Key terms and definitions

When you generate structure functions with FluidSF, you are returned a dictionary with the keys provided below. Each key corresponds to a structure function that can be calculated from the data, except for the key dir-diffs, which provides the separation distances in each direction. To learn more about the structure functions, see What are structure functions?

SF_advection_velocity_dir: Advective velocity structure function in the direction of the separation vector (dir = x, y, z).

SF_advection_scalar_dir: Advective scalar structure function in the direction of the separation vector (dir = x, y, z).

SF_LL_dir: Longitudinal second order velocity structure function in the direction of the separation vector (dir = x, y, z).

SF_LLL_dir: Longitudinal third order velocity structure function in the direction of the separation vector (dir = x, y, z).

SF_LTT_dir: Longitudinal-transverse-transverse third order velocity structure function in the direction of the separation vector (dir = x, y, z).

SF_LSS_dir: Longitudinal-scalar-scalar third order velocity structure function in the direction of the separation vector (dir = x, y, z).

dir-diffs: Separation distances in each direction (dir = x, y, z). These are calculated as the Euclidean distance between pairs of data points in the flow field. Provided in the same units as the input data.

Important

All non-advective structure functions have naming conventions with the subscripts L, and T to denote the longitudinal and transverse velocities. The longitudinal direction is typically aligned with the flow direction, while the transverse direction is perpendicular to the flow direction.

For SF_LL_x, SF_LLL_x, SF_LTT_x, and SF_LSS_x, L denotes the longitudinal velocity differences in the x-direction \(v_x(\mathbf{x}) - v_x(\mathbf{x}+\mathbf{r})\) and T denotes the transverse velocity differences in the x-direction \(v_y(\mathbf{x}) - v_y(\mathbf{x}+\mathbf{r})\). S denotes the scalar differences \(s(\mathbf{x}) - s(\mathbf{x}+\mathbf{r})\).