Parameter Error Analysis for Some α-Models of Turbulence

Resumo

The difficulty of dealing with 3D Navier-Stokes equations (NSE) is due to the fact that global regularity results for this model are still unknown, being one of the most challenging problems in partial differential equations theory, since the control of vorticity stretching term in the 3D vorticity equation is the main obstacle. As an analytical and computational alternative, some subgrid-scale models of turbulence, called in literature as α-models, were developed and have been extensively studied as a regularization of NSE, which make use of a special smoothing kernel, the one associated with the Green function of the Helmholtz operator v = u − α2∆u, where α is a given length-scale parameter. The first member of the family was introduced in the late 1990s (see [3]) called the Navier-Stokes-α (NS-α), as a closure model for the Reynolds averaged equations of the NSE. Posteriorly, similar models such as Leray-α [4] and the Modified Bardina model (see [5]) were introduced and have been object of interest specially in simulation in computational fluid dynamics. Computationally, explicit solutions for these models give excellent agreement with experimental data for a wide range of huge Reynolds numbers.