Bedload traveling in a lab flume by jumping, rolling, and sliding (under water footage). Source: Sebastian Schwindt@ Hydro-Morphodynamics channel on YouTube.

```{admonition} Bedload basics :class: important For a better reading experience of this section, the {ref}`glossary` helps with explanations of the terms {term}`Sediment transport`, (dimensionless) {term}`Bedload` transport $\Phi_b$, {term}`Dimensionless bed shear stress` $\tau_{x}$, and the {term}`Shields parameter` $\tau_{x,cr}$ (in that order). ``` (bl-principles)= ## Principles The calculation of {term}`Bedload` transport requires expert knowledge about the modeled ecosystem for judging whether the system is sediment supply-limited or transport capacity-limited {cite:p}`church_morphodynamics_2015`. Sediment supply-limited rivers : A sediment supply-limited river is characterized by clearly visible incision trends indicating that the river's runoff could potentially transport more sediment than is available in the river. Sediment-supply limited river sections typically occur downstream of dams, which represent an insurmountable barrier for sediment. Thus, in a supply-limited river, the **flow competence** (hydrodynamic force or **transport capacity**) is insufficient to mobilize a typically coarse riverbed, but it is sufficient for transporting external sediment supply. Transport capacity-limited (alluvial) rivers : A transport capacity-limited river is characterized by sediment abundance where the river's runoff is too small to transport all available sediment during a flood. Sediment accumulations (i.e., the alluvium) are present and the channel tends to braid into {term}`anabranchesby Sebastian Schwindt@ Hydro-Morphodynamics channel on YouTube.

By default, Gaia does not account for turbulence (i.e., roughness effects) of bedforms, but it can be enabled by setting the **COMPUTE BED ROUGHNESS AT SEDIMENT SCALE** keyword to `YES` (default is `NO`). Then, one of the following options for the **BED ROUGHNESS PREDICTOR OPTION** keyword can be defined: * `1` for using the default approach of using a multiple of the characteristic grain diameter for calculating $k'_{s}$ in Equation {eq}`eq-cf-skin`. * `2` for ripple bedforms with waves and currents as a function of flow velocity and the characteristics grain size {cite:p}`rijn2007,wiberg1994`. * `3` for ripple bedforms with currents only as a function of flow velocity, water depth, the characteristic grain size, and an additional sand grain diameter {cite:p}`rijn2007,huybrechts2010`. The {{ gaia }} (section 3.1.9) summarizes the set of equations that go into the calculation of the **BED ROUGHNESS PREDICTOR OPTION**. ```` (gaia-dir)= ### Direction and Magnitude (Intensity) Natural rivers are characterized by non-straight lines of the {term}`Thalweg`, which involves that water and sediment are subjected to curve effects. However, water and sediment behave differently in a curve because sediment has greater inertia than water {cite:p}`mosselman_five_2016`. Gaia accounts for the inertia of sediment transport as a function of water depth, curve radius, a spiral flow coefficient (`A`), and the depth-averaged, 2d velocities *U* and *V*. In addition, sediment transport reacts more inert to horizontal (transversal) channel slope and can be considered in $x$ and $y$ directions (see also the explanation of the {term}`Exner equation`). To this end, Gaia calculates the slope-corrected unit bedload transport $q_{b,sc}$ as follows: $$ q_{b,sc} = q_{b} \left[1 + \beta \left(\cos \alpha \frac{\partial z_{b}}{\partial x} + \sin \alpha \frac{\partial z_{b}}{\partial y} \right)\right] $$ (eq-qb-corr) where $\alpha$ is the angle between the longitudinal channel ($x$) axis and the bedload transport vector (see also the {term}`Exner equation`), $\beta$ is an empiric bedload intensity correction factor from {cite:t}`koch1980`, and $z_{b}$ is the riverbed elevation. The degree of bedload deviation (through $\alpha$) and the $\beta$ factor can be defined in Gaia with the **FORMULA FOR DEVIATION** and **FORMULA FOR SLOPE EFFECT** (horizontal) keywords. To use one or both keywords, the **SLOPE EFFECT** keyword must be set to `YES` (disable by setting it to `NO`). The **FORMULA FOR DEVIATION** keyword can take the following integer values to define a particular formula for the sediment shape function (cf. section 3.1.4 in {{ gaia }}): * `1` for bed level computation according to {cite:t}`koch1980` (**default**). * `2` for the {cite:t}`talmon1995` approach based on laboratory experiments, which should be used with the **PARAMETER FOR DEVIATION** keyword for setting the `BETA2` parameter (its default is `PARAMETER FOR DEVIATION : 0.85`, but an optimum was found with `1.6` {cite:p}`mendoza2017`). The **FORMULA FOR SLOPE EFFECT** keyword affects not only the direction of sediment transport but also the bedload magnitude (or intensity) and it can take the following values: * `1` for bed level computation according to {cite:t}`koch1980` (**default** and similar to FORMULA FOR DEVIATION). The `1`-setting enables the definition of the empiric bed slope correction factor $\beta$ in Equation {eq}`eq-qb-corr` through the **BETA** keyword (default is `BETA : 1.3`). - To increase bed elevation change, increase **BETA**. - To decrease bed elevation change, decrease **BETA**. * `2` for slope correction in sand-bed rivers based on an approach from {cite:t}`soulsby1997`, which applies a correction of the {term}`Shields parameter` as a function of the friction angle of the sediment and the riverbed slope. The friction angle can be defined with the additional **FRICTION ANGLE OF THE SEDIMENT** keyword (default is `40.`). (gaia-secondary)= ### Secondary Currents Secondary currents may occur in curved channels (i.e., in most near-census natural rivers) where water moves like a gyroscope through river bends. More specifically, secondary flows are helical motions in which water near the surface is driven toward the outer bend, while water near the riverbed is driven toward the inner bend. Thus, secondary flows are a 3d phenomenon that can be represented in 2d models only with auxiliary approaches. For {term}`Bedload` transport, the near-bed current toward the inner bend is especially important, because it promotes erosion at the outer bend and may lead to deposition at the inner bend. By default, Telemac2d and Gaia do not consider secondary currents, but an approach based on {cite:t}`engelund1974` can be enabled by setting the **SECONDARY CURRENTS** keyword to `YES` (default is `NO`). In addition, the **SECONDARY CURRENTS ALPHA COEFFICIENT** keyword can be used to adapt the roughness length as a function of channel bottom roughness (i.e., smooth or rough riverbeds). For instance, use `SECONDARY CURRENTS ALPHA COEFFICIENT : 0.75` for a very rough riverbed, or `SECONDARY CURRENTS ALPHA COEFFICIENT : 1.` (default) for a smooth riverbed. For **this tutorial use**: ```fortran / continued: gaia-morphodynamics.cas / ... SECONDARY CURRENTS : YES SECONDARY CURRENTS ALPHA COEFFICIENT : 0.8 ``` (gaia-bc-bl)= ## Boundary Conditions The {ref}`Gaia Basis section on boundary conditions