## Publication Abstracts

### Canuto and Dubovikov 1996

**8**, 571-585, doi:10.1063/1.868842.

We propose new dynamical equations to describe fully developed turbulence. We begin with the Wyld equations (WE), which are exact solutions of the NSE. The WE, and their langevin-like representation, show that nonlinearities induce a turbulent force f^{t}(k) and a turbulent velocity ν_{t}(k), which are given by an infinite series of Wyld diagrams. The series for ν_{t}(k) is renormalizable, and its sum can be found using RNG methods. The result, Eq. (2a), holds for stirring forces f^{ext} with an arbitrary correlation function φ and generalizes previous RNG results, which neglected f^{t} and were limited to power law φ∼k^{1-2ε}. To recover Kolmogorov law, these earlier RNG-based theories were forced to introduce an ad hoc stirring force with a proscribed φ∼k^{-3}. By contrast, we show that ∼k^{-3} belongs to φ̅, which is the correlation function of f^{t}, and that in the inertial range f^{t} ≫ f^{ext}. The series for φ̅ cannot be summed because of a nonrenormalizable infrared divergence (IR) with an infinite number of divergent irreducible diagrams. To overcome this difficulty, we use the well-accepted notion of local energy transfer and we derive an expression for the energy flux Pi(k), Eq. (2d), as well as a dynamical equation for the energy spectrum E(k), Eq. (2b). We also construct the dynamical equations for Reynolds stress spectra (solved in papers II and III). An analogous approach is developed for the temperature field. The model contains no free parameters. Some of its predictions are Kolmogorov spectrum E(k)∼k^{-5/3} with Ko=5/3, in agreement with recent data; temperature spectrum in the inertial-convective region E_{θ}∼Ba ε̅^{1/3} ε_{θ}k^{-5/3}, in agreement with the data; Batchelor constant Ba = σ_{t}Ko. In addition, in papers II and III we carry out extensive comparisons with the laboratory, DNS, LES data, and phenomenological models. The model can be used to construct a subgrid model for LES calculations.

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#### BibTeX Citation

@article{ca04100j, author={Canuto, V. M. and Dubovikov, M. S.}, title={A dynamical model for turbulence. I. General formalism}, year={1996}, journal={Physics of Fluids}, volume={8}, pages={571--585}, doi={10.1063/1.868842}, }

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#### RIS Citation

TY - JOUR ID - ca04100j AU - Canuto, V. M. AU - Dubovikov, M. S. PY - 1996 TI - A dynamical model for turbulence. I. General formalism JA - Phys. Fluids JO - Physics of Fluids VL - 8 SP - 571 EP - 585 DO - 10.1063/1.868842 ER -

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