Universal statistical properties of inertial-particle trajectories in three-dimensional, homogeneous, isotropic, fluid turbulence

• We obtain new universal statistical properties of heavy-particle trajectories in three-dimensional, statistically steady, homogeneous, and isotropic turbulent flows by direct numerical simulations. We show that the probability distribution functions (PDFs) P(φ), of the angle φ between the Eulerian velocity u and the particle velocity v, at a point and time, scales as P(φ) ∼ φ−γ, with a new universal exponent γ ≃ 4. The PDFs of the trajectory curvature κ and modulus θ of the torsion ϑ scale, respectively, as P(κ) ∼ κ−hκ, as κ → ∞, and P(θ) ∼ θ−hθ, as θ → ∞, with exponents hκ ≃ 2.5 and hθ ≃ 3 that do not depend on the Stokes number St. We also show that γ, hκ and hθ can be obtained by using simple stochastic models. We show that the number NI(t,St) of points (up until time t), at which ϑ changes sign, is such that nI(St) ≡ limt→∞ NI(tSt) ∼ St−∆, with ∆ ≃ 0.4 a universal exponent. t 

Subject headings

NATURVETENSKAP  -- Fysik (hsv//swe)

NATURAL SCIENCES  -- Physical Sciences (hsv//eng)

Keyword

Distribution functions

Stochastic systems

Trajectories

Turbulence

Velocity control

Fluid turbulence

Heavy particles

Inertial particles

Isotropic turbulent flow

Particle velocities

Simple stochastic

Statistical properties

Stokes number

Stochastic models

Publication and Content Type

ref (subject category)

kon (subject category)