论文标题
全面的分形维数，用于耗散性多骨架级联模型，用于完全发育的湍流
Generalized Fractal Dimension for a Dissipative Multi-fractal Cascade Model for Fully Developed Turbulence
论文作者
论文摘要
In this paper (Shivamoggi et al.), we explore a variant for the simple model based on a binomial multiplicative process of Meneveau and Sreenivasan that mimics the multi-fractal nature of the energy dissipation field in the inertial range of fully developed turbulence (FDT), and uses the generalized fractal dimension (GFD) prescription of Hentschel and Proccacia, Halsey et al。但是，在惯性范围内存在均匀的无限耗散，这证明会导致gfd $ d_q $（$ q = 1 $）的奇异性，并导致Meneveau-Sreenivasan二进制二进制多重性表格的崩溃，以消失。本文的目的是证明可以通过引入新的适当的ANSATZ来解决这一问题，以定义GFD $ d_q $，以通过现象学耗散参数$ k $ $ $ $（0 <k <1）$结合规模不变耗散的效果。该耗散参数还显示出在惯性范围内引起较陡峭的能量光谱。然后将此Ansatz推广到通过两个耗散参数$ k_1，$和$ k_2 $ $（0 <k_1 $和$ k_2 <1）$的更对称耗散。
In this paper (Shivamoggi et al.), we explore a variant for the simple model based on a binomial multiplicative process of Meneveau and Sreenivasan that mimics the multi-fractal nature of the energy dissipation field in the inertial range of fully developed turbulence (FDT), and uses the generalized fractal dimension (GFD) prescription of Hentschel and Proccacia, Halsey et al. However, the presence of an even infinitesimal dissipation in the inertial range is shown to lead to a singularity in the GFD $D_q$ (at $q=1$) of the energy dissipation field and leads to a breakdown of the Meneveau-Sreenivasan binomial multiplicative formulation for a dissipative inertial cascade. The purpose of this paper is to demonstrate that this can be resolved by introducing a new appropriate ansatz for the definition of the GFD $D_q$ to incorporate the effect of a scale-invariant dissipation via a phenomenological dissipative parameter $K$ $( 0 < K < 1)$. This dissipation parameter is also shown to cause a steeper energy spectrum in the inertial range, as to be expected. This ansatz is then generalized to incorporate a more symmetric dissipation via two dissipative parameters $K_1,$ and $K_2$ $( 0 < K_1$ and $K_2 < 1)$
