Euler Flow Research Articles

Analysis of Downstream Sediment Transport Trends Based on In Situ Data and Numerical Simulation

This study conducted an in-depth analysis of the sediment dynamics in the lower reaches of the Changhua River and its estuary on Hainan Island. Through field collection of topographic data and sediment sampling, combined with advanced computational techniques, the study explored the transport pathways and depositional patterns of sediments. The grain size trend analysis (GSTA) method was utilized, in conjunction with the Flemming triangle diagram method, to classify the dynamic environment of the sediments. Furthermore, hydrodynamic modeling results were integrated to further analyze the transport trends of the sediments. The study revealed that the sediment types in the research area are complex, primarily consisting of gravelly sand and sandy gravel, indicating a generally coarse sedimentary environment in the region. The sediments in the lower reaches of the Changhua River generally transport towards the south and southwest (in the direction of Beili Bay). The net sediment transport directions inferred from the GSTA model are largely consistent with the Eulerian residual flow patterns, especially in the offshore area, where discrepancies are observed in the nearshore zone. The nearshore transport is influenced by the combined effects of alongshore currents, residual flows, and river inputs, while the offshore transport exhibits a shift from the northwest to southwest directions, reflecting the regional circulation patterns.

1-D Isentropic Euler Flows: Self-similar Vacuum Solutions

1-D Isentropic Euler Flows: Self-similar Vacuum Solutions

Upscaling transport in heterogeneous media featuring local-scale dispersion: Flow channeling, macro-retardation and parameter prediction

Many theoretical treatments of transport in heterogeneous Darcy flows consider advection only. When local-scale dispersion is neglected, flux weighting persists over time; mean Lagrangian and Eulerian flow velocity distributions relate simply to each other and to the variance of the underlying hydraulic conductivity field. Local-scale dispersion complicates this relationship, potentially causing initially flux-weighted solute to experience lower-velocity regions as well as Taylor-type macrodispersion due to transverse solute movement between adjacent streamlines. To investigate the interplay of local-scale dispersion with conductivity log-variance, correlation length, and anisotropy, we perform a Monte Carlo study of flow and advective-dispersive transport in spatially-periodic 2D Darcy flows in large-scale, high-resolution multivariate Gaussian random conductivity fields. We observe flow channeling at all heterogeneity levels and quantify its extent. We find evidence for substantial effective retardation in the upscaled system, associated with increased flow channeling, and observe limited Taylor-type macrodispersion, which we physically explain. A quasi-constant Lagrangian velocity is achieved within a short distance of release, allowing usage of a simplified continuous-time random walk (CTRW) model we previously proposed in which the transition time distribution is understood as a temporal mapping of unit time in an equivalent system with no flow heterogeneity. The numerical data set is modeled with such a CTRW; we show how dimensionless parameters defining the CTRW transition time distribution are predicted by dimensionless heterogeneity statistics and provide empirical equations for this purpose.

A Shifted Boundary Method for the compressible Euler equations

The Shifted Boundary Method (SBM) is applied to compressible Euler flows, with and without shock discontinuities. The SBM belongs to the class of unfitted (or immersed, or embedded) finite element methods and avoids integration over cut cells (and the associated implementation/stability issues) by reformulating the original boundary value problem over a surrogate (approximate) computational domain. Accuracy is maintained by modifying the original boundary conditions using Taylor expansions. Hence the name of the method, that shifts the location and values of the boundary conditions. We specifically discuss the advantages the proposed method offers in avoiding spurious numerical artifacts in two scenarios: (a) when curved boundaries are represented by body-fitted polygonal approximations and (b) when the Kutta condition needs to be imposed in immersed simulations of airfoils. An extensive suite of numerical tests is included.

Comparison of the effects on heat transfer through oil oscillation in a steel piston cooling gallery: Friction welding versus laser welding

Piston cooling gallery plays a critical role in managing the temperature of the piston and its performance. This paper aims to study the effect of oscillatory heat transfer within the cooling galleries, focusing on two distinct types: flanged (friction-welded) and smooth structures (laser-welded). To do so, the Eulerian multiphase flow model and the k-ω SST turbulence model were used to simulate the oil and air flow through the cooling gallery. Key parameters such as the oil filling rate, wall heat transfer coefficient, oil outlet flow rate, heat removal rate by the oil, and overall wall heat transfer rate were assessed for both gallery designs at an engine speed of 1800 r/min. The results indicate significant disparities between the two cooling gallery structures: the smooth structure exhibits an oil filling rate that is 5.41% higher and an oil outlet flow rate that is 33.48% greater compared to the flanged structure. The flange structure impedes internal oil movement, which leads to boundary layer separation, secondary wall contact, and the emergence of a double vortex phenomena. Collectively, these factors influence the oil fill ratio. This, in turn, affects the distribution of oil within the gallery and, subsequently, the efficiency of heat transfer. Comparative analyses of heat transfer within both galleries, under the same studied conditions, revealed that the smooth structure outperforms the flanged one. However, the presence of a flange significantly alters the heat contribution from different walls, thereby highlighting the substantial impact of flanges on the overall efficiency of heat transfer.

Study of heat transfer coefficients of multiple high-pressure fan-shaped water impinging on the lower surface of high-temperature steel billets

The lack of research on the boiling heat transfer coefficient on billet surfaces during the high-pressure fan-shaped water descaling process significantly affects the cooling, quality, and rolling efficiency of the billet surface. This paper utilizes the Eulerian multiphase flow model in Fluent 19.0 software to simulate the boiling heat transfer behavior of multiple high-pressure fan-shaped water jets impinging the surface of high-temperature steel billets during descaling. The study highlights the correlation between the boiling heat transfer coefficient and three key parameters: the Reynolds number, dimensionless target distance, and dimensionless temperature. The simulation’s accuracy was validated by comparing the simulation results against experimental data. Findings indicate that the boiling heat transfer coefficients were respectively higher in the stagnation area, the lower side of the overlap zone, and at the edges of the flow strands on the billet surface, reaching up to approximately 6000 W·m−2·K−1. Additionally, the heat transfer coefficients were higher in the downstream region compared to the upstream area. The boiling heat transfer coefficient increased by 13.7 % and 9.38 % as the Reynolds number increased from 278,031 to 340,486 and as the initial temperature increased from 1373.15 K to 1573.15 K, respectively. On the other hand, the boiling heat transfer coefficient decreased by 19.0 % when reducing the target distance from 20 de to 54 de. Finally, a function was established to describe the boiling heat transfer coefficient based on the Reynolds number, dimensionless target distance, and dimensionless temperature.

Numerical heat transfer analysis of steam injection into subcooled water

Steam direct contact condensation (DCC) into subcooled water may be encountered in different important industrial process applications, such as steam jet pumps, steam ejectors, pressurizers, and emergency cooling systems of nuclear reactor core. In this work, a numerical simulation study has been done for injection of steam into a tank full of subcooled water. In the simulations, the Eulerian multiphase flow in addition to a realizable k-epsilon turbulence model has been utilized. Moreover, a DCC model has been used for condensation capturing. Fluent software with a user-defined function (UDF) for the DCC model was employed for simulations. The results obtained from simulations were validated with experimental results, and a fair agreement was observed. This study considered the local Nusselt number (LNN) the most suitable parameter for investigating the heat transfer rate (HTR) at the computational cell level. Therefore, the contours of the LNN, its axial distribution, and radial distribution were studied with respect to the inlet pressure of injected steam, temperature of tank water, and location along the axis of the nozzle. The results reveal the fact that the value of the LNN reaches a maximum at the nozzle exit along the axis of the nozzle at 323 K tank water temperature. LNN decreases by increasing or decreasing the tank water temperature beyond 323 K. It is claimed that the heat transfer (HT) study at such a local scale has been conducted for the first time to the best of our knowledge, and it unfolds various crucial facts regarding steam-water interaction.

A Josephson–Anderson relation for drag in classical channel flows with streamwise periodicity: Effects of wall roughness

The detailed Josephson–Anderson relation equates the instantaneous work by pressure drop over any streamwise segment of a general channel and the wall-normal flux of spanwise vorticity spatially integrated over that section. This relation was first derived by Huggins for quantum superfluids, but it holds also for internal flows of classical fluids and for external flows around solid bodies, corresponding there to relations of Burgers, Lighthill, Kambe, Howe, and others. All of these prior results employ a background potential Euler flow with the same inflow/outflow as the physical flow, just as in Kelvin's minimum energy theorem, so that the reference potential incorporates information about flow geometry. We here generalize the detailed Josephson–Anderson relation to streamwise periodic channels appropriate for numerical simulation of classical fluid turbulence. We show that the original Neumann b.c. used by Huggins for the background potential creates an unphysical vortex sheet in a periodic channel, so that we substitute instead Dirichlet b.c. We show that the minimum energy theorem still holds and our new Josephson–Anderson relation again equates work by pressure drop instantaneously to integrated flux of spanwise vorticity. The result holds for both Newtonian and non-Newtonian fluids and for general curvilinear walls. We illustrate our new formula with numerical results in a periodic channel flow with a single smooth bump, which reveals how vortex separation from the roughness element creates drag at each time instant. Drag and dissipation are thus related to vorticity structure and dynamics locally in space and time, with important applications to drag-reduction and to explanation of anomalous dissipation at high Reynolds numbers.

Inertial migration of rigid particles in shear-thinning fluids under asymmetric wall slip conditions

The determination of flow-induced equilibrium positions in pressure-driven flows in microchannels is of great practical importance in particle manipulation. In the computational analysis presented in this paper, the inertial ordering of neutrally buoyant rigid spheres in shear-thinning fluid flow through a hydrophobic microchannel is investigated. The combined effect of the viscosity index n of a power-law fluid and fluid slippage at the wall on the lateral focusing of microspheres is examined in detail. Using the finite element method, the Eulerian flow field between partially slipping parallel walls is simulated, and the Lagrangian movement of particles is continuously tracked. The Navier slip model is used to ensure a finite fluid velocity at the wall, and it is tuned by modifying the slip-length. It is observed that inertial particles concentrate at a standard equilibrium position of 0.6 times the channel half-width H, irrespective of fluid slip due to the symmetry of the flow field. However, this equilibrium position shifts closer to the walls as the viscosity index increases; for instance, when n = 0.5, particles stabilize at 0.75H. As a consequence of asymmetry in hydrodynamic behavior due to different fluid slippages at the upper and lower walls, the particle migration path is altered. In a channel with a no-slip upper wall and a partially slipping lower wall (β/H = 0.4), particles settle closer to the lower wall at 0.8H. Most importantly, the lateral movement of a particle released at a given vertical position can be altered by tailoring the wall hydrophobicity and viscosity index, thus enabling multiple equilibrium locations to be achieved.

Asymptotic stability of rarefaction wave with non-slip boundary condition for radiative Euler flows

This paper is devoted to studying the initial-boundary value problem for the radiative full Euler equations, which are a fundamental system in the radiative hydrodynamics with many practical applications in astrophysical and nuclear phenomena, with the non-slip boundary condition on an impermeable wall. Due to the difficulty from the disappearance of the velocity on the impermeable boundary, quite few results for compressible Navier-Stokes equations and no result for the radiative Euler equations are available at this moment. So the asymptotic stability of the rarefaction wave proven in this paper is the first rigorous result on the global stability of solutions of the radiative Euler equations with the non-slip boundary condition. It also contributes to our systematical study on the asymptotic behaviors of the rarefaction wave with the radiative effect and different boundary conditions such as the inflow/outflow problem and the impermeable boundary problem in our series papers including [5,6].

Scaling laws and exact results in turbulence *

In this note, we address the validity of certain exact results from turbulence theory in the deterministic setting. The main tools, inspired by the work of Duchon and Robert (2000 Nonlinearity 13 249–55) and Eyink (2003 Nonlinearity 16 137), are a number of energy balance identities for weak solutions of the incompressible Euler and Navier–Stokes equations. As a consequence, we show that certain weak solutions of the Euler and Navier–Stokes equations satisfy deterministic versions of Kolmogorov’s 45 , 43 , 415 laws. We apply these computations to improve a recent result of Hofmanova et al (2023 arXiv:2304.14470), which shows that a construction of solutions of forced Navier–Stokes due to Bruè et al (2023 Commun. Pure Appl. Anal.) and exhibiting a form of anomalous dissipation satisfies asymptotic versions of Kolmogorov’s laws. In addition, we show that the globally dissipative 3D Euler flows recently constructed by Giri et al (2023 arXiv:2305.18509) satisfy the local versions of Kolmogorov’s laws.

An elementary proof of existence and uniqueness for the Euler flow in localized Yudovich spaces

We revisit Yudovich’s well-posedness result for the 2-dimensional Euler equations for an inviscid incompressible fluid on either a sufficiently regular (not necessarily bounded) open set Ω⊂R2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Omega \\subset \\mathbb {R}^2$$\\end{document} or on the torus Ω=T2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Omega =\\mathbb {T}^2$$\\end{document}. We construct global-in-time weak solutions with vorticity in L1∩Lulp\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L^1\\cap L^p_{ul}$$\\end{document} and in L1∩YulΘ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L^1\\cap Y^\\Theta _{ul}$$\\end{document}, where Lulp\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L^p_{ul}$$\\end{document} and YulΘ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Y^\\Theta _{ul}$$\\end{document} are suitable uniformly-localized versions of the Lebesgue space Lp\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L^p$$\\end{document} and of the Yudovich space YΘ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Y^\\Theta $$\\end{document} respectively, with no condition at infinity for the growth function Θ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Theta $$\\end{document}. We also provide an explicit modulus of continuity for the velocity depending on the growth function Θ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Theta $$\\end{document}. We prove uniqueness of weak solutions in L1∩YulΘ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L^1\\cap Y^\\Theta _{ul}$$\\end{document} under the assumption that Θ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Theta $$\\end{document} grows moderately at infinity. In contrast to Yudovich’s energy method, we employ a Lagrangian strategy to show uniqueness. Our entire argument relies on elementary real-variable techniques, with no use of either Sobolev spaces, Calderón–Zygmund theory or Littlewood–Paley decomposition, and actually applies not only to the Biot–Savart law, but also to more general operators whose kernels obey some natural structural assumptions.

The steady Prandtl boundary layer expansions for non-shear Euler flow

We continue the study on the validity of the Prandtl boundary layer expansions in [Gao et al., Sci. China Math. 66, 679–722 (2023)], whereby estimating the stream-function of the remainder, we proved the case when the Euler flow is the perturbation of shear flow in a narrow domain. In this paper, we obtain a new derivatives estimate of stream-function away from the boundary layer and then prove the validity of expansions for any non-shear Euler flow, provided that the width of the domain is small.

Hypersonic similarity for steady compressible full Euler flows over two-dimensional Lipschitz wedges

We establish the optimal convergence rate to the hypersonic similarity law, which is also called the Mach number independence principle, for steady compressible full Euler flows over two-dimensional slender Lipschitz wedges. Mathematically, it can be formulated as the comparison of the entropy solutions in BV∩L1 between the two initial-boundary value problems for the compressible full Euler equations with parameter τ>0 and the hypersonic small-disturbance equations (the scaled compressible full Euler equations with parameter τ=0) with curved characteristic boundaries. We establish the L1–convergence estimate of these two solutions with the optimal convergence rate, which justifies the Van Dyke's similarity theory rigorously for the compressible full Euler flows. This is the first mathematical result on the comparison of two solutions of the compressible Euler equations with characteristic boundary conditions. To achieve this, we first employ the special structures of the two systems and establish the global existence and the L1–stability of the entropy solutions via the wave-front tracking scheme under the smallness assumption on the total variation of both the initial data and the tangential slope function of the wedge boundary. Based on the L1–stability properties of the approximate solutions to the scaled equations with parameter τ>0, a uniform Lipschtiz continuous map with respect to the initial data and the wedge boundary is obtained, which is the first time for the characteristic boundary conditions. Next, we compare the solutions given by the Riemann solvers of the two systems by taking the boundary perturbations into account case by case. Then, for a given fixed hypersonic similarity parameter, as the Mach number tends to infinity, by employing the Lipschitz continuous properties of the map, we establish the desired L1–convergence estimate with the optimal convergence rate. Finally, we show the optimality of the convergence rate by investigating a special solution.

Rough solutions of the relativistic Euler equations

We prove that the time of classical existence of smooth solutions to the relativistic Euler equations can be bounded from below in terms of norms that measure the “(sound) wave-part” of the data in Sobolev space and “transport-part” in higher regularity Sobolev space and Hölder spaces. The solutions are allowed to have nontrivial vorticity and entropy. We use the geometric framework from [M. M. Disconzi and J. Speck, The relativistic Euler equations: Remarkable null structures and regularity properties, Ann. Henri Poincaré 20(7) (2019) 2173–2270], where the relativistic Euler flow is decomposed into a “wave-part”, that is, geometric wave equations for the velocity components, density and enthalpy, and a “transport-part”, that is, transport-div-curl systems for the vorticity and entropy gradient. Our main result is that the Sobolev norm [Formula: see text] of the variables in the “wave-part” and the Hölder norm [Formula: see text] of the variables in the “transport-part” can be controlled in terms of initial data for short times. We note that the Sobolev norm assumption [Formula: see text] is the optimal result for the variables in the “wave-part”. Compared to low-regularity results for quasilinear wave equations and the three-dimensional (3D) non-relativistic compressible Euler equations, the main new challenge of the paper is that when controlling the acoustic geometry and bounding the wave equation energies, we must deal with the difficulty that the vorticity and entropy gradient are four-dimensional space-time vectors satisfying a space-time div-curl-transport system, where the space-time div-curl part is not elliptic. Due to lack of ellipticity, one cannot immediately rely on the approach taken in [M. M. Disconzi and J. Speck, The relativistic Euler equations: Remarkable null structures and regularity properties, Ann. Henri Poincaré 20(7) (2019) 2173–2270] to control these terms. To overcome this difficulty, we show that the space-time div-curl systems imply elliptic div-curl-transport systems on constant-time hypersurfaces plus error terms that involve favorable differentiations and contractions with respect to the four-velocity. By using these structures, we are able to adequately control the vorticity and entropy gradient with the help of energy estimates for transport equations, elliptic estimates, Schauder estimates and Littlewood–Paley theory.

Smooth Transonic Flows with Nonzero Vorticity to a Quasi Two Dimensional Steady Euler Flow Model

Smooth Transonic Flows with Nonzero Vorticity to a Quasi Two Dimensional Steady Euler Flow Model

Lagrangian Measurements Of Surface Water Waves: Relation Between Drift Velocities And Set-Down

Since the work of Stokes on steady progressive surface waves (Stokes, 1847), there has been interest in fluid particle trajectories and associated mass flux. The original result obtained by Stokes was based on linear theory, and implied that there is a net forward drift in the fluid beneath a propagating surface wave. In the non-dimensional case, the drift velocity for a sinusoidal wave on a fluid of depth h is given by Recent works suggest that in many cases, particularly in waves propagating over a shear flow, a net Eulerian flow may develop, which is opposed to the Stokes drift. Monismith et al. (2007) suggested that in a deep-water setting, the net Eulerian backflow may cancel the Lagrangian Stokes drift on a pointwise basis. Further, Grue & Kolaas (2017) found good agreement with the theoretical findings of Longuet-Higgins (1953), except near the bottom and near the free surface, where boundary layers have a discernable impact on the induced flow. In recent field measurements, it was observed that the drift velocity correlates positively with the local average fluid depth (Bjørnestad et al., 2021). In other words, a wave with a set-up features a large forward drift, while a wave with a set-down features a negative net drift. The present work aims at investigating what observed in the field by means of laboratory experiments carried out in a wave flume, where monochromatic and bichromatic waves of different characteristics have been run.

On Λ-Fractional fluid mechanics

Λ-fractional analysis has already been presented as the only fractional analysis conforming with the Differential Topology prerequisites. That is, the Leibniz rule and chain rule do not apply to other fractional derivatives; This, according to Differential Topology, makes the definition of a differential impossible for these derivatives. Therefore, this leaves Λ-fractional analysis the only analysis generating differential geometry necessary to establish the governing laws in physics and mechanics. Hence, it is most necessary to use Λ-fractional derivative and Λ-fractional transformation to describe fractional mathematical models. Other fractional “derivatives” are not proper derivatives, according to Differential Topology; they are just operators. This fact makes their application to mathematical problems questionable while Λ-derivative faces no such problems. Basic Fluid Mechanics equations are studied and revised under the prism of Λ-Fractional Continuum Mechanics (Λ-FCM). Extending the already presented principles of Continuum Mechanics in the area of solids into the area of fluids, the basic Λ-fractional fluid equations concerning the Navier-Stokes, Euler, and Bernoulli flows are derived, and the Λ-fractional Darcy’s flow in porous media is studied. Since global minimization of the various fields is accepted only in the Λ-fractional analysis, shocks in the Λ-fractional motion of fluids are exhibited.

The stability of simple plane-symmetric shock formation for three-dimensional compressible Euler flow with vorticity and entropy

The stability of simple plane-symmetric shock formation for three-dimensional compressible Euler flow with vorticity and entropy

Regressing bubble cluster dynamics as a disordered many-body system

The coherent dynamics of bubble clusters are of fundamental and industrial importance, and are elusive due to the complex interactions of disordered bubble oscillations. Here we introduce and demonstrate a method for decomposition of the Lagrangian time series of bubble dynamics data by combining theory and principal component analysis. The decomposition extracts coherent features of bubble oscillations based on their energy, in a way similar to proper orthogonal decomposition of Eulerian flow field data. This method is applied to a dataset of spherical clusters under harmonic excitation at different amplitudes, with various nuclei density and polydispersity parameters. Results indicate that the underlying correlated mode of oscillations is isolated in a single dominant feature in cavitating regimes, independent of the nuclei's parameters. A systematic data analysis procedure further suggests that this feature is globally controlled by the dynamic cloud interaction parameter of Maeda and Colonius (J. Fluid Mech., vol. 862, 2019, pp. 1105–1134) that quantifies the mean-field interactions, regardless of initial polydispersity or nonlinearity. The method provides a simplified and comprehensive representation of complex bubble dynamics as well as a new path to reduced-order modelling of cavitation and nucleation.