Streamlines

The flow pattern is visually brought out in terms of streamlines. For this purpose, the stream function is first calculated by integrating the velocity field as per the formula

starting from an exterior point where Here, u and v indicate the time-averaged velocity components of the flow field. The streamlines are then plotted simply as contours of constant stream function in the flow domain.

Turbulent kinetic energy budget

The turbulent kinetic energy budget helps in examining how turbulence is spatially distributed after being produced in the flow field. It also explores the development of the cascade process that directs the kinetic energy of velocity fluctuations from large scales towards the small scales, ultimately to be dissipated by molecular-level processes. Under unique circumstances, reverse cascading, namely energy transfer towards the large scale structures is also possible.

The equation describing the transport of turbulent kinetic energy is