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Current theory |
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Current theory |
When vertical stretching is applied, the current at position $(X,Y,Z)$ is calculated by replacing $Z$ with a stretched coordinate, $Z_\mathrm{s}$, given by \begin{equation} Z_\mathrm{s} = Z_\mathrm{o} + \lambda (Z - Z_\mathrm{b}(X, Y)) \end{equation} where
$Z_\mathrm{o}$ is the Z coordinate of the seabed origin
$\lambda = D_\mathrm{o}/D_\mathrm{b}$
$D_\mathrm{o}$ is the water depth at the seabed origin, measured from the still water level to the seabed
$D_\mathrm{b}$ is the water depth at $(X,Y)$, measured from the still water level to the seabed
$Z_\mathrm{b}(X, Y)$ is the Z coordinate of the seabed directly below $(X,Y)$.
Vertical stretching is primarily intended to provide horizontal variation of current, based on water depth, in cases where the underlying current data has no explicit dependence on $X$ and $Y$. If this is the case, then it means that the current data determine the profile at the seabed origin, and this profile is then stretched linearly to match the instantaneous water depth for points away from the seabed origin; whereas, when vertical stretching is not applied, the vertical variation would be the same everywhere and have no dependence on $(X,Y)$ position.
| Note: | It is permissible to have vertical stretching apply in conjunction with explicit $(X,Y)$ dependence in the data when using the tabular current method. This might be useful for a model with varying water depth where the current field was originally calculated on the assumption of a flat seabed. |
The vertical current variation may be specified by one of two methods when using the variation scheme current model. The two methods are interpolated and power law.
Horizontal current is specified as a full 3D profile, variable in magnitude and direction, at discrete depths. The values for intermediate depths are obtained by linear interpolation. The profile should be specified from the still water surface to the seabed; if the data do not cover the full depth, then extrapolation will be applied.
Current direction is fixed and does not vary with depth. Speed $S$ varies with position $(X,Y,Z)$ according to the formula \begin{equation} S = S_\mathrm{b} + (S_\mathrm{f}-S_\mathrm{b}) \left[\frac{Z-Z_\mathrm{b}}{Z_\mathrm{f}-Z_\mathrm{b}}\right]^{1/p} \end{equation} where
$S_\mathrm{f}$ and $S_\mathrm{b}$ are the current speeds at the surface and seabed, respectively
$p$ is the power law exponent
$Z_\mathrm{f}$ is the Z coordinate of the still water level
$Z_\mathrm{b}$ is the Z coordinate of the seabed directly below $(X,Y)$.
In the presence of waves, the current must be extrapolated vertically above the still water level (or above the smallest depth given, for the interpolated method); in OrcaFlex, we adopt the convention that the surface current applies everywhere above this level.
The current at the greatest depth for which it is specified is applied to all greater depths – including those below the seabed. If a non-horizontal seabed is specified, the boundary is inconsistent with a horizontal current: this effect is not usually important, and is not corrected for in OrcaFlex.
For both of these methods, extrapolation beyond the ends of the data may be required.