Kolmogorov turbulence in a random-force-driven Burgers equation: Anomalous scaling and probability density functions.
Kolmogorov turbulence in a random-force-driven Burgers equation: Anomalous scaling and probability density functions.
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DOI：
10.1103/physreve.52.5681
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发表时间：
1995-07
期刊：
影响因子：
--
通讯作者：
A. Chekhlov;V. Yakhot
中科院分区：
文献类型：
--
作者：
A. Chekhlov;V. Yakhot
High-resolution numerical experiments, described in this work, show that velocity fluctuations governed by the one-dimensional Burgers equation driven by a white-in-time random noise with the spectrum \ensuremath{\Vert}f(k)${\mathrm{\ensuremath{\Vert}}}^{2}$\ifmmode\bar\else\textasciimacron\fi{}\ensuremath{\propto}${\mathit{k}}^{\mathrm{\ensuremath{-}}1}$ exhibit a biscaling behavior: All moments of velocity differences ${\mathit{S}}_{\mathit{n}\mathrm{\ensuremath{\le}}3}$(r)=\ensuremath{\Vert}u(x+r)-u(x)${\mathrm{\ensuremath{\Vert}}}^{\mathit{n}}$\ifmmode\bar\else\textasciimacron\fi{}\ensuremath{\equiv}\ensuremath{\Vert}\ensuremath{\Delta}u${\mathrm{\ensuremath{\Vert}}}^{\mathit{n}}$\ifmmode\bar\else\textasciimacron\fi{} \ensuremath{\propto}${\mathit{r}}^{\mathit{n}/3}$, while ${\mathit{S}}_{\mathit{n}g3}$(r)\ensuremath{\propto}${\mathit{r}}_{\mathit{n}}^{\ensuremath{\xi}}$ with ${\ensuremath{\xi}}_{\mathit{n}}$\ensuremath{\approxeq}1 for real ng0 [Chekhlov and Yakhot, Phys. Rev. E 51, R2739 (1995)]. The probability density function, which is dominated by coherent shocks in the interval \ensuremath{\Delta}u0, is scrP(\ensuremath{\Delta}u,r)\ensuremath{\propto}(\ensuremath{\Delta}u${)}^{\mathrm{\ensuremath{-}}\mathit{q}}$ with q\ensuremath{\approxeq}4. A phenomenological theory describing the experimental findings is presented.
High-resolution numerical experiments, described in this work, show that velocity fluctuations governed by the one-dimensional Burgers equation driven by a white-in-time random noise with the spectrum \ensuremath{\Vert}f(k)${\mathrm{\ensuremath{\Vert}}}^{2}$\ifmmode\bar\else\textasciimacron\fi{}\ensuremath{\propto}${\mathit{k}}^{\mathrm{\ensuremath{-}}1}$ exhibit a biscaling behavior: All moments of velocity differences ${\mathit{S}}_{\mathit{n}\mathrm{\ensuremath{\le}}3}$(r)=\ensuremath{\Vert}u(x+r)-u(x)${\mathrm{\ensuremath{\Vert}}}^{\mathit{n}}$\ifmmode\bar\else\textasciimacron\fi{}\ensuremath{\equiv}\ensuremath{\Vert}\ensuremath{\Delta}u${\mathrm{\ensuremath{\Vert}}}^{\mathit{n}}$\ifmmode\bar\else\textasciimacron\fi{} \ensuremath{\propto}${\mathit{r}}^{\mathit{n}/3}$, while ${\mathit{S}}_{\mathit{n}g3}$(r)\ensuremath{\propto}${\mathit{r}}_{\mathit{n}}^{\ensuremath{\xi}}$ with ${\ensuremath{\xi}}_{\mathit{n}}$\ensuremath{\approxeq}1 for real ng0 [Chekhlov and Yakhot, Phys. Rev. E 51, R2739 (1995)]. The probability density function, which is dominated by coherent shocks in the interval \ensuremath{\Delta}u0, is scrP(\ensuremath{\Delta}u,r)\ensuremath{\propto}(\ensuremath{\Delta}u${)}^{\mathrm{\ensuremath{-}}\mathit{q}}$ with q\ensuremath{\approxeq}4. A phenomenological theory describing the experimental findings is presented.