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 ‖f(k)${\mathrm{\Vert }}^2$¯∝${\mathit{k}}^{\mathrm{-}1}$ exhibit a biscaling behavior: All moments of velocity differences ${\mathit{S}}_{\mathit{n}\mathrm{\le }3}$(r)=‖u(x+r)-u(x)${\mathrm{\Vert }}^{\mathit{n}}$¯≡‖Δu${\mathrm{\Vert }}^{\mathit{n}}$¯ ∝${\mathit{r}}^{\mathit{n}/3\mathrm{}}$, while ${\mathit{S}}_{\mathit{n}>3\mathrm{}}$(r)∝${\mathit{r}}_{\mathit{n}}^{\xi }$ with ${\xi }_{\mathit{n}}$≊1 for real n>0 [Chekhlov and Yakhot, Phys. Rev. E 51, R2739 (1995)]. The probability density function, which is dominated by coherent shocks in the interval Δu<0, is scrP(Δu,r)∝(Δu${)}^{\mathrm{-}\mathit{q}}$ with q≊4. A phenomenological theory describing the experimental findings is presented.

Close

PrevNext

View figure in article