2008/12/13 by Jian-Zhou Zhu, Mark Taylor, Mark A. Taylor +2
Engineering · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Dissipation #Energy cascade #Exponent #Fluid Dynamics and Turbulent Flows #Intermittency #Mathematics #Mechanics #Navier-Stokes equation solutions #Physics #Quantum mechanics #Statistical physics #Thermalisation #Truncation (statistics) #Turbulence #Wave turbulence #Wavenumber #nlin.CD #physics.flu-dyn
paper · pdf · doi:10.48550/arxiv.0812.2495
openalex publication_date 2008/12/13 · arxiv created 2009/09/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A dissipation rate, which grows faster than any power of the wave number in Fourier space, may be scaled to lead a hydrodynamic system \it actually or \it potentially converge to its Galerkin truncation. Actual convergence we name for the asymptotic truncation at a finite wavenumber kG above which modes have no dynamics; and, we define potential convergence for the truncation at kG which, however, grows without bound. Both types of convergence can be obtained with the dissipation rate μ[cosh(k/kc)-1] who behaves as k2 (newtonian) and exp\k/kc\ for small and large k/kc respectively. Competition physics of cascade, thermalization and dissipation are discussed with numerical Navier-Stokes turbulence, emphasizing on the intermittency growth.