ISSN:
1089-7666
Source:
AIP Digital Archive
Topics:
Physics
Notes:
A new approach for modeling turbulent rotating flows is presented. The main objective of this model is to take into account the complex effects of background rotation, which have been elucidated by homogeneous spectral analysis. The model is based on the following elements. First, it is shown, or recalled, that the use of the deviatoric part aij=Rij/Rll−δij/3 of the Reynolds stress tensor Rij as the unique tensorial argument for closing unknown terms (a basic principle in actual models) is no longer valid in the presence of solid body rotation. A decomposition of this tensor into two parts (aij=aeij+aZij), namely aeij (directional dependence) and aZij (polarization), is suggested from pure inviscid and homogeneous rapid distortion theory.It is shown that the first part aeij is preserved while the second aZij is damped by the pressure-velocity correlations through the action of the Coriolis force. This decomposition appears to provide the minimum amount of information in physical space needed to deal with the complexity of the problem. A system of equations for aeij and aZij is then given for predicting in an "ad hoc'' way some phenomena consistent with those identified by spectral models, recent direct numerical simulations (DNS), and experimental results. These phenomena are: (1) damping of any term attached to nonlinear interactions at very low Rossby numbers, in accordance with a convenient modification (for rotation) in the ε (dissipation rate) equation, (2) linear "rapid'' reorganization of an initial anisotropy, as shown by pure inviscid rapid distortion theory, and (3) nonlinear "Taylor–Proudman structuring'' at intermediate Rossby numbers. Although the present model is restricted to the case of pure solid body rotation, developments that could lead to a more general version that takes into account any kind of mean velocity gradient are discussed at the end of the paper. For this purpose, a consistent closure is provided for the "rapid'' pressure rate of the strain correlation tensor Φ2ij=eΦ2ij+ZΦ2ij (involved in the Rij equation), and for the related contribution involved in the equation for Reij=Rllaeij, without introducing any adjustable constant. Finally, we present a general two-tensor model (Rij,Reij;ε) of which we hope will encourage new efforts in second-order modeling.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.858298
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