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

Area of Science:

• * Fluid dynamics
• * Computational physics

Background:

• * Standard shell models are crucial for studying turbulence.
• * These models often rely on self-similar scaling, which can be limiting.
• * Exploring alternative wave number structures is key to advancing turbulence modeling.

Purpose of the Study:

• * To propose and analyze novel shell models based on recurrent wave number sequences.
• * To investigate the conservation properties of energy and helicity in these new models.
• * To compare the performance of these models against standard shell models in simulating turbulence.

Main Methods:

• * Defining shell variables on recurrent sequences (e.g., Fibonacci, Padovan).
• * Generalizing interaction coefficients for invariant conservation without exact self-similarity.
• * Analyzing power-law spectra, spectral fluxes, and structure function scaling.
• * Considering both local and long-range interactions, including helical models.

Main Results:

• * Proposed shell models conserve inviscid invariants like energy and helicity.
• * These models exhibit features identical to standard shell models, including power-law spectra and spectral fluxes.
• * Analogous deviations from self-similar scaling in structure functions indicate comparable turbulent intermittency.
• * A helical model with long-range interactions shows an inverse cascade.

Conclusions:

• * Recurrent wave number shell models offer a viable alternative to standard models.
• * These models can be used as diagnostic tools or subgrid models in direct numerical simulations.
• * The formulation allows for sparse wave number representations on regular grids.
• * Novel helical models can capture inverse cascades, broadening the scope of shell model applications.