such ‘active carpets’ shape their aquatic environment by driving biogenic transport in the water column beneath them. The hydrodynamic stirring that active carpets generate leads to diffusive upward fluxes of nutrients from deeper water layers, and downward fluxes of oxygen and carbon. Combining analytical theory and simulations, we examine the biogenic transport by studying fundamental metrics, including the single and pair diffusivity, the first passage time for particle pair encounters and the rate of particle aggregation. Our findings reveal that the hydrodynamic fluctuations driven by active carpets have a region of influence that reaches orders of magnitude further in distance than the size of the organisms. These non-equilibrium fluctuations lead to a strongly enhanced diffusion of particles, which is anisotropic and space dependent. Fluctuations also facilitate encounters of particle pairs, which we quantify by analysing their velocity pair correlation functions as a function of distance between the particles. We found that the size of the particles plays a crucial role in their encounter rates, with larger particles situated near the active carpet being more favourable for aggregation. Overall, this research broadens our comprehension of aquatic systems out of equilibrium and how biologically driven fluctuations contribute to the transport of fundamental elements in biogeochemical cycles.

Hydrodynamic fluctuations and topological susceptibility in chiral magnetohydrodynamics

Chiral magnetohydrodynamics is devoted to understanding the late-time and long-distance behavior of a system with an Adler-Bell-Jackiw anomaly at finite temperatures. The non-conservation of the axial charge is determined by the topological density \vec{E} \cdot \vec{B}E→⋅B→; in a classical hydrodynamic description this decay rate can be suppressed by tuning the background magnetic field to zero. However it is in principle possible for thermal fluctuations of \vec{E} \cdot \vec{B}E→⋅B→ to result in a non-conservation of the charge even at vanishing BB-field; this would invalidate the classical hydrodynamic effective theory. We investigate this by computing the real-time susceptibility of the topological density at one-loop level in magnetohydrodynamic fluctuations, relating its low-frequency limit to the decay rate of the axial charge. We find that the frequency-dependence of this susceptibility is sufficiently soft as to leave the axial decay rate unaffected, validating the classical hydrodynamic description. We show that the susceptibility contains non-analytic frequency-dependence which is universally determined by hydrodynamic data. We comment briefly on possible connections to the recent formulation of the ABJ anomaly in terms of non-invertible symmetry.

Barrier crossing in a viscoelastic medium under active noise: Predictions of Kramers’ flux-over-population method

The biochemical activity inside a cell has recently been suggested to act as a source of hydrodynamic fluctuations that can speed up or slow down enzyme catalysis [Tripathi et al., Commun. Phys. 5, 101 (2022).] The idea has been tested against and largely corroborated by simulations of activated barrier crossing in a simple fluid in the presence of thermal and athermal noise. The present paper attempts a wholly analytic solution to the same noise-driven barrier crossing problem but generalizes it to include viscoelastic memory effects of the kind likely to be present in cellular interiors. A calculation of the model’s barrier crossing rate, using Kramers’ flux-over-population formalism, reveals that in relation to the case where athermal noise is absent, athermal noise always accelerates barrier crossing, though the extent of enhancement depends on the duration τ0 over which the noise acts. More importantly, there exists a critical τ0—determined by the properties of the medium—at which Kramers’ theory breaks down and, on approach to which, the rate grows significantly. The possibility of such a giant enhancement is potentially open to experimental validation using optically trapped nanoparticles in viscoelastic media that are acted on by externally imposed colored noise.

Consistent inclusion of fluctuations in first-order causal and stable relativistic hydrodynamics

Consistent inclusion of fluctuations in first-order causal and stable relativistic hydrodynamics

Prediction and analysis for airflow generated noise inside mufflers based on large eddy simulation and Morhing acoustic analogy

The airflow generated noise inside a simple expansion chamber muffler is predicted by combining large eddy simulation and Morhing acoustic analogy in the present work, and a good agreement is observed between the prediction and measurement. Research indicates that wall pressure fluctuations are dominated by hydrodynamic pressure fluctuations at the distance of first three pipe diameters in the outlet pipe, and wall pressure fluctuations at the distance of six pipe diameters downstream are dominated by sound pressure fluctuations. The airflow generated noise is mainly attributed to the vortex generated by structural change in the muffler, and one observes strong influences at the longitudinal resonance frequency and antiresonance frequency of the expansion chamber. In addition, the effects of expansion chamber lengths, extensions of inlet/outlet, filleted structure, conical tube, and perforated tube on airflow generated noise are studied. Predicted results show that the filleted structure, conical tube, and perforated tube structure may reduce the airflow generated noise effectively.

Hydrodynamic fluctuations, diffusion and correlation functions in systems of particles adsorbed on solid surfaces

We present the detailed derivation of the equations describing the evolution of the hydrodynamic fluctuations of the coverage of particles adsorbed on homogeneous lattices. Using the method of the non-equilibrium statistical operator, we reduce the balance equation governing the behavior of the individual particles to the diffusion equation. On a macroscopic level, this equation describes the approach to equilibrium of the hydrodynamic coverage fluctuations. We obtain the analytical expressions for the Fickian diffusivity and Onsager phenomenological coefficient. These expressions are derived with account of the lateral interaction between the particles. They are simple functions of the thermodynamic quantities — derivatives of the thermodynamic potential over its arguments. The transport coefficients accurately describe the development of fluctuations in the entire coverage region and in the wide range of lateral interactions. We presented an elementary introduction to the theory of fluctuations in the lattice gas systems. For calculations of the correlation function and spectral density of fluctuations, we use the Langevin approach and the method of moments. The exact coincidence of the analytical expressions for the diffusion coefficients obtained by the two independent calculations is the direct proof of the accuracy of the approach developed in Chumak and Tarasenko (1980).

Metastable and unstable hydrodynamics in multiphase lattice Boltzmann.

Metastability in liquids is at the foundation of complex phase transformation dynamics such as nucleation and cavitation. Intermolecular interaction details, beyond the equationof state, and thermal hydrodynamic fluctuations play a crucial role. However, most numerical approaches suffer from a slow time and space convergence, thus hindering the convergence to the hydrodynamic limit. This work shows that the Shan-Chen lattice Boltzmann model has the unique capability of simulating the hydrodynamics of the metastable state. The structure factor of density fluctuations is theoretically obtained and numerically verified to a high precision, for all simulated wave vectors, reduced temperatures, and pressures, deep into the metastable region. Such remarkable agreement between the theory and simulations leverages the exact implementation at the lattice level of the mechanical equilibrium condition. The static structure factor is found to consistently diverge as the temperature approaches the critical point or the density approaches the spinodal line at a subcritical temperature. Theoretically predicted critical exponents are observed in both cases. Finally, the phase separation in the unstable branch follows the same pattern, i.e., the generation of interfaces with different topology, as observed in molecular dynamics simulations.

Numerical study of the pulsatile flow and aeroacoustics of straight and curved pipes

From an engineering point of view pulsatile pipe flows, which include the hydrodynamic and acoustic fluctuations, can cause many problems such as vibration, noise and structural fatigue etc. Knowledge of the characteristics of hydrodynamic fluctuations (pseudo sound) and acoustic waves inside pipes particularly those with bends make is crucial to pipeline vibration and noise reduction. Numerical simulation of the pulsatile pipe flows shows challenges especially in curved pipes with different flow modes compounded, and predicting the acoustic fluctuations is even tougher. In this work, the unsteady flows of a straight and curved pipe with a 90° elbow induced by a pulsatile pressure inlet were calculated by Detached Eddy Simulations (DES). The pipe acoustic fields are solved through an acoustic perturbation equation, which takes the time derivative of hydrodynamic pressure as the aeroacoustic source. The characteristics of the flow and sound fields are discussed detailly, and special attention is paid to the influence of the 90° elbow on the curved pipe flow. The results show that the amplitude of hydrodynamic pressure fluctuations decrease almost linearly along the straight pipe, and the 90° elbow has obvious local influence on the flow pressure and velocity especially in the downstream side. The acoustic field is of 1-D standing wave pattern because of the fundamental pulsation frequency lower than the pipe cutoff frequency, and the 90° elbow has only negligible effect on the acoustic field in the flow frequency range.

Goldilocks Fluctuations: Dynamic Constraints on Loop Formation in Scale-Free Transport Networks.

Adaptive transport networks are known to contain loops when subject to hydrodynamic fluctuations. However, fluctuations are no guarantee that a loop will form, as shown by loop-free networks driven by oscillating flows. We provide a complete stability analysis of the dynamical behavior of any loop formed by fluctuating flows. We find a threshold for loop stability that involves an interplay of geometric constraints and hydrodynamic forcing mapped to constant and fluctuating components. Loops require fluctuation in the relative size of the flux between nodes, not just a temporal variation in the flux at a given node. Hence, there is both a minimum and a maximum amount of fluctuation relative to the constant-flux component where loops are supported.

Dynamic Light Scattering for the Measurement of Transport Properties of Fluids

The present article summarizes experimental and theoretical considerations required for a proper use of dynamic light scattering (DLS) for the measurement of transport properties of fluids. It addresses not only recent advancements of the method, but also aims to provide recommendations to researchers who intend to apply the technique in the future. As outlined in this study, DLS is based on the analysis of scattered light governed by microscopic statistical or periodic fluctuations that originate from the thermal movement of molecules and/or particles at macroscopic thermodynamic equilibrium. The dynamics of these hydrodynamic fluctuations in the bulk of fluids or at their phase boundaries are related to the underlying diffusive processes and, thus, to the associated transport properties, and are reflected by the time-dependent correlation function of the scattered light intensity. The fundamentals of this type of detection, known as photon correlation spectroscopy (PCS), will be discussed in the present contribution in some more detail. It is emphasized that the experiments need to be designed carefully in accordance with theory in order to assign the measurement signals to the corresponding hydrodynamic fluctuations. If the necessary conditions are fulfilled, DLS allows the accurate determination of several transport properties including kinematic and dynamic viscosity, thermal diffusivity, mutual diffusivity, and sound attenuation, which may be accessed together with other thermophysical properties such as speed of sound and surface or interfacial tension. In some instances, also the simultaneous determination of several transport properties is possible. With the exception of the sound attenuation, expanded uncertainties for the mentioned transport properties down to 1 % can be achieved for various types of fluid systems over a wide range of thermodynamic states up to elevated temperatures and pressures as well as in the vicinity of critical points. This performance and versatility of the DLS technique is documented in the present study by highlighting measurement examples from recent thermophysical property research on different classes of working fluids relevant for process and energy technology.

Causal hydrodynamic fluctuations in a one-dimensional expanding system

Causal hydrodynamic fluctuations in a one-dimensional expanding system

A Comparative Study of Scarfed Nozzle for Jet-Installation Noise Reduction

The experimental investigation of the effects of scarfed nozzles on jet-installation noise was conducted using unheated subsonic jets in an anechoic jet noise facility. Four different types of scarfed nozzles with increasing nozzle lip angles were examined to study the installation effects at various plate distances away from the jet. Mach numbers ranging from 0.3 to 0.8 were investigated in the experiments. The use of scarfed nozzles is known to result in the deflection of flow away from the centre axis, inducing asymmetry in the jet shears, leading to azimuthal variation in the spectra, and ultimately, noise reduction. This study aims to explore the possibility of reducing jet-installation noise using scarfed nozzles at subsonic flow conditions. The characteristics of jet hydrodynamic pressure fluctuations were investigated in the axial direction using far-field measurements. The near-field flow features were studied using surface pressure transducers installed on the flat plate for the installed configurations. Detailed spectral, coherence, and correlation analyses were carried out to determine the noise reduction mechanisms associated with scarfed nozzles in the proximity of a flat plate. The results of the study showed that the use of scarfed nozzles significantly reduced the jet-installation noise. The reduction was attributed to the generation of an asymmetric flow field induced by the nozzle geometry. The reduction in noise levels was also observed to increase with increasing nozzle lip angle. The detailed analyses revealed that the noise reduction mechanism was associated with a decrease in the acoustic power generated by the jet. Overall, the results suggest that scarfed nozzles can be an effective means of reducing jet-installation noise in subsonic flow conditions.

Entanglement Rényi entropies from ballistic fluctuation theory: The free fermionic case

The large-scale behaviour of entanglement entropy in finite-density states, in and out of equilibrium, can be understood using the physical picture of particle pairs. However, the full theoretical origin of this picture is not fully established yet. In this work, we clarify this picture by investigating entanglement entropy using its connection with the large-deviation theory for thermodynamic and hydrodynamic fluctuations. We apply the universal framework of Ballistic Fluctuation Theory (BFT), based the Euler hydrodynamics of the model, to correlation functions of branch-point twist fields, the starting point for computing Rényi entanglement entropies within the replica approach. Focusing on free fermionic systems in order to illustrate the ideas, we show that both the equilibrium behavior and the dynamics of Rényi entanglement entropies can be fully derived from the BFT. In particular, we emphasise that long-range correlations develop after quantum quenches, and accounting for these explain the structure of the entanglement growth. We further show that this growth is related to fluctuations of charge transport, generalising to quantum quenches the relation between charge fluctuations and entanglement observed earlier. The general ideas we introduce suggest that the large-scale behaviour of entanglement has its origin within hydrodynamic fluctuations.

Subdiffusive dynamics and hydrodynamic fluctuations: how the latter affect the former.

The characteristics of subdiffusion are influenced by hydrodynamic fluctuations, not the scaling of the mean square displacement (MSD) at the long time limit, but rather the transition of this property from ballistic behaviour at early times to its final scaling at large times. Additionally, since a significant portion of the normalised velocity autocorrelation function (NVAF), a widely used motion descriptor, no longer adequately describes the antipersistent character that is typical of a subdiffusive motion, it is also impacted by these fluctuations. The combined findings can lead to misleading conclusions if hydrodynamic fluctuations are not taken into account. Diffusing and vorticity time scales are crucial for the way the motion turns into the final subdiffusion dynamics, whose exponent is determined by the scaling of the friction.

Schwinger-Keldysh effective field theory for stable and causal relativistic hydrodynamics

We construct stable and causal effective field theories (EFTs) for describing statistical fluctuations in relativistic diffusion and relativistic hydrodynamics. These EFTs are fully non-linear, including couplings to background sources, and enable us to compute n-point time-ordered correlation functions including the effects of statistical fluctuations. The EFTs we construct are inspired by the Maxwell-Cattaneo model of relativistic diffusion and Müller-Israel-Stewart model of relativistic hydrodynamics respectively, and have been derived using both the Martin-Siggia-Rose and Schwinger-Keldysh formalisms. The EFTs non-linearly realise the dynamical Kubo-Martin-Schwinger (KMS) symmetry, which ensures that n-point correlation functions and interactions in the theory satisfy the appropriate fluctuation-dissipation theorems. Since these EFTs typically admit ultraviolet sectors that are not fixed by the low-energy infrared symmetries, we find that they simultaneously admit multiple realisations of the dynamical KMS symmetry. We also comment on certain obstructions to including statistical fluctuations in the recently-proposed stable and causal Bemfica-Disconzi-Noronha-Kovtun model of relativistic hydrodynamics.

Hydrodynamics of a relativistic charged fluid in the presence of a periodically modulated chemical potential

We study charged hydrodynamics in a periodic lattice background. Fluctuations are Bloch waves rather than single momentum Fourier modes. At boundaries of the unit cell where hydrodynamic fluctuations are formally degenerate with their Umklapped copy, level repulsion occurs. Novel mode mixings between charge, sound, and their Umklapped copies appear at finite chemical potential - both at zero and finite momentum. We provide explicit examples for an ionic lattice, i.e. a periodic external chemical potential, and verify our results with numerical computations in fluid-gravity duality.

Quantum effects on dynamic structure factors in dense magnetized plasmas

We extend the classical magnetohydrodynamics formalism to include nonlocal quantum behavior via the phenomenological Bohm potential. We then solve the quantum magnetohydrodynamics equations to obtain a new analytical form of the dynamic structure factor (DSF), a fundamental quantity linking theory and experiments. Our results show that the three-peak structure—one central Rayleigh peak and two Brillouin peaks—of the DSF arising from quantum hydrodynamic fluctuations becomes (in general) a five-peak structure—one central Rayleigh peak and two pairs of peaks associated with fast and slow magnetosonic waves. The Bohm contribution influences the positions and characteristics (height, width, and intensity) of the peaks by introducing three significant modifications: (i) an increase in effective thermal pressure, (ii) a reduction in the adiabatic index, and (iii) an enhancement of effective thermal diffusivity. The multiple DSF peaks enable concurrent measurements of diverse plasma properties, transport coefficients, and thermodynamic parameters in magnetized dense plasmas. The potential for experimental validation of our theory looms large, particularly through future experiments conducted at state-of-the-art laser facilities. Published by the American Physical Society 2024