# 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.

## 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:

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.