SSW BBL
Wave-orbital calculations
<wikitex>Near-bed wave-orbital characteristics, including representative orbital velocity $u_{br}$, representative period $T_r$, and average direction of wave propagation $\theta_w$ (degrees, nautical convention, which is positive clockwise from north) are defined according to Madsen (1994). When SWAN results are used, these correspond to UBOT, PWAVE, and DWAVE. If surface-wave statistics (e.g., $H_s$, $T_d$, and $\theta_w$) are provided, they can be converted to bottom orbital velocity externally (using, for example, the routines suggested in Wiberg and Sherwood (2008) and provided as UBOT in a SWAN input file. Alternatively, if SSW_CALC_UB is defined, orbital velocity $u_{br}$ is calculated according to linear wave theory as follows: $$ u_{br} = \frac{H_s}{2\sinh (kh)} $$ where $kh$ is wavenumber x depth, and $k$ can be approximated using one of the methods described here.</wikitex>
Ripple Geometry
<wikitex> Ripple height $\eta_r$ and wavelength $\lambda_r$ are calculated using information from the previous time step and the Malarkey and Davies (2003) implementation of the Wiberg and Harris (1994) formulation, which is valid for wave-dominated conditions. They approximate ripple wavelength as 535$D_{50} and ripple steepness as: $$ \fracTemplate:\eta r Template:\lambda r = \exp \left[ { - 0.095\left( {\ln \left( {\fracTemplate:d 0 Template:\eta r} \right)} \right)^2 + 0.442\left( {\ln \left( {\fracTemplate:d 0 Template:\eta r} \right)} \right) - 2.28} \right] $$ where $d_0$ = $u_{br}T/\pi$ is the wave-orbital diameter. When transport stage is below the threshold for sediment transport ($T_* = frac{ \tau_{wc}}(\tau_{ce} < 1 $), ripple dimensions from the previous time step are retained.
An alternative formulation for time-dependent ripple roughness is in development branches and is described here.</wikitex>
Bottom Roughness
<wikitex>Roughness lengths associated with grain roughness $z_{0N}$, sediment transport roughness $z_{0ST}$, and bedform roughness (ripples) $z_{0BF}$ are estimated as: $$ z_{0N} = 2.5D_{50} /30 $$
$$ z_{0ST} = \alpha D_{50} \cdot a_1 \fracTemplate:T * Template:1 + a 2 T * $$
$$ z_{0BF} = a_r \eta _r^2 /\lambda _r $$ where the sediment transport coefficients are $\alpha$ = 0.056, $a1$ = 0.068, and $a_2 = 0.0204\ln (100D_{50}^2 ) + 0.0709\ln (100D_{50} )$ (Wiberg and Rubin, 1989) with the bedform roughness $D_50$ expressed in meters, and where $a_r$ is a coefficient that may range from 0.3 to 3 (Soulsby, 1997). Grant and Madsen (1982) proposed $a_r$ = 27.7/30, but we use a default value of $a_r$ = 0.267, as suggested by Nielsen (1992). The roughness lengths are additive, so subsequent BBL calculations use $z_0 = \max \left[ {z_{0N} + z_{0ST} + z_{0BF} ,\quad z_{0MIN} } \right]$, where $z_{0MIN}$ allows setting a lower limit on bottom drag (default $z_{0MIN}$ = 5e-5m).</wikitex>
Wave-current combined stress and roughness
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Skin friction - form drag partitioning
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Maximum shear stress
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