Shear Rate

The shear rate is an important variable which is utilized in the rheological models. Vertically averaged models - such as those in HEC-RAS – make assumptions on the vertical profile of the current velocity in order to estimate a vertically-averaged shear rate. Common profiles found in literature include:

Linear (e.g. Bird et al., 1960)
Parabolic (e.g. Julien 1995; Iverson and Denlinger, 2001)

The general formula for the vertically-averaged shear rate is given by:

$\begin{array}{l}\displaystyle \dot { \gamma } = \frac{B |V| }{h \cos \varphi \cos\psi }\end{array}$

where $\begin{array}{l}|V|\end{array}$ is the current velocity magnitude, $\begin{array}{l}h\end{array}$ is the flow depth, $\begin{array}{l}\varphi\end{array}$ is the water surface slope, and $\begin{array}{l}\psi\end{array}$ is the inclination angle of the current velocity direction. The shear rate coefficient $\begin{array}{l}B\end{array}$ is equal to 2 and 3 for the linear and parabolic profiles, respectively. The parabolic velocity profile was original used in the Quadratic model (O'Brien and Julien 1988), and is the profile currently used in HEC-RAS. The Voellmy (1955) model does not require a shear rate and only utilizes the average velocity for the turbulent-dispersive stress.