Environment: Sea data

Sea surface Z

Specifies the global Z coordinate of the mean (or still) water level.

Kinematic viscosity

This value is used to calculate Reynolds number (see below). The viscosity can be constant or vary with temperature.

Temperature

The temperature of the water may be constant or vary with depth below the mean water level.

The temperature can affect the kinematic viscosity (if that is specified as varying with temperature), which in turn has an effect on Reynolds number. This, in its turn, may affect line drag and lift coefficients if they have been defined to have such a dependency.

Reynolds number calculation

Reynolds number, $\Reyn$, is a measure of the flow regime defined as \begin{equation} \label{Re} \Reyn = \frac{v l}{\nu} \end{equation} where $v$ and $l$ are velocity and length parameters chosen to characterise the flow, and $\nu$ is the kinematic viscosity of the fluid. Different values of $\Reyn$ result from different selections of characteristic velocity and length.

OrcaFlex calculates Reynolds number in order to calculate line drag and lift coefficients that are specified to vary with Reynolds number. Accordingly the characteristic velocity is based on the relative flow velocity at a node, $v_\mathrm{r} = v_\mathrm{fluid} - v_\mathrm{node}$, and the characteristic length is always related to the normal drag / lift diameter of the node, $d$.

OrcaFlex offers the following options for characteristic velocity and length.

Nominal

$\Reyn\nom$, is defined by setting $v{=}\lvert\vr\rvert$ and $l{=}d$ in (\ref{Re}). That is \begin{equation} \Reyn\nom = \frac{\lvert\vr\rvert\ d}{\nu} \end{equation}

Cross flow

$\Reyn\cross$ is defined by setting $v{=}\lvert\vn\rvert$ and $l{=}d$ in (\ref{Re}), where $\vn$ is the component of $\vr$ normal to the line. If we define $\alpha$ to be the angle between the relative flow direction and the normal to the line, then $\lvert\vn\rvert = \lvert\vr\rvert \cos\alpha$ and we can write \begin{equation} \Reyn\cross = \frac{\lvert\vr\rvert\ d \cos\alpha}{\nu} \end{equation}

Flow direction

$\Reyn\flow$ is defined by setting, in (\ref{Re}), $v{=}\lvert\vr\rvert$ and $l=d/\cos\alpha$. Here, $l$ represents the length of the line cross section in the relative flow direction. This gives \begin{equation} \Reyn\flow = \frac{\lvert\vr\rvert\ d}{\nu \cos\alpha} \end{equation} Note that the division by $\cos\alpha$ means that $\Reyn\flow$ can be arbitrarily large when the relative flow is very near axial: this turns out not to matter, since the normal component of relative velocity is then very small, so the resulting drag and lift forces are also very small.

These three options are all related by $\Reyn\cross/\cos\alpha = \Reyn\nom = \Reyn\flow\cos\alpha$, from which it follows that $\Reyn\cross \leq \Reyn\nom \leq \Reyn\flow$.

Reynolds number is itself available as a line result.