arXiv subjects

Daniel W. Meyer

Publications and source records attributed to Daniel W. Meyer.

7 recordsLinked to original sources

arXiv2026

Polydisperse collision kernels in droplet-laden turbulence with implications for rain formation

The collision kernel of droplets in warm clouds is a crucially important quantity for the parameterization of precipitation in weather and climate models. Nevertheless, its accurate representation remains a challenge, specifically in the bottleneck range $15\,μ\text{m}<r<40\,μ\text{m}$ within which turbulence is believed to substantially contribute to droplet growth. In this work, we address this problem by performing direct numerical simulations of polydisperse inertial particles suspended in three-dimensional turbulence at Reynolds number up to $Re_λ=418$. Collision statistics are compiled for droplet pairs across the Stokes number range $St\in[0.02,2]$, yielding comprehensive bidisperse maps of collision kernels, radial relative velocities, and radial distribution functions at contact. Our analysis reveals that polydispersity enhances collisions between light droplets through differential sampling, but attenuates collisions at larger Stokes numbers by rapidly reducing the spatial overlap of droplet clusters. By benchmarking existing models, we show that dominant bidisperse errors arise from overpredicted cross-species clustering. In light of these results, we propose an adapted model for the bidisperse radial distribution function, as well as a novel parameterization for the associated collision kernel, applicable to the smallest droplets in the bottleneck range with small settling velocities. Finally, we study the broadening of the droplet size distribution due to collision-coalescence and demonstrate that droplet growth is markedly accelerated in parcels of large local dissipation rate, supporting the hypothesis that turbulent intermittency may help overcome the bottleneck barrier.

physics.flu-dyn↗

arXiv2025

Shape modes and jet formation on ultrasound-driven wall-attached bubbles

Understanding how substrate-attached bubbles respond to ultrasound is important for applications from industrial cleaning to biomedical therapy. Under ultrasonic excitation, bubbles can deform through Faraday instability and periodically emit high-speed jets. Although this behavior is increasingly well understood for free bubbles, the dynamics of wall-attached bubbles remain largely unexplored. In particular, the three-dimensional selection and evolution of non-spherical modes and their relation to jetting have not been resolved. We investigate micrometric air bubbles in contact with a rigid substrate and driven by ultrasound, using a dual-view imaging setup combining top-view bright-field microscopy with side-view phase-contrast X-ray imaging. This approach reveals a stepwise evolution of bubble shape through four regimes: spherical oscillations, harmonic axisymmetric meniscus waves, half-harmonic axisymmetric Faraday waves, and the superposition of half-harmonic sectoral Faraday waves. This contrasts with free bubbles, which jump directly to their final Faraday pattern at instability onset. For the chosen substrate, the observed shape-mode spectrum is degenerate and spans a continuous range of mode degrees, consistent with theoretical predictions based on kinematic arguments. Free bubbles, although also degenerate, remain limited to discrete spherical harmonics. Measured ultrasound pressure thresholds for Faraday instability agree with classical interface-stability theory modified for a rigid boundary. Complementary 3D boundary-element simulations reproduce the observed shape evolution. Finally, we identify the acceleration threshold for cyclic jetting: unlike free bubbles, wall-attached bubbles always jet from the side not constrained by the substrate.

physics.flu-dyn↗

arXiv2024

Dissecting inertial clustering and sling dynamics in high-Reynolds number particle-laden turbulence

In this work, we aim to deepen the understanding of inertial clustering and the role of sling events in high-Reynolds number ($Re$) particle-laden turbulence. To this end, we perform one-way coupled particle tracking in flow fields obtained from direct numerical simulations (DNS) of forced homogeneous isotropic turbulence. Additionally, we examine the impact of filtering utilized in large eddy simulations (LES) by applying a sharp spectral filter to the DNS fields. Our analysis reveals that while instantaneous clustering through the centrifuge mechanism explains clustering at early times, the path history effect--the sampling of fluid flow along particle trajectories--becomes important later on. The filtered fields expose small-scale fractal clustering that cannot be predicted by the instantaneous flow field. We show that there exists a filter-effective Stokes number that governs the degree of fractal clustering and preferential sampling, revealing scale-similarity in the spatial distributions and fractal dimensions. Sling events are prevalent throughout our simulations and impose prominent patterns on the particle fields. In pursuit of investigating the sling dynamics, we compute the relative velocity, ensemble-averaged over proximal neighboring particles, to identify particles undergoing caustics. As postulated in recent theories, we find that in fully resolved, high-$Re$ turbulence, sling events occur in thin sheets of high strain, situated between turbulent vortices. This behavior is driven by rare, extreme events of compressive straining, manifested by fluctuations of the flow velocity gradients that propagate back and forth the positive branch of the Vieillefosse line.

physics.flu-dyn↗

arXiv2019

Flow in bounded and unbounded pore networks with different connectivity

This work is concerned with the intricate interplay between node or pore pressures and connection or throat conductivities in flow or pore networks. A setting similar to pore networks is given by fracture networks. Recently, a non-local generalization of Darcy's law for flow and transport in porous media was presented in the context of unbounded or periodic pore networks. In this work, we first outline a robust method for the extraction of the hydraulic conductivity distribution, which is at the heart of the non-local Darcy formulation. Second, a theory for mean pressure and flow in bounded networks is outlined. Predictions of that theory are validated against numerical network results and it is demonstrated that the theory works well for networks with high connectivity involving pores with high coordination numbers. For other networks, improvements to the outlined theory are proposed and their accuracy is assessed.

physics.flu-dyn↗

arXiv2018

(Un)Conditional Sample Generation Based on Distribution Element Trees

Recently, distribution element trees (DETs) were introduced as an accurate and computationally efficient method for density estimation. In this work, we demonstrate that the DET formulation promotes an easy and inexpensive way to generate random samples similar to a smooth bootstrap. These samples can be generated unconditionally, but also, without further complications, conditionally utilizing available information about certain probability-space components.

stat.ME↗

arXiv2017

An efficient distribution method for nonlinear two-phase flow in highly heterogeneous multidimensional stochastic porous media

In the context of stochastic two-phase flow in porous media, we introduce a novel and efficient method to estimate the probability distribution of the wetting saturation field under uncertain rock properties in highly heterogeneous porous systems, where streamline patterns are dominated by permeability heterogeneity, and for slow displacement processes (viscosity ratio close to unity). Our method, referred to as the frozen streamline distribution method (FROST), is based on a physical understanding of the stochastic problem. Indeed, we identify key random fields that guide the wetting saturation variability, namely fluid particle times of flight and injection times. By comparing saturation statistics against full-physics Monte Carlo simulations, we illustrate how this simple, yet accurate FROST method performs under the preliminary approximation of frozen streamlines. Further, we inspect the performance of an accelerated FROST variant that relies on a simplification about injection time statistics. Finally, we introduce how quantiles of saturation can be efficiently computed within the FROST framework, hence leading to robust uncertainty assessment.

physics.flu-dyn↗

arXiv2017

Density Estimation with Distribution Element Trees

The estimation of probability densities based on available data is a central task in many statistical applications. Especially in the case of large ensembles with many samples or high-dimensional sample spaces, computationally efficient methods are needed. We propose a new method that is based on a decomposition of the unknown distribution in terms of so-called distribution elements (DEs). These elements enable an adaptive and hierarchical discretization of the sample space with small or large elements in regions with smoothly or highly variable densities, respectively. The novel refinement strategy that we propose is based on statistical goodness-of-fit and pair-wise (as an approximation to mutual) independence tests that evaluate the local approximation of the distribution in terms of DEs. The capabilities of our new method are inspected based on several examples of different dimensionality and successfully compared with other state-of-the-art density estimators.

stat.ME↗