Buoyancy variation with depth

The buoyancy of an object is normally assumed to be constant and not vary significantly with position. The buoyancy is equal to $\rho V g$, where $\rho$ is the water density, $V$ is the object's volume and $g$ is acceleration due to gravity. In reality, buoyancy does vary due to the following effects:

If the object is compressible then its volume $V$ will reduce with depth, due to the increasing pressure.
The water density $\rho$ can vary with position, due to the compressibility of the water or from temperature or salinity variations. Normally the density increases with depth, since otherwise the water column would be unstable (the lower density water below would rise up through the higher density water above).

These effects can be modelled in OrcaFlex for buoys and lines.

Note:

The bulk modulus and density variation facilities in OrcaFlex only affect the buoyancy of objects. OrcaFlex does not allow for compressibility or density variation when calculating hydrodynamic effects such as drag, added mass, etc. The calculation of hydrodynamic effects uses the uncompressed volume and a nominal sea density which is taken to be that at the sea density origin.

Compressibility of buoys and lines

All things are compressible to some extent. The effect is usually not significant, but in some cases it can have a significant effect on the object's buoyancy. To allow these effects to be modelled, you can specify the compressibility of a 3D buoy, 6D buoy or line type by setting the bulk modulus on the object's data form.

The bulk modulus, $B$, governs the way in which the object's volume changes with pressure. If we denote by $V$ the compressed volume of the object, then $V$ is given by \begin{equation} \label{CompressedVolume} V = V_0 \left(1-\frac{P}{B}\right) \end{equation} where $V_0$ is the uncompressed volume at atmospheric pressure and $P$ is the pressure excess over atmospheric pressure.

The bulk modulus has the same units as pressure, $FL^{-2}$, and formula (\ref{CompressedVolume}) can be interpreted as saying that the volume reduces linearly with pressure, at a rate that would see the object shrink to zero volume if the pressure ever reached $B$. For an incompressible object the bulk modulus is infinite.

Formula (\ref{CompressedVolume}) breaks down when $P \gt B$; in this case, OrcaFlex uses a compressed volume $V$ of zero. However, the relationship between pressure and volume would become inaccurate well before the pressure exceeded the bulk modulus. In practice $B$ is normally very large, so the object normally only experiences pressures that are small compared to $B$.