# Eulerian results

The following are a few Eulerian statistics plotted as profiles across the channel.

All of these plots can be recreated by downloading the the data, the wall_scalesand the matlab plotting script

The data is quite simply structured---it consists of several vectors which represent various quantities from bins at various distances from the wall. The data within each bin is averaged, and the location of that quantity is the center of gravity of all those points, i.e.

**ybinCenter:** Center of gravity of y location for that bin

**v_x_mean, v_y_mean, v_z_mean:** Simple mean of full velocity components

**a_x_mean, a_y_mean, a_z_mean:** Simple mean of full acceleration components

**Vxx, Vyy, Vzz, Vxy, Vxz, Vyz:** Components of the Reynolds stress tensor, defined as:

I used an interpolated velocity profile when calculating the fluctuating velocity, which is a fitted curve through the measured mean velocity points and is V=0 at the wall. This has some minor effects on the fluctuating velocity near the wall where the shear is very large compared to other methods of calculating the fluctuating velocity.

**Axx, Ayy, Azz, Axy, Axz, Ayz:** Components of acceleration tensor, defined analogously to Reynolds stress tensor:

**AVxx, AVyy, AVzz, AVxy, AVxz, AVyx, AVyz, AVzx, AVzy:** Components of using the full accelerations and velocites, defined as:

**av_mean** is simply the trace of

**av_var** is defined as: