Maximum energy dissipation to explain velocity fields in shallow reservoirs

Abstract

Shallow reservoirs are often used as sediment traps or storage basins, in which sedimentation depends on the flow pattern. Short rectangular reservoirs reveal a straight jet from inlet to outlet with identical recirculation zones on both sides. In longer reservoirs, the main jet reattaches to the side of the reservoir leading to small and large recirculation zones. Previous studies have found an empirical geometric relation describing the switch between these two flow patterns. In this study, we demonstrate, with a simple analytical model, that this switch coincides with a maximization of energy dissipation in the shear layer between the main jet and recirculation zones: short reservoirs dissipate more energy when the flow pattern is symmetric, while longer reservoirs dissipate more energy with an asymmetric pattern. This approach enables the prediction of the flow patterns without detailed knowledge of small scale processes, potentially useful in the early phase of reservoir design.

Effects of Geometry and Hydraulic Characteristics of Shallow Reservoirs on Sediment Entrapment

“…Camnasio concluded that deposits could modify the direction of the main jet and flow pattern. Moreover, a theoretical approach based on thermodynamic optimality was presented recently by Westhoff et al (2018) that proves this fact [26].…”

Flow recession behavior of preferential subsurface flow patterns with minimum energy dissipation

“…As an alternative to forward modeling, there is an increasing number of studies attempting to derive preferred states of the atmosphere and the hydrosphere from principles of optimality (e.g., Kleidon and Schymanski, 2008;Kleidon and Renner, 2013;Kleidon et al, 2014;Kleidon and Savenije, 2017;Kleidon et al, 2019;Zehe et al, 2010Zehe et al, , 2013Zehe et al, , 2021Westhoff and Zehe, 2013;Westhoff et al, 2014Westhoff et al, , 2017Zhao et al, 2016;Schroers et al, 2022). In the context of fluid flow, minimum energy dissipation seems to be a promising concept, and it has been successfully applied to river networks (Howard, 1990;Rodriguez-Iturbe et al, 1992a, b;Rinaldo et al, 1992;Maritan et al, 1996) and to the cardiovascular system of mammals (West et al, 1997;Enquist et al, 1998Enquist et al, , 1999Banavar et al, 1999;West et al, 1999a, b).…”

Unsteady shallow meandering flows in rectangular reservoirs: A modal analysis of URANS modelling

“…The hydraulic and geometric conditions leading to symmetric and asymmetric jets were extensively studied experimentally (Aloui and Souhar, 2000;Camnasio et al, 2011;Canbazoglu and Bozkir, 2004;Dufresne et al, 2010a;Kantoush et al, 2008;Mullin et al, 2003;Oca and Masaló, 2007), numerically (Camnasio et al, 2013;Dewals et al, 2008;Dufresne et al, 2011;Esmaeili et al, 2016;Khan et al, 2013;Peltier et al, 2015;Peng et al, 2011;Stovin and Saul, 2000) and analytically (Westhoff et al, 2018). In contrast, less attention was given to the case of a meandering jet, despite its engineering relevance.…”