# Morison model and force¶

## Morison model¶

The Morison model is generally designed to incorporate in the simulation second order wave loads on a structure coming from drag and inertial effects such as viscous effects or turbulence. The Morison model is also used in case of a small body compared to the wave length. In the FRyDoM framework, the Morison model can be applied to any offshore structure. A Morison model can be composed of multiple Morison elements, corresponding to a cylinder with drag and added mass coefficients. The following figure represents the definition a Morison structure applied on a platform. A Morison element is defined by a couple of two points (represented by red dots) corresponding to the extremity of the cylinder and a discretization.

Fig. 10 Example of an Morison model for a platform

## Morison force on a Morison element¶

Each Morison element is associated to a local frame located at the middle of the Morison element. By default, this local frame has its third axis $$\mathbf{e3}$$ parallel to the direction of the Morison element, the first axis $$\mathbf{e1}$$ is parallel to the horizontal plane XY and $$\mathbf{e2}$$ is defined such that the frame $$(\mathbf{e1}, \mathbf{e2}, \mathbf{e3})$$ is orthonormal direct.

The Morison force in the local frame coordinates is defined as follows:

$f_M^i = \rho V \left[\dot{u}^i + C_a^i \left(\dot{u}^i - \ddot{X}^i\right)\right] + \frac{1}{2} \rho D L C_d^i \left(u^i - \dot{X}^i\right)\left|u^i - \dot{X}^i\right|$

where

• $$i$$ can be 1 or 2,
• $$f^i$$ is the force component along the ith axis,
• $$C_a^i$$ is the added mass, along the ith axis,
• $$C_d^i$$ is the drag coefficient, along the ith axis,
• $$\rho$$ is the water density,
• $$V, D$$ and $$L$$ are the volume, diameter and length of the Morison element respectively,
• $$u^i$$ is the flow velocity,
• $$\dot{X}^i$$ is the absolute velocity of the center at the middle of the Morison element,

In this formulation, anisotropic Morison element can be represented by a set of anisotropic definition of the added mass and drag coefficients in function of the axis direction.