Stochastic numerical analysis of anomalous longitudinal dispersion and dilution in shallow decelerating stream flows

Simplified Entropic Model for the Evaluation of Suspended Load Concentration

“…Humans can alter fine sediment supply to river networks and solid transport processes within them via activities, such as agriculture, mining, forestry operations, and the construction of dams. Particularly, a dam creates an upstream area with low water velocity, which affects solute/sediment dynamics and river morphology and induces sedimentation in reservoirs that gradually lose their useful capacity [1][2][3][4][5][6][7][8]. Even reservoir sediment trapping reduces the supply of sediments to the downstream river, where modifications of peak flow rate and sediment load impact on channel morphological equilibrium, and on the stability of river banks and fluvial engineering works (e.g., bridges, embankments, etc.).…”

“…Analytical solutions of the transient advection-dispersion equation for dissolved chemicals and fine sediments in open channels were given by the authors in the case of deterministic depth-averaged velocity distributions and different initial conditions by the method of moments (e.g., [34]); in the case of randomly uniform flows in the presence of morphologic heterogeneity by a stochastic Lagrangian approach (e.g., [35,36]); and in terms of second-order concentration statistics based on a stochastic Eulerian approach (e.g., [37]). An analytical-numerical model was proposed to solve ADE in a stochastic Lagrangian framework in the case of backwater flows, highlighting the occurrence of a global re-densification of the cloud and a permanent transverse non-uniformity (e.g., [4]). Finally, a stochastic Lagrangian numerical model was developed to handle ADE in the case of non-uniform transverse mixing, highlighting the occurrence of concentration boundary side-pockets (e.g., [38]).…”

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

“…Compute the tentative parameter M from Equations (10) and (13), with U replacing u. Compute the tentative expected dip position from Equations (22) and (24). Measure the velocity along the deepest vertical in correspondence of < Y d >.…”

“…Kitanidis [22] and Pannone and Kitanidis [23] respectively introduce and apply a dilution index expressed in terms of concentration distribution entropy for the investigation of groundwater pollutant dynamics. Pannone and De Vincenzo [24] extend the approach by [22] to solute dispersion in backwater river flows, where the stream deceleration is associated with a gradual decline in solute concentration entropy and dilution. Finally, the principle of maximum entropy has also been used as an effective approach for stochastic generation of stream flows and hydrological variables [25].…”

“…Specifically, the reduction in free flow section is associated with local minima of velocity entropy and reduction in secondary circulation. Other applications of the entropic approach are documented in the field of environmental fluid mechanics, e.g., [22][23][24]. Kitanidis [22] and Pannone and Kitanidis [23] respectively introduce and apply a dilution index expressed in terms of concentration distribution entropy for the investigation of groundwater pollutant dynamics.…”