Lattice Boltzmann method for Casimir invariant of two-dimensional turbulence

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• 作者：Yu-xian XIA ((夏玉显)) ^{xiayuxian2008.com@163.com" class="auth_mail" title="E-mail the corresponding author}Author Vitae ; Yue-hong QIAN ((钱跃竑)) ; ^{qian@shu.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：2-D turbulence ; Casimir invariants ; lattice Boltzmann method
• 刊名：Journal of Hydrodynamics, Ser. B
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：28
• 期：2
• 页码：319-324
• 全文大小：922 K

文摘

The Casimir invariants of the 2-D turbulence are investigated by the lattice Boltzmann method. A coarse-graining approach is used, that allows to resolve the flux of the Casimir invariant in scale and in space. It is found that the flux of the enstrophy cascades to small scales and the direction cascade of the energy flux is upscaled. Moveover, the probability distribution function (PDF) of the enstrophy flux gives a clear evidence that the enstrophy cascades to smaller scales. Finally, the behavior of the cascade of the high-order Casimir invariants Zⁿ is discussed. The flux of the fourth-order Casimir invariant Z⁴ cascades to small scales. The flux of Zⁿ   has a logarithmic relationship with the scale, that is,${\Pi }_l^{Z^n}\sim l^{{\zeta }_n}\left(n=2,4,6\right)$.