**1. Introduction**

River damming produces alterations on the natural river functionality, both in the water discharge, as well as in the sediment transport and connectivity [1,2]. In particular, large dams [3] are estimated to trap more than 99% of the sediments entering the reservoir [4]. This causes the progressive silting of the reservoir and inhibits the sediment load in the river flow downstream of the dam, thus altering the river morphology [5] and the aggradation/degradation dynamics that are closely linked to the balance between upstream sediment supply and local transport capacity conditions [6]. Sediment supply-limited conditions from upstream cause the (selective) erosion of finer particles from the granular bed, until the flow is unable to move the coarser grains and new equilibrium conditions are reached [7]. During this degradation process, the median size of the bed material progressively coarsens and the sediment transport rate decreases, leading to a process known as bed armoring [8–10].

Occasionally, armored stream beds may be subject to high sediment loads, for example during dam flushing or removal operations, or during flood events associated to large sediment input from lateral inflows. Under these conditions, finer particles infiltrate into the void spaces of the immobile coarse bed grains, according to a selective trapping mechanism that is reciprocal to the selective erosion that caused bed armoring [11]. If the infiltration of fine particles into the coarse bed interstices is extensive, the volume of voids drops increasing the compactness of the stream bed texture, thus decreasing its hydraulic conductivity and increasing its resistance to flow (e.g., [12,13]). This process is known as colmation or clogging (see, for example, [14] for a review), and has significant impacts on stream ecology (e.g., [15–18]), exchanges of water, dissolved substances and heat with the underlying hyporheic zone and groundwater [19], and flow and turbulence structure [20–22]. Under high flow conditions, the armour layer can break up and the entire river bed becomes mobilized, hence resetting the bed morphology and grain size distribution. However, if the erosion capacity of the flow is not sufficient to remove the coarse grains, as soon as the sediment load from upstream declines, the reestablishment of sediment supply-limited conditions reactivates selective erosion of finer particles, sustaining the armoring of the stream bed.

The cleaning dynamics controlling the erosion of finer particles from coarse granular beds is inherently different from that typical of uniform sized beds. In fact, in armored beds, the presence of macro-roughness due to the coarser particles alters the flow structure and, consequently, the distribution of the stress components below the gravel crest level. In these beds, besides turbulent stresses, form-induced stresses and form drag also contribute to the total shear stress distribution [23]. In addition, the vertical component of the stress responsible for lifting and transporting fine material was found to be decreasing below gravel crest level [22,24,25]. This alteration is mirrored in the reduced sediment entrainment and transport capacity of the flow, which is affected also by the smaller fine sediment-water active interface with respect to that of a uniform bed.

It is therefore clear that the traditional formulae derived for uniform bed cases fail to describe erosion and sediment transport processes over immobile gravel beds. In fact, these formulae do not account for the reduction in the effective part of the shear stress, nor the reduction in the fine sediment-water active interface. In this respect, performing laboratory experiments is a common methodological practice for investigating selective transport dynamics in armored beds and gaining useful elements to derive empirical formulas of fine sediment transport (e.g., [26–29]). Experimental research is typically carried out in laboratory flumes using laser-scanner (e.g., [29]) or digital photogrammetry (e.g., [30]) to measure the changes in the topography. The track of these changes in the fine sediment level inside the gravel matrix is usually coupled with measures of transport rate (trough sieves or density cells (e.g., [27,29]) or concentration (e.g., [26,31]) to quantify the fine sediment transport and/or erosion rate between the gravel. Based on these experimental approaches, useful fine sediment transport formulae has been proposed in previous literature, as for instance in [26–29].

Despite the above cited empirical formulae and despite the examples of direct measurements of the flow field in the roughness layer [23] (e.g., [22,24,25,32]), a comprehensive framework on the inter-grain flow and sediments dynamics in gravel bed rivers still poses some scientific challenges. These challenges are primarily due to the operational difficulties to perform velocity measurements far below the gravel crest level and to quantify the relative contribution of the form drag to the total shear stress [25]. In addition, a fair comparison among existing studies is not obvious due to the differences in the bed topographies, which chiefly controls the distribution of the shear stress components [25], thus hampering the derivation of general considerations. In this context, fine-scale numerical models can offer a valid alternative to overcome the inherent difficulties of fine-resolution, inter-grain experimental measurements. At the same time, they can easy the investigation of the role of the geometry in affecting the stresses distribution, provided that the setup and repetition of laboratory experiments with different configurations is not a minor matter. While examples of Direct Numerical

Simulation (DNS) over rough bed configurations do exist (e.g., [33–35]), the inclusion of sediment active layers in fine-resolution hydrodynamics model is a relatively unexplored area of research.

In this study, we present and test a new semi-implicit numerical scheme for the solution of the two-dimensional Navier-Stokes equations, in which we included the possibility to easily simulate sediment entertainment and transport processes. The scheme, based on the method proposed by [36–38], is mass-conservative, computationally efficient, and able to solve the small-scale structures that characterize inter-grain flow field. In this study, we present proof-of-concept and preliminary results of this model as a first step towards its extension to a complete three-dimensional model coupled with a turbulence closure scheme. To this end, we focus on the validation of the proposed model against numerical tests and on showing its potential for applications in the context of fine sediment transport dynamics in gravel bed rivers.
