Inertial Manifolds for Certain Subgrid-Scale α-Models of Turbulence

نویسندگان

  • Mohammad Abu Hamed
  • Yanqiu Guo
  • Edriss S. Titi
چکیده

In this note we prove the existence of an inertial manifold, i.e., a global invariant, exponentially attracting, finite-dimensional smooth manifold, for two different sub-grid scale α-models of turbulence: the simplified Bardina model and the modified Leray-α model, in two-dimensional space. That is, we show the existence of an exact rule that parameterizes the dynamics of small spatial scales in terms of the dynamics of the large ones. In particular, this implies that the long-time dynamics of these turbulence models is equivalent to that of a finite-dimensional system of ordinary differential equations. MSC Classification: 35Q30, 37L30, 76B03, 76F20, 76F55, 76F65

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

A modified-Leray-α subgrid scale model of turbulence

Inspired by the remarkable performance of the Leray-α (and the Navier–Stokes alpha (NS-α), also known as the viscous Camassa–Holm) subgrid scale model of turbulence as a closure model to Reynolds averaged equations (RANS) for flows in turbulent channels and pipes, we introduce in this paper another subgrid scale model of turbulence, the modified Leray-α (ML-α) subgrid scale model of turbulence....

متن کامل

Analytical Study of Certain Magnetohydrodynamic-α Models

In this paper we present an analytical study of a subgrid scale turbulence model of the threedimensional magnetohydrodynamic (MHD) equations, inspired by the Navier-Stokes-α (also known as the viscous Camassa-Holm equations or the Lagrangian-averaged Navier-Stokes-α model. Specifically, we show the global well-posedness and regularity of solutions of a certain MHD-α model (which is a particular...

متن کامل

The Dissipation Rate Transport Equation and Subgrid-Scale Models in Rotating Turbulence

The dissipation rate transport equation remains the most uncertain part of turbulence modeling. The difficulties are increased when external agencies like rotation prevent straightforward dimensional analysis from determining the correct form of the modelled equation. In this work, the dissipation rate transport equation and subgrid scale models for rotating turbulence are derived from an analy...

متن کامل

Large-eddy simulation of turbulent flow over an array of wall-mounted cubes submerged in an emulated atmospheric boundary-layer

Turbulent flow over an array of wall-mounted cubic obstacles has been numerically investigated using large-eddy simulation. The simulations have been performed using high-performance computations with local cluster systems. The array of cubes are fully submerged in a simulated deep rough-wall atmospheric boundary-layer with high turbulence intensity characteristics of environmental turbulent fl...

متن کامل

ذخیره 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 نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • SIAM J. Applied Dynamical Systems

دوره 14  شماره 

صفحات  -

تاریخ انتشار 2015