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Entropy Wake Law for Streamwise Velocity Profiles in Smooth Rectangular Open Channels

1
School of Engineering, Basilicata University, Viale dell’Ateneo Lucano 10, 85100 Potenza, Italy
2
Department of Mathematics, Computer Science and Economics, Basilicata University, Viale dell’Ateneo Lucano 10, 85100 Potenza, Italy
*
Author to whom correspondence should be addressed.
Entropy 2020, 22(6), 654; https://doi.org/10.3390/e22060654
Received: 2 May 2020 / Revised: 6 June 2020 / Accepted: 12 June 2020 / Published: 13 June 2020
In narrow open channels, the three-dimensional nature of the flow and the transport momentum from the sidewalls to the central region cause the maximum longitudinal velocity to occur below the water surface. The entropy model is unable to accurately describe the velocities near the free surface when the dip phenomenon exists. The present paper proposes a new dip-modified entropy law for steady open channel flows, which consists of three additional terms: the first one similar to Coles’ function; the second one linearly proportional to the logarithmic distance from the free surface; and the third one depending on the cubic correction near the maximum velocity. The validity of the new model was tested on a set of laboratory measurements carried out in a straight rectangular flume with smooth boundaries and for different values of water discharge, bottom slope, and aspect ratio. A detailed error analysis showed good agreement with the data measured through the present research and a more accurate prediction of the velocity-dip-position compared with the one evaluated through the original entropy model. In addition, the modified entropy wake law matched very well with other literature data collected in rectangular cross-sections with different flow conditions. View Full-Text
Keywords: Shannon’s information entropy; wake law; streamwise velocity profiles; velocity-dip-position; open channel flows; laboratory experiences; error analysis; rectangular cross-section Shannon’s information entropy; wake law; streamwise velocity profiles; velocity-dip-position; open channel flows; laboratory experiences; error analysis; rectangular cross-section
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Mirauda, D.; Russo, M.G. Entropy Wake Law for Streamwise Velocity Profiles in Smooth Rectangular Open Channels. Entropy 2020, 22, 654.

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