论文标题
在低prandtl数字下强烈分层的湍流的临界平衡和缩放
Critical Balance and Scaling of Strongly Stratified Turbulence at Low Prandtl Number
论文作者
论文摘要
我们将稳定分层的湍流从统一的地球物理状态扩展到适用于适用于稳定分层的恒星和气体巨人区域的极小prandtl数量的天体物理状态。当PrandTL数量下降到浮力Reynolds数字的倒数以下时，发现向新的湍流制度的过渡会发生，即$ PRRB <1 $，这表明浮力方程中的主要余额变化。然后，临界平衡参数的应用得出了各向异性能源谱和Boussinesq方程的主要平衡的新预测。我们发现，如果Froude编号（$ fr $）被修改后的Froude号码，$ fr_m \ equiv fr/（prrb）^{1/4} $取代，则从Unity $ pr $稳定分层的稳定湍流限制的所有标准缩放关系都可以延长。因此，地球物理和天体物理机制在$ prrb = 1 $转换之间平稳连接。讨论了在恒星辐射区域中的垂直传输和小规模发电机的不稳定性标准的修改。
We extend the scaling relations of stably stratified turbulence from the geophysical regime of unity Prandtl number to the astrophysical regime of extremely small Prandtl number applicable to stably stratified regions of stars and gas giants. A transition to a new turbulent regime is found to occur when the Prandtl number drops below the inverse of the buoyancy Reynolds number, i.e. $PrRb<1$, which signals a shift of the dominant balance in the buoyancy equation. Application of critical balance arguments then derives new predictions for the anisotropic energy spectrum and dominant balance of the Boussinesq equations in the $PrRb\ll1$ regime. We find that all the standard scaling relations from the unity $Pr$ limit of stably stratified turbulence simply carry over if the Froude number, $Fr$, is replaced by a modified Froude number, $Fr_M\equiv Fr/(PrRb)^{1/4}$. The geophysical and astrophysical regimes are thus smoothly connected across the $PrRb=1$ transition. Applications to vertical transport in stellar radiative zones and modification to the instability criterion for the small-scale dynamo are discussed.
