Analysis of Cliff-Ramp Structures in Homogeneous Scalar Turbulence by the Method of Line Segments

The local structure of a turbulent scalar field in homogeneous isotropic turbulence is analyzed by direct numerical simulations (DNS). A novel signal decomposition approach is introduced where the signal of the scalar along a straight line is partitioned into segments based on the local extremal points of the scalar field. These segments are then parameterized by the distance between adjacent extremal points and a segment-based gradient. Joint statistics of the length and the segment-based gradient provide novel understanding about the local structure of the turbulent field and particularly about cliff-ramp-like structures. Ramp-like structures are unveiled by the asymmetry of joint distribution functions. Cliff-like structures are further analyzed by conditional statistics and it is shown from DNS that the width of cliffs scales with the Kolmogorov length scale.