Localness of energy cascade in hydrodynamic turbulence. I. Smooth coarse graining
By Gregory L. Eyink, Hussein Aluie. 2009
202 citations recorded by the source corpus.
We introduce a novel approach to scale decomposition of the fluid kinetic energy (or other quadratic integrals) into band-pass contributions from a series of length scales. Our decomposition is based on a multiscale generalization of the “Germano identity” for smooth, graded filter kernels. We employ this method to derive a budget equation that describes the transfers of turbulent kinetic energy both in space and in scale. It is shown that the interscale energy transfer is dominated by local triadic interactions, assuming only the scaling properties expected in a turbulent inertial range. We derive rigorous upper bounds on the contributions of nonlocal triads, extending the work of Eyink [Physica D 207, 91 (2005)] for low-pass filtering. We also propose a physical explanation of the differing exponents for our rigorous upper bounds and for the scaling predictions of Kraichnan [Phys. Fluids 9, 1728 (1966); J. Fluid Mech. 47, 525 (1971)]. The faster decay predicted by Kraichnan is argued to be the consequen...
Subfields: Computational Mechanics, Fluid Flow and Transfer Processes, Ocean Engineering
View Paper: https://www.semanticscholar.org/paper/c6207601221bf50c84c904372f87a6ac9f622dea
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Citations in the corpus
- Statistical mechanics of two-dimensional and geophysical flows (2011, background): “For these we refer the reader to [179,185,112, 9,74,3,66,43] respectively.”
- Scale decomposition in compressible turbulence (2010, background): “Other definitions of an energy flux are possible, such as the “unsubtracted flux” of an incompressible flow critiqued in [6] and [2], Π l (x) ≡ ui NLi, NLi = ∂j(ρuiuj) which is often employed in literature that considers the sharp-spectral filter.”
- Mapping the Energy Cascade in the North Atlantic Ocean: The Coarse-Graining Approach (2017, methodology): “g the term ‘cascade’ when unwarranted since we are not making any statement about the scale-locality of the transfer, which can be diagnosed through a more rened analysis similar to what was done in Eyink and Aluie (2009); Aluie and Eyink (2009). 11 While spatial maps of ‘(x) unravel a wealth of inf”