A classification scheme for turbulent flows based on their joint velocity-intermittency structure

Kolmogorov's classic theory for turbulence assumed an independence between velocity increments and the value for the velocity itself. However, this assumption is questionable, particularly in complex geophysical flows. Here we propose a framework for studying velocity-intermittency coupling that is similar in essence to the popular quadrant analysis method for studying near-wall flows. However, we study the dominant (longitudinal) velocity component along with a measure of the roughness of the signal, given mathematically by its series of Hölder exponents. Thus, we permit a possible dependence between velocity and intermittency. We compare boundary layer data obtained in a wind tunnel to turbulent jets and wake flows. These flow classes all have distinct velocity-intermittency characteristics, which cause them to be readily distinguished using our technique. Our method is much simpler and quicker to apply than approaches that condition the velocity increment statistics at some scale, r, on the increment statistics at a neighbouring, larger spatial scale, r+Δ, and the velocity itself. Classification of environmental flows is then possible based on their similarities to the idealised flow classes and we demonstrate this using laboratory data for flow in a parallel-channel confluence where the region of flow recirculation in the lee of the step is discriminated as a flow class distinct from boundary layer, jet and wake flows. Hence, using our method, it is possible to assign a flow classification to complex geophysical, turbulent flows depending upon which idealised flow class they most resemble.