Statistical Estimates for 2D stochastic Navier-Stokes Equations
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866908581490589696 |
|---|---|
| author | Kumar, Anuj Pakzad, Ali |
| author_facet | Kumar, Anuj Pakzad, Ali |
| contents | The statistical features of homogeneous, isotropic, two-dimensional stochastic turbulence are discussed. We derive some rigorous bounds for the mean value of the bulk energy dissipation rate $\mathbb{E} [\varepsilon ]$ and enstrophy dissipation rates $\mathbb{E} [χ] $ for 2D flows sustained by a variety of stochastic driving forces. We show that $$\mathbb{E} [ \varepsilon ] \rightarrow 0 \hspace{0.5cm}\mbox{and} \hspace{0.5cm} \mathbb{E} [ χ] \lesssim \mathcal{O}(1)$$ in the inviscid limit, consistent with the dual-cascade in 2D turbulence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_18213 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Statistical Estimates for 2D stochastic Navier-Stokes Equations Kumar, Anuj Pakzad, Ali Fluid Dynamics Analysis of PDEs 35Q30, 76F55, 35R60, 35Q35 The statistical features of homogeneous, isotropic, two-dimensional stochastic turbulence are discussed. We derive some rigorous bounds for the mean value of the bulk energy dissipation rate $\mathbb{E} [\varepsilon ]$ and enstrophy dissipation rates $\mathbb{E} [χ] $ for 2D flows sustained by a variety of stochastic driving forces. We show that $$\mathbb{E} [ \varepsilon ] \rightarrow 0 \hspace{0.5cm}\mbox{and} \hspace{0.5cm} \mathbb{E} [ χ] \lesssim \mathcal{O}(1)$$ in the inviscid limit, consistent with the dual-cascade in 2D turbulence. |
| title | Statistical Estimates for 2D stochastic Navier-Stokes Equations |
| topic | Fluid Dynamics Analysis of PDEs 35Q30, 76F55, 35R60, 35Q35 |
| url | https://arxiv.org/abs/2501.18213 |