Hyperviscosity, Galerkin truncation, and bottlenecks in turbulence.
نویسندگان
چکیده
It is shown that the use of a high power alpha of the Laplacian in the dissipative term of hydrodynamical equations leads asymptotically to truncated inviscid conservative dynamics with a finite range of spatial Fourier modes. Those at large wave numbers thermalize, whereas modes at small wave numbers obey ordinary viscous dynamics [C. Cichowlas et al., Phys. Rev. Lett. 95, 264502 (2005)10.1103/Phys. Rev. Lett. 95.264502]. The energy bottleneck observed for finite alpha may be interpreted as incomplete thermalization. Artifacts arising from models with alpha>1 are discussed.
منابع مشابه
Convergence results for a class of spectrally hyperviscous models of 3-D turbulent flow
We consider the spectrally hyperviscous Navier–Stokes equations (SHNSE) which add hyperviscosity to the NSE but only to the higher frequencies past a cutoff wavenumberm0. In Guermond and Prudhomme (2003) [18], subsequence convergence of SHNSE Galerkin solutions to dissipative solutions of the NSE was achieved in a specific spectral-vanishingviscosity setting. Our goal is to obtain similar resul...
متن کاملA hybrid numerical simulation of isotropic compressible turbulence
A novel hybrid numerical scheme with built-in hyperviscosity has been developed to address the accuracy and numerical instability in numerical simulation of isotropic compressible turbulence in a periodic domain at high turbulent Mach number. The hybrid scheme utilizes a 7th-order WENO (Weighted Essentially Non-Oscillatory) scheme for highly compressive regions (i.e., shocklet regions) and an 8...
متن کاملModels for turbulent plane Couette flow using the proper orthogonal decomposition
We model turbulent plane Couette flow ~PCF! by expanding the velocity field as a sum of optimal modes calculated via the proper orthogonal decomposition from numerical data. Ordinary differential equations are obtained by Galerkin projection of the Navier–Stokes equations onto these modes. For a minimal truncation including only the most energetic modes having no streamwise variation, we show u...
متن کاملStability under Galerkin Truncation of A-stable Runge–kutta Discretizations in Time
We consider semilinear evolution equations for which the linear part is normal and generates a strongly continuous semigroup and the nonlinear part is sufficiently smooth on a scale of Hilbert spaces. We approximate their semiflow by an implicit, A-stable Runge–Kutta discretization in time and a spectral Galerkin truncation in space. We show regularity of the Galerkintruncated semiflow and its ...
متن کاملGalerkin Spectral Methods for Higher-order Boundary Value Problems Arising in Fluid Mechanics
We develop Galerkin spectral technique for solving boundary value problems arising in natural convection. They consist of a fourth-order b.v.p. for the stream function coupled to a second-order b.v.p. for the temperature. As a basis are used the set of socalled Beam functions introduced by Lord Rayleigh and the set of Fourier functions. The formulas for the cross expansions between the two sets...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Physical review letters
دوره 101 14 شماره
صفحات -
تاریخ انتشار 2008