Turbulence-induced relative velocity of dust particles. II. The bidisperse case
- Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138 (United States)
- ICREA and ICC, University of Barcelona, Marti i Franquès 1, E-08028 Barcelona (Spain)
- Department of Astronomy, University of Texas, Austin, TX 78712 (United States)
We extend our earlier work on turbulence-induced relative velocity between equal-size particles (Paper I, in this series) to particles of arbitrarily different sizes. The Pan and Padoan (PP10) model shows that the relative velocity between different particles has two contributions, named the generalized shear and acceleration terms, respectively. The generalized shear term represents the particles' memory of the spatial flow velocity difference across the particle distance in the past, while the acceleration term is associated with the temporal flow velocity difference on individual particle trajectories. Using the simulation of Paper I, we compute the root-mean-square relative velocity, (w {sup 2}){sup 1/2}, as a function of the friction times, τ{sub p1} and τ{sub p2}, of the two particles and show that the PP10 prediction is in satisfactory agreement with the data, confirming its physical picture. For a given τ{sub p1} below the Lagrangian correlation time of the flow, T{sub L}, (w {sup 2}){sup 1/2} as a function of τ{sub p2} shows a dip at τ{sub p2} ≅ τ{sub p1}, indicating tighter velocity correlation between similar particles. Defining a ratio f ≡ τ{sub p,{sub l}}/τ{sub p,{sub h}}, with τ{sub p,{sub l}} and τ{sub p,{sub h}} the friction times of the smaller and larger particles, we find that (w {sup 2}){sup 1/2} increases with decreasing f due to the generalized acceleration contribution, which dominates at f ≲ 1/4. At a fixed f, our model predicts that (w {sup 2}){sup 1/2} scales as τ{sub p,h}{sup 1/2} for τ{sub p,{sub h}} in the inertial range of the flow, stays roughly constant for T{sub L} ≲ τ{sub p,{sub h}} ≲ T{sub L}/f, and finally decreases as τ{sub p,h}{sup −1/2} for τ{sub p,{sub h}} >> T{sub L}/f. The acceleration term is independent of the particle distance, r, and reduces the r dependence of (w {sup 2}){sup 1/2} in the bidisperse case.
- OSTI ID:
- 22365370
- Journal Information:
- Astrophysical Journal, Vol. 791, Issue 1; Other Information: Country of input: International Atomic Energy Agency (IAEA); ISSN 0004-637X
- Country of Publication:
- United States
- Language:
- English
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