<< ️Turbulence remains one of the central open problems in classical physics, largely due to the absence of a closed dynamical description of the Reynolds stress. Existing approaches typically rely either on local constitutive assumptions or on high-dimensional statistical representations, without identifying a minimal set of dynamical variables governing the cascade response. >>
<< ️Here (AA) show that the non-local stress response implied by the Navier-Stokes equations admits a systematic reduction onto a low-dimensional anisotropic sector of the turbulent cascade. This reduction leads to a minimal dynamical system with the structure of a damped oscillator, arising from the coupling between the leading angular mode and its nonlinear transfer to higher-order sectors. >>
<< ️Within this framework, classical turbulent behaviors -- including inertial-range scaling, shear-driven transport, and wall-bounded logarithmic profiles -- emerge as different realizations of the same underlying dynamical structure. Universal quantities such as the Kolmogorov constant and the von Kármán constant appear as leading-order consequences of internal consistency conditions applied across homogeneous and shear-driven regimes. >>
<< ️These results suggest that turbulence admits a minimal dynamical backbone governed by non-local cascade response, providing a unified perspective that connects spectral transfer, anisotropy, and mean-flow interaction within a single reduced framework. >>
Alejandro Sevilla. Geometric Dynamics of Turbulence: A Minimal Oscillator Structure from Non-local Closure. arXiv: 2603.18913v3 [physics.flu-dyn]. Mar 24, 2026.
Also: turbulence, in https://www.inkgmr.net/kwrds.html
Keywords: gst, turbulence, cascade response, non-local stress response, damped oscillators, inertial-range scaling, shear-driven transport, wall-bounded log profiles, spectral transfer, anisotropy, mean-flow interaction.
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