By Ed. by P. F. Hodnett
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35) With this representation, we come to an end of the “classical theories,” and our interest must now be to find theories in which turbulence is introduced in a more modern form. Our goal is to receive a theory based on the local pressure distribution on the bed. 4. The Concept of Coherent Structures The situation changed drastically as it was recognized that turbulent flows contain socalled coherent structures. In other words, a turbulent regime is at least partially composed of flow structures, which can be described in a deterministic form.
This is the so-called hydraulically rough wall condition, and it is this kind of flow for which the constant in Eq. 35 holds. For the case, Eq. 42b which covers the transition from smooth to rough walls, the constant varies and many approximations exist depending also on the height at which the fully turbulent profile starts. For an open channel flow, D has to be replaced by an adequate length scale. 43) 4 BH dH = B + 2H for a rectangular channel with B being the width of the channel and Per standing for the wetted perimeter.
Such a representation can always be produced whether coherent structures exist or not, and the JPDF does not even react much whether we have or do not have these coherent structures. 2). 2 The quadrant definitions The boundaries of the quadrants u'x ≥ 0 ; u'z ≥ 0 Contributions to the momentum transfer (%) +20% Name of the events u ≤0;u ≥0 –70% Ejection u ≤0;u ≤0 +20% Inflexion u ≥0;u ≤0 –70% Sweep ' x ' x ' x ' z ' z ' z Inflexion This representation is dangerous insofar as the contributions by the 2nd and the 4th quadrant are also called “coherent structures,” which is the origin of a lot of misunderstanding in the literature.
Sediment Transport by Ed. by P. F. Hodnett