2024/08/28 by V. J. Valadão, G. Boffetta, Valadão, V. J. +7 · 3 citations
Engineering · Mathematics · #Computational Fluid Dynamics and Aerodynamics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Turbulent Flows #Lattice Boltzmann Simulation Studies #Mathematical analysis #Mathematics #Mechanics #Navier–Stokes equations #Physics #Quantum mechanics #Spectrum (functional analysis)
paper · pdf · doi:10.48550/arxiv.2408.15735
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2024/08/28 · openalex created_date 2024/09/22 · openalex updated_date 2026/08/05
The presence of a linear friction drag affects significantly the dynamics of turbulent flows in two-dimensions. At small scales, it induces a correction to the slope of the energy spectrum in the range of wavenumbers corresponding to the direct enstrophy cascade. Simple arguments predict that this correction is proportional to the ratio of the friction coefficient to the characteristic deformation rate of the flow. In this work, we examine this phenomenon by means of a set of GPU-accelerated numerical simulations at high resolutions, varying both the Reynolds number and the friction coefficient. Exploiting the relation between the energy spectrum and the enstrophy flux, we obtain accurate measurements of the spectral scaling exponents. Our results show that the exponent of the spectral correction follows a universal linear law in which the friction coefficient is rescaled by the enstrophy injection rate.