Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 0905.0082

Eulerian and Lagrangian Statistics from high resolution Numerical Simulations of weakly compressible turbulence

R. Benzi·L. Biferale·R. Fisher·D. Q. Lamb·F. Toschi
View original source ↗Read source document ↗Export metadata ↓

Abstract

We report a detailed study of Eulerian and Lagrangian statistics from high resolution Direct Numerical Simulations of isotropic weakly compressible turbulence. Reynolds number at the Taylor microscale is estimated to be around 600. Eulerian and Lagrangian statistics is evaluated over a huge data set, made by $1856^3$ spatial collocation points and by 16 million particles, followed for about one large-scale eddy turn over time. We present data for Eulerian and Lagrangian Structure functions up to ten order. We analyse the local scaling properties in the inertial range and in the viscous range. Eulerian results show a good superposition with previous data. Lagrangian statistics is different from existing experimental and numerical results, for moments of sixth order and higher. We interpret this in terms of a possible contamination from viscous scale affecting the estimate of the scaling properties in previous studies. We show that a simple bridge relation based on Multifractal theory is able to connect scaling properties of both Eulerian and Lagrangian observables, provided that the small differences between intermittency of transverse and longitudinal Eulerian structure functions are properly considered.

Explore related subjects

physics.flu-dyn

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

R. Benzi, L. Biferale, R. Fisher, D. Q. Lamb, F. Toschi. 2009-05-01. Eulerian and Lagrangian Statistics from high resolution Numerical Simulations of weakly compressible turbulence. https://arxiv.org/abs/0905.0082

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Splashing-regime transitions and secondary-droplet scaling in oblique drop impacts on a deep pool

Oblique drop impact onto a deep liquid pool produces asymmetric crowns, directional jetting, and splashing transitions that cannot be characterized by the total impact inertia alone. We numerically investigate water drops impacting a quiescent deep pool over $41\leq We\leq1790$ and $10^\circ\leqθ\leq90^\circ$. The simulations reproduce the principal features observed experimentally and identify five post-impact regimes in the $We$--$θ$ plane: deposition, front splashing, side splashing, side-front splashing, and crown splashing. The deposition--front-splashing transition is described by the tangential-inertial parameter $K_s=We\cosθ$, with $K_s^c\approx120$. This criterion follows from the competition between downstream crown-rim inertia and capillary retraction at the Taylor--Culick velocity. The transition from front to side-front splashing is instead governed primarily by normal impact inertia, with a critical normal Weber number $We_N^c\approx318$. Beyond these regime transitions, the secondary-droplet statistics reveal fragmentation behavior common to the different splashing regimes. The droplet-size distributions are positively skewed, and the median diameter follows $d_{s,\mathrm{med}}/D\sim We^{-3/5}$. Second-order velocity structure functions support a scale-dependent capillary--inertial description of rim and ligament breakup. Combined with mass conservation, this scaling gives $N_s\sim We^{9/5}$, providing a numerical explanation for the secondary-droplet-number scaling observed experimentally. Thus, directional impact inertia governs the macroscopic selection of splashing regimes, whereas the secondary-droplet populations across these regimes exhibit a common capillary--inertial fragmentation scaling.

physics.flu-dyn↗
arXiv2026

Hydrodynamic Resistance on Oscillating Planar Interfacial Bodies

We study the unsteady dynamics of floating planar bodies undergoing lateral oscillations along an air--water interface. Scaling arguments indicate that when the viscous penetration depth and oscillation amplitude are both small compared to the body size, the flow beneath the body can be approximated by an oscillatory Stokes boundary layer, yielding a leading-order description of the hydrodynamic resistance. Using magnetic actuation, we drive the interfacial bodies harmonically and measure the amplitude response and phase lag in steady state over a range of frequencies, masses, sizes, and shapes. This frequency-response framework enables direct extraction of effective added mass and damping coefficients, which we find to be consistent with oscillatory boundary-layer theory in the limit of small interfacial deformation. The transient behavior during startup is also shown to be accurately predicted by a history integral that captures the development of the oscillatory boundary layer beneath the body. This work also establishes a simple experimental platform for quantifying unsteady hydrodynamic forces at fluid interfaces.

physics.flu-dyn↗
arXiv2026

Perturbation Theory for Translating Oblate-Spheroidal Droplets with Internal Circulation

Liquid droplets deform from spherical shape due to aerodynamic variation of pressure along the surface as the droplet moves through a gas. The deformation is predicted for axisymmetric droplets translating through a gas with low Weber numbers, We < 1, and Reynolds number Re = O(10). That deformation analysis is based on the relations between local pressure jump and the two radii of curvature. A thin boundary layer on both sides of the gas-liquid interface is considered with a surface-velocity jump due to pressure-gradient-driven flow with a large density jump and a pressure jump due to surface tension. A near-ellipsoidal shape is predicted using $We$ as a perturbation parameter. Then, the quasi-steady internal liquid-phase stream function and velocity field are predicted, describing internal circulation and a vortex ring structure with vorticity distributed through an inviscid liquid. The gas-phase flow over the oblate droplet is described using a ring doublet as an image within the droplet. The ring-doublet radius is related to We. Gas potential flow results are presented and compared using both the exact analytical solution and a perturbation analysis based on the square root of We. The perturbation analysis provides a lower computational cost. Three analyses for local curvature, liquid circulation, and gas potential flow are matched to yield the velocity and pressure fields. The appropriate radius for the image ring doublet is matched to the square root of We. Liquid-phase stream function, two velocity components in each fluid, and gas potential field are predicted. S Some comments on droplet drag are presented.

physics.flu-dyn↗