A non-inertial model for particle aggregation under turbulence
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866912183729782784 |
|---|---|
| author | Flandoli, Franco Huang, Ruojun |
| author_facet | Flandoli, Franco Huang, Ruojun |
| contents | We consider an abstract non-inertial model of aggregation under the influence of a Gaussian white noise with prescribed space-covariance, and prove a formula for the mean collision rate $R$, per unit of time and volume. Specializing the abstract theory to a non-inertial model obtained by an inertial one, with physical constants, in the limit of infinitesimal relaxation time of the particles, and the white noise obtained as an approximation of a Gaussian noise with correlation time $τ_η$, up to approximations the formula reads $R\simτ_η\left\langle \left\vert Δ_{a}u\right\vert ^{2}\right\rangle a\cdot n^{2}$ where $n$ is the particle number per unit of volume and $\left\langle \left\vert Δ_{a}u\right\vert ^{2}\right\rangle $ is the square-average of the increment of random velocity field $u$ between points at distance $a$, the particle radius. If we choose the Kolmogorov time scale $τ_η\sim\left( \frac{ν}{\varepsilon}\right) ^{1/2}$ and we assume that $a$ is in the dissipative range where $\left\langle \left\vert Δ_{a}u\right\vert ^{2}\right\rangle \sim\left( \frac{\varepsilon}ν\right) a^{2}$, we get Saffman-Turner formula for the collision rate $R$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_05233 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A non-inertial model for particle aggregation under turbulence Flandoli, Franco Huang, Ruojun Probability We consider an abstract non-inertial model of aggregation under the influence of a Gaussian white noise with prescribed space-covariance, and prove a formula for the mean collision rate $R$, per unit of time and volume. Specializing the abstract theory to a non-inertial model obtained by an inertial one, with physical constants, in the limit of infinitesimal relaxation time of the particles, and the white noise obtained as an approximation of a Gaussian noise with correlation time $τ_η$, up to approximations the formula reads $R\simτ_η\left\langle \left\vert Δ_{a}u\right\vert ^{2}\right\rangle a\cdot n^{2}$ where $n$ is the particle number per unit of volume and $\left\langle \left\vert Δ_{a}u\right\vert ^{2}\right\rangle $ is the square-average of the increment of random velocity field $u$ between points at distance $a$, the particle radius. If we choose the Kolmogorov time scale $τ_η\sim\left( \frac{ν}{\varepsilon}\right) ^{1/2}$ and we assume that $a$ is in the dissipative range where $\left\langle \left\vert Δ_{a}u\right\vert ^{2}\right\rangle \sim\left( \frac{\varepsilon}ν\right) a^{2}$, we get Saffman-Turner formula for the collision rate $R$. |
| title | A non-inertial model for particle aggregation under turbulence |
| topic | Probability |
| url | https://arxiv.org/abs/2404.05233 |