RPM2

Ripple Predictor Mark 2

Time-dependent ripple geometry is implemented in subroutine RPM2 using the approach described in Soulsby and Whitehouse (2005). <wikitex> Ripple geometry is described by ripple height $\eta$ (m), wavelength $\lambda$ (m), and orientation $\theta$ (positive clockwise from the $y$-axis). The orientation is defined as follows. Under unidirectional flow (no waves), ripple orientation is the same as the current direction. Under pure waves, ripple orientation is in the direction of wave propagation. For linear ripples (assumed here), ripple orientation is perpendicular to the ripple crest. The ripple orientation is actually stored as $u$- and $v$- components.

The Soulsby and Whitehouse (2005) approach is to calculate equilibrium ripple geometry under existing conditions, and then nudge the existing ripple geometry toward equilibrium at a rate that depends on sediment-transport conditions. Ripples remain unchanged if the transport threshold is not exceeded. The formula for updating ripple height is as follows. $$ \eta _{t} = \eta _{t-1} + (\eta _{eq} - \eta _{t-1} )(1 - \exp ( -\frac{\beta}{T_e} \Delta t) ) $$ where $\eta_t$ is the ripple height to be calculated for the present time, $\eta_{t-1}$ is ripple height at the previous step, $\eta_{eq}$ is the equilibrium ripple height under present conditions, $\beta$ is the evolution rate of ripple height under present conditions, $\T_{ev}$ is the time scale for ripple evolution, and $\Delta t$ is the time step. Similar equations are used to nudge $\lambda$ and components of ripple direction$\theta_x$ and $\theta_y$ toward the equilibrium associated with present sediment-transport conditions.

The Shields parameters for waves alone and for currents alone are calculated, and the equilibrium geometry and evolution rate is determined by the larger of the two.

One potential modification to this routine might be to calculate wash-out criteria and evolution rates based on the combined wave-current stress.

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