Shell models on recurrent sequences: Fibonacci, Padovan, and other series.

IF 2.2 3区 物理与天体物理 Q2 PHYSICS, FLUIDS & PLASMAS
L Manfredini, Ö D Gürcan
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引用次数: 0

Abstract

A class of shell models is proposed where the shell variables are defined on a recurrent sequence of integer wave numbers such as the Fibonacci or the Padovan series or their variations, including a sequence made of square roots of Fibonacci numbers rounded to the nearest integer. Considering the simplest model, which involves only local interactions, the interaction coefficients can be generalized in such a way that the inviscid invariants, such as energy and helicity, can be conserved even though there is no exact self-similarity. It is shown that these models basically have identical features with standard shell models and produce the same power-law spectra, similar spectral fluxes, and analogous deviation from self-similar scaling of the structure functions, implying comparable levels of turbulent intermittency. Such a formulation potentially opens up the possibility of using shell models, or their generalizations along with discretized regular grids such as those found in direct numerical simulations, as either diagnostic tools or subgrid models. It also allows us to develop models where the wave-number shells can be interpreted as sparsely decimated sets of wave numbers over an initially regular grid. In addition to conventional shell models with local interactions that result in forward cascade, a particular a helical shell model with long-range interactions is considered on a similarly recurrent sequence of wave numbers, corresponding to the Fibonacci series, and found to result in the usual inverse cascade.

循环序列的壳模型:斐波那契、帕多万和其他序列。
提出了一类壳模型,其中壳变量定义在整数波数的循环序列上,如斐波那契或帕多万系列或其变体,包括由斐波那契数的平方根四舍五入到最接近的整数组成的序列。考虑到最简单的模型,它只涉及局部相互作用,相互作用系数可以推广到这样一种方式,即即使没有精确的自相似性,能量和螺旋度等非粘不变量也可以守恒。结果表明,这些模型与标准壳模型具有基本相同的特征,并产生相同的幂律谱、相似的谱通量和类似的结构函数自相似标度偏差,表明湍流间歇性水平相当。这种公式潜在地开启了使用壳模型的可能性,或者它们的推广以及离散规则网格(如直接数值模拟中发现的那些)作为诊断工具或子网格模型。它还允许我们开发模型,其中波数壳可以解释为初始规则网格上稀疏抽取的波数集。除了具有导致正向级联的局部相互作用的传统壳模型外,还考虑了具有远程相互作用的特殊a -螺旋壳模型,该模型适用于类似的循环波数序列,对应于斐波那契序列,并发现会导致通常的逆级联。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Physical Review E
Physical Review E PHYSICS, FLUIDS & PLASMASPHYSICS, MATHEMAT-PHYSICS, MATHEMATICAL
CiteScore
4.50
自引率
16.70%
发文量
2110
期刊介绍: Physical Review E (PRE), broad and interdisciplinary in scope, focuses on collective phenomena of many-body systems, with statistical physics and nonlinear dynamics as the central themes of the journal. Physical Review E publishes recent developments in biological and soft matter physics including granular materials, colloids, complex fluids, liquid crystals, and polymers. The journal covers fluid dynamics and plasma physics and includes sections on computational and interdisciplinary physics, for example, complex networks.
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