Local geometry of isoscalar surfaces

Abstract

PACS:47.51.+a, 47.27.Gs, 47.27.tb ; An inert dynamically passive scalar in a constant density fluid forced by a statistically homogeneous field of turbulence has been investigated using the results of a 2563 grid direct numerical simulation. Mixing characteristics are characterized in terms of either principal curvatures or mean and Gauss curvatures. The most probable small-scale scalar geometries are flat and tilelike isosurfaces. Preliminary correlations between flow and scalar small-scale structures associate highly curved saddle points with large-strain regions and elliptic points with vorticity-dominated zones. The concavity of the scalar profiles along the isosurface normal coordinate xn correlates well with negative mean curvatures, Gauss curvatures displaying any sign, which correspond to scalar minima, tiles, or saddle points; on the other hand, convexity along xn is associated with positive mean curvatures, Gauss curvatures ranging from negative to positive signs, featuring maxima, tiles, or saddle points; inflection points along xn correlate well with small values of the mean curvature and zero or negative values of kg, corresponding to plane isosurfaces or saddle points with curvatures of equal and opposite signs. Small values of the scalar gradient are associated with elliptic points, either concave or convex (kg>0), for both concave and convex scalar profiles along xn. Large values of the scalar gradient (or, equivalently, scalar fluctuation dissipation rates) are generally connected with small values of the Gauss curvature (either flat or moderate-curvature tilelike local geometries), with both concave and convex scalar profiles along xn equally probable. Vortical local flow structures correlate well with small and moderate values of the scalar gradient, while strain-dominated regions are associated with large values. ; A part of this work has been performed under the auspices of the INTAS project 353 of the European Union. Juan Hierro would like to thank the Spanish Government and the Fulbright Commission for their support to spend one year at the Johns Hopkins University. The financial support of the DGA to the Computational Fluid Mechanics Group of the University of Zaragoza/LITEC is also acknowledged. ; Peer reviewed