Current Velocities

Bladed allows current velocities to be calculated based on three current profiles, either separately or in combination:

• a near-surface (wind/wave generated) current: \(\bvector{u}_{cw}\)
• a sub-surface (tidal and thermo-saline) current: \(\bvector{u}_{cs}\)
• a near-shore (wind induced surf) current: \(\bvector{u}_{cn}\)

These three velocity vectors have the form:

\[ \begin{align} \begin{aligned} \bvector{u}_{c w}=u_{c w}(z)\begin{pmatrix}\cos \mu_{c w}\\ -\sin \mu_{c w}\\ 0\end{pmatrix} \qquad \bvector{u}_{c s}=u_{c s}(z)\begin{pmatrix}\cos \mu_{c s}\\ -\sin \mu_{c s}\\ 0\end{pmatrix} \qquad \bvector{u}_{c n}=u_{c n}(z)\begin{pmatrix}\cos \mu_{c n}\\ -\sin \mu_{c n}\\ 0\end{pmatrix} \end{aligned} \end{align} \]

where \(\mu_{c w}\), \(\mu_{c s}\) and \(\mu_{c n}\) are the directions from which the three current components arrive at the tower. Components of the calculated current velocities are then combined linearly:

\[ \begin{equation} \bvector{u}_c=\bvector{u}_{c w}+\bvector{u}_{c s}+\bvector{u}_{c n} \end{equation} \]

Note

Many equations for the calculation of current velocity make reference to the mean water depth. The mean water depth is a combination of the mean water depth defined for an offshore tower and the tide height correction.

Near-surface current

The near-surface current velocity profile varies linearly with depth \(\bscalar{z}\) from a specified velocity at the surface to zero velocity at the reference depth. The following equation is used

\[ \begin{equation} \bscalar{u_{c s}(z)}= \max \left(0, \left(\frac{z+ d_r }{d_r } \right) u_{c 0} \right) \end{equation} \]

where \(\bscalar{0 \geq z \geq-d}\), where \(d_r\) is the reference depth and \(u_{c 0}\) is the velocity at the sea surface (\(z=0\)).

Sub-surface current

There exists two options for the sub-surface current velocity profile. The first option is a power law profile

\[ \begin{equation} \bscalar{u_{c s}(z)}=\bscalar{\left[\left(\frac{z+d}{d}\right)^\alpha\ \right]} u_{s 0}, \end{equation} \]

for \(\bscalar{0 \geq z \geq-d}\), where \(\bscalar{d}\) is the water depth and \(u_{s 0}\) is the velocity at the sea surface(\(\bscalar{z}=0\)). The standard power law exponent \(\bscalar{\alpha}\) is normally taken as \(1/7\), but can be changed by the user.

The second options is to define a custom shear profile such that the normalised current speed at each height above the seabed is specified.

The height above seabed data must be entered as values normalised by the mean water depth for the simulation.

\[ \begin{equation} \hat{z} = \frac{ d + z}{d} \end{equation} \]

where \(\hat{z}\) is the normalised height above the seabed where \(0<\hat{z}<1\).

The current shear factor at each height is defined as the mean current speed at that height divided by the mean sea surface current speed.

\[ \begin{equation} \hat{u}_{c s}(z) = \frac{ u_{c s}(z)}{u_{s 0}} \end{equation} \]

The values in the first row of the lookup table represent the normalised height and the current shear factor at the sea surface. The values in this first row therefore always each take the value 1. Subsequent data points must be entered in descending order of normalised sea surface height.

Near-shore current

The near-shore current velocity has a uniform profile, independent of depth.

If desired, a suitable current velocity at the location of the breaking wave can be calculated by the user as:

\[ \begin{equation} \bscalar{u_{c n}}=\bscalar{2 s \sqrt{g H_B}} \end{equation} \]

where \(\bscalar{g}\) is the acceleration due to gravity, \(\bscalar{s}\) is the beach slope and \(\bscalar{H_B}\) is the breaking wave height given by:

\[ \begin{equation} \bscalar{H_B}=\bscalar{\frac{b}{\frac{1}{d_B}+\frac{a}{g T_B^2}}} \end{equation} \]

where:

\[ \begin{equation} \begin{aligned} \bscalar{a} & =44[1-\exp (-19 s)] \\ \bscalar{b} & =1.6 /[1+\exp (-19 s)] \end{aligned} \end{equation} \]

Here \(\bscalar{d_B}\) is the water depth at the location of the breaking wave and \(\bscalar{T_B}\) is the period of this wave. For very small beach slopes, \(\bscalar{H_B}\) may be estimated using the formula \(\bscalar{H_B}=0.8 \ \bscalar{d_B}\).

Last updated 10-09-2024