An Entropic Model for the Assessment of Streamwise Velocity Dip in Wide Open Channels.

Domenica Mirauda,Marilena Pannone,Annamaria De Vincenzo

doi:10.3390/e20010069

Abstract

The three-dimensional structure of river flow and the presence of secondary currents, mainly near walls, often cause the maximum cross-sectional velocity to occur below the free surface, which is known as the “dip” phenomenon. The present study proposes a theoretical model derived from the entropy theory to predict the velocity dip position along with the corresponding velocity value. Field data, collected at three ungauged sections located along the Alzette river in the Grand Duchy of Luxembourg and at three gauged sections located along three large rivers in Basilicata (southern Italy), were used to test its validity. The results show that the model is in good agreement with the experimental measurements and, when compared with other models documented in the literature, yields the least percentage error.

Highlights

The velocity dip position is a ubiquitous feature of open channel flows, and describes the phenomenon by which maximum streamwise velocity is detected below the free surface
The present study provides an analytical solution for ensemble mean and variance of streamwise velocity dip position, due to cross-sectional vorticity and secondary currents, based on the maximisation of the related information entropy, e.g., [19]
The present study proposes a general theoretical model to compute the velocity dip position in open channels, based on a probabilistic approach originating from the maximisation of the related information entropy

Summary

Introduction

The velocity dip position is a ubiquitous feature of open channel flows, and describes the phenomenon by which maximum streamwise velocity is detected below the free surface. This phenomenon was first observed about a century ago by [1,2], and further experimental studies showed that it was induced by the presence of secondary cross-sectional flow structures. Secondary currents of the second kind, whose origin is more complex, are observed in straight and non-circular channels as a consequence of turbulence related to the formation of bed ridges, e.g., [5]. Such corner-induced secondary currents consist of upward flow moving into the apex of the corner, and backward flow moving away from the corner along the channel boundaries

Methods

Results

Conclusion