Remarks on the KLB theory of two-dimensional turbulence
| dc.creator | Tran, Chuong V. | |
| dc.creator | Shepherd, Theodore G. | |
| dc.date | 2004-12-10 | |
| dc.date.accessioned | 2026-07-07T05:36:08Z | |
| dc.date.available | 2026-07-07T05:36:08Z | |
| dc.description | We study the inverse energy transfer in forced two-dimensional (2D) Navier--Stokes turbulence in a doubly periodic domain. It is shown that an inverse energy cascade that carries a nonzero fraction of the injected energy to the large scales via a power-law energy spectrum $\propto k^{-α}$ requires that $α\ge5/3$. This result is consistent with the classical theory of 2D turbulence that predicts a $k^{-5/3}$ inverse-cascading range, thus providing for the first time a rigorous basis for this important feature of the theory. We derive bounds for the Kolmogorov constant $C$ in the classical energy spectrum $E(k)=Cε^{2/3}k^{-5/3}$, where $ε$ is the energy injection rate. Issues related to Kraichnan's conjecture of energy condensation and to power-law spectra as the quasi-steady dynamics become steady are discussed. | |
| dc.description | 14 pages, submitted to JFM | |
| dc.identifier | https://arxiv.org/abs/nlin/0412026 | |
| dc.identifier | http://arxiv.org/abs/nlin/0412026 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/80889 | |
| dc.subject | Chaotic Dynamics | |
| dc.title | Remarks on the KLB theory of two-dimensional turbulence | |
| dc.type | text |