Smart-Jaeggi¶

The adjustable Smart-Jaeggi formula:

\[ \phi = a_{1}\ \left( \frac{d_{90}}{d_{30}} \right)^{a_{2}}\ I^{a_{3}}\left( \frac{C}{\sqrt{g}} \right)^{a_{4}}\theta^{a_{5}}\left( a_{6}\theta^{a_{7}} - \theta_{c} \right)^{a_{8}} \]

Equation: Adjustable Smart-Jaeggi sediment transport formula.

Where:

\(\phi\) — non-dimensional sediment transport (bed-load or suspended load)
\(a_{1} - a_{8}\) — input constants for each fraction and mode
\(d_{90}/d_{30}\) — input parameter for each fraction and mode
\(I\) — bed or surface slope
\(\theta\) — Shields parameter (total or skin)
\(\theta_{c}\) — critical Shields parameter
\(C\) — Chezy number (total or skin friction)
\(g\) — acceleration of gravity 9.81 [m/s²]

In addition to the listed input parameters (\(d_{90}/d_{30}\) and \(a_{1}\)-\(a_{8}\)) the following can also be selected:

Angle of repose
Skin/total friction
Bed/surface slope

The Smart-Jaeggi formula is a bed-load formula, but the adjustable formula is allowed for both bed-load and suspended load.

Graded sediment¶

The term \(d_{90}/d_{30}\) is not updated in graded models; it is kept at its input value. The reason for this is that Smart-Jaeggi is a single fraction model with \(d_{90}/d_{30}\) calculated from the gradation of the single fraction.

Sediment transport rates are multiplied by the local weight.

Smart-Jaeggi reacts to Egiazaroff. This means that the critical Shields parameter when using Smart-Jaeggi will reacts to the slope and hiding effects. The basic Smart-Jaeggi formula was developed for single fraction sediment (hence the \(d_{90}/d_{30}\) term), so extensions to graded sediment models happens only via the relative weights.