Technical University of Denmark
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Matlab implementation of the third-order, multi-directional, irregular wave theory of Madsen & Fuhrman (2012, J. Fluid Mech. 698, 304-334)

Version 4 2024-02-08, 12:12
Version 3 2023-09-13, 09:03
Version 2 2023-06-26, 09:23
Version 1 2023-02-13, 15:09
posted on 2024-02-08, 12:12 authored by David R. FuhrmanDavid R. Fuhrman

This is an an implementation of the third-order, directionally-spread, irregular wave theory of Madsen and Fuhrman (2012), with corrections as indicated in the appendix of Fuhrman et al. (2023). Any publications in which results from this code are used are kindly asked to please cite both of these works appropriately.

The code provided can compute both free surface elevations and kinematics for irregular waves to a desired order (1, 2 or 3). Several examples demonstrating its full use can be found in the Examples folder, which are intended as self explanatory. These include some regular, as well as irregular, wave examples, including time series generation, surface elevation maps, as well as wave kinematics. All source code used by these examples can be found within the Source folder. As a first example, it is suggested to execute e.g. the example_ThreeWaves.m script, which confirms the coefficient values in Tables 2 and 3 of Madsen and Fuhrman (2012).

This research has been financially supported by the Independent Research Fund Denmark project STORM: STatistics and fOrces on stRuctures from extreMe water waves in finite depth (grant ID: 10.46540/2035-00064B). This support is greatly appreciated.

Find the project in DTU Data here: STORM:STatistics and fOrces on stRuctures from extreMe water waves in finite depth

Version updates:

February 8, 2024: A bug has been fixed in kinematicsMF12.m, line 103 - Variable p was doubly used as a counter and also for the dynamics pressure, which has been fixed.


Fuhrman, D.R., Klahn, M. & Zhai, Y. (2023) A new probability density function for the surface elevation in irregular seas. J. Fluid Mech. 970, A38.

Madsen, P.A. & Fuhrman, D.R. (2012) Third-order theory for multi-directional irregular waves. J. Fluid Mech. 698, 304-334.

© 2023 Technical University of Denmark


Independent Research Fund Denmark, grant ID: 10.46540/2035-00064B


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