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Lookup NU author(s): Dr Lian Gan
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In this paper we examine the invariants p and q of the reduced 2 × 2 velocity gradient tensor (VGT) formed from a two-dimensional (2D) slice of an incompressible three-dimensional (3D) flow. Using data from both 2D particle image velocimetry (PIV) measurements and 3D direct numerical simulations of various turbulent flows, we show that the joint probability density functions (p.d.f.s) of p and q exhibit a common characteristic asymmetric shape consistent with (pq) <0. An explanation for this inequality is proposed. Assuming local homogeneity we derive (p) = 0 and (q) = 0. With the addition of local isotropy the sign of (pq) is proved to be the same as that of the skewness of ∂u1/∂x1, hence negative. This suggests that the observed asymmetry in the joint p.d.f.s of p-q stems from the universal predominance of vortex stretching at the smallest scales. Some advantages of this joint p.d.f. compared with that of Q-R obtained from the full 3 × 3 VGT are discussed. Analysing the eigenvalues of the reduced strain-rate matrix associated with the reduced VGT, we prove that in some cases the 2D data can unambiguously discriminate between the bi-axial (sheet-forming) and axial (tube-forming) strain-rate configurations of the full 3 × 3 strain-rate tensor.
Author(s): Cardesa JI, Mistry D, Gan L, Dawson JR
Publication type: Article
Publication status: Published
Journal: Journal of Fluid Mechanics
Year: 2013
Volume: 716
Pages: 597-615
Print publication date: 01/02/2013
ISSN (print): 0022-1120
ISSN (electronic): 1469-7645
Publisher: Cambridge University Press
URL: http://dx.doi.org/10.1017/jfm.2012.558
DOI: 10.1017/jfm.2012.558
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