The 12 generators used to compute increments in the plane and the generator in the direction. The crossings of dotted lines indicate grid points in the numerical simulation.
Second order structure functions at in run B with . The dotted lines indicate the different structure functions in the 12 directions given by the generators in the plane, and the thick solid curve is the average . The thick dashed curve corresponds to increments in the direction and is .
Second order structure functions and in run B at different times, between and 30. A dissipative range scaling is indicated at small scales, and the average slope is indicated in the inertial range.
Sixth order structure functions and in run B at different times, between and 30. A dissipative range scaling is indicated at small scales, and two average slopes are indicated in the inertial ranges (see text). Note that the perpendicular part of the structure function dominates the parallel one at all scales.
Second-order helicity structure functions and (see Eq. (7)) in run B with . at different times between and 30. The dissipative range scales as , consistent with the fact that is quartic in the velocity; the average slope is indicated for the inertial range.
Fourth-order helicity structure functions and in run B at different times, between and 30. The average slope is indicated for the inertial range.
Scaling exponents (with error bars, see Table I) as a function of the order , for the velocity (stars) and the helicity (pluses) in run A with , and for the velocity (triangles) and the helicity (diamonds) in run B with . The dotted line corresponds to Kolmogorov scaling , and the dashed line to , which represents the velocity exponents best.
PDFs at different intervals in the direct cascade for velocity (solid) and helicity (dashed) increments in the direction perpendicular to the axis of rotation. Increments are normalized by their variance. The dotted curve represents a Gaussian distribution with the same variance.
Slices of the energy density (top left), vorticity intensity (top right), component of the velocity (bottom left), and helicity density (bottom right) in run B at . Note the imprint of small scales in the vorticity and helicity (right column).
Three dimensional rendering of the component of the velocity in the entire domain in run B at (above) and a zoom on a subregion (below) showing the component of the velocity in a columnlike structure (left) and its helicity density (right).
Order and scaling exponents for the velocity and for the helicity, with errors, for run A and run B .
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