论文标题
通过通量分析重新审视强制性湍流的广义缩放
A revisit of generalized scaling of forced turbulence through flux analysis
论文作者
论文摘要
In this investigation, we theoretically studied the transports of kinetic energy and scalar variance in turbulence driven by a scalar-based volume force in $M{\nabla}^β s'$ form associated with scalar fluctuations $s'$ in wavenumber space relies on flux conservation equation.该方程具有一种实际溶液和两种复杂的解决方案，这些解决方案导致四个不同的级联过程，包括惯性子段（动能的恒定通量和标量方差的恒定通量），CEF子量（动能的准稳定通量），CSF子范围的csf subrange（质量量表差异），以及新的量表的量表，以及新的量表范围，并构成了新的量表，并构成了新的量表。除耗散子范围外。 $β$控制级联过程和缩放指数。对于真正的解决方案，在CEF子范围中，$ξ_u$始终为-5/3，而$ξ_s= - （6β+1）/3 $。在CSF子范围中，$ξ_U=（4β-11）/5 $和$ξ_s= - （2β+7）/5 $，都与Zhao和Wang的理论一致（2021）。依靠$β$，可以将动能和标量方差的运输方式区分为四种情况。 （1）当$β<3/2 $（$β= 2/3 $除外）时，CEF和CSF子弹共存，前者位于后者的下波数侧。在$β= 2/3 $时，存在$ξ_u$和$ξ_s$等于-5/3的新惯性子量。 （2）当$ 3/2 <=β<2 $时，仅预测CEF子量。 （3）$β= 2 $，$ξ_u= -1 $，$ξ_s= -3 $，$λ_U= 1 $ = 1 $和$λ_s= -1 $的特殊和单数指数，如果$ MN = 1 $。否则，将预测CSF子量。 （4）当$ 2 <β<= 4 $时，仅预测CSF子量。因此，为强制湍流的类型建立了动能和标量方差的完整传输图片。
In this investigation, we theoretically studied the transports of kinetic energy and scalar variance in turbulence driven by a scalar-based volume force in $M{\nabla}^β s'$ form associated with scalar fluctuations $s'$ in wavenumber space relies on flux conservation equation. The equation has one real solution and two complex solutions, which lead to four different cascade processes, including inertial subrange (constant fluxes of kinetic energy and scalar variance), CEF subrange (quasi-constant flux of kinetic energy), CSF subrange (quasi-constant flux of scalar variance), and a new subrange with both non-constant fluxes of kinetic energy and scalar variance in addition to dissipation subrange. $β$ controls the cascade processes and the scaling exponents. For the real solution, in the CEF subrange, $ξ_u$ is always -5/3, while $ξ_s=-(6β+1)/3$. In the CSF subrange, $ξ_u=(4β-11)/5$ and $ξ_s=-(2β+7)/5$ which are both consistent with the theory of Zhao and Wang (2021). Relying on $β$, the transport of kinetic energy and scalar variance can be distinguished as four cases. (1) When $β<3/2$ (except $β=2/3$), the CEF and CSF subranges are coexisted, with the former located on the lower wavenumber side of the latter. At $β=2/3$, a new inertial subrange with both $ξ_u$ and $ξ_s$ equal to -5/3 is present. (2) When $3/2<=β<2$, only the CEF subrange is predicted. (3) At $β=2$, special and singular exponents of $ξ_u=-1$, $ξ_s=-3$, $λ_u=1$, and $λ_s=-1$ can be found, if $MN=1$. Otherwise, a CSF subrange is predicted. (4) When $2<β<=4$, only the CSF subrange is predicted. Thus, a complete transport picture of both kinetic energy and scalar variance has been established for the type of forced turbulence.
