Difference between revisions of "SSW BBL"
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class="title">SSW bottom boundary layer formulation</div> | <div class="title">SSW bottom boundary layer formulation</div> | ||
__TOC__ | __TOC__ | ||
==Wave-orbital calculations== | ==Wave-orbital calculations== | ||
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$$ | $$ | ||
where $kh$ is wavenumber x depth, and $k$ can be approximated using one of the methods described [[SoulsbyKH | here]].</wikitex> | where $kh$ is wavenumber x depth, and $k$ can be approximated using one of the methods described [[SoulsbyKH | here]].</wikitex> | ||
==Ripple Geometry== | ==Ripple Geometry== | ||
<wikitex> | <wikitex> | ||
</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: | ||
$$ | |||
\frac{{\eta _r }} | |||
{{\lambda _r }} = \exp \left[ { - 0.095\left( {\ln \left( {\frac{{d_0 }} | |||
{{\eta _r }}} \right)} \right)^2 + 0.442\left( {\ln \left( {\frac{{d_0 }} | |||
{{\eta _r }}} \right)} \right) - 2.28} \right] | |||
$$ | |||
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 [[RPM2 | here]].</wikitex> | |||
==Bottom Roughness== | ==Bottom Roughness== | ||
<wikitex> | <wikitex> | ||
Revision as of 19:29, 3 November 2008
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> </wikitex>
Wave-current combined stress and roughness
<wikitex> </wikitex>
Skin friction - form drag partitioning
<wikitex> </wikitex>
Maximum shear stress
<wikitex> </wikitex>
