Technical note
A comparison of a heuristic wave drift damping formula with
experimental results
D. Trassoudaine
*
, M. Naciri
Single Buoy Moorings Inc., 24 Avenue de Fontvieille BP199, 98007 Monaco Cedex, France
Received 17 March 1998; accepted 2 November 1998
Abstract
This paper reviews several approaches to wave drift damping experienced by floating bodies. A heuristic approach first introduced by
Aranha giving the wave drift damping tensor for the surge and sway modes of motion in finite depth is used. Results for the surge wave drift
damping are compared with experimental results from model tests. These tests were carried out with three different floaters, one tanker and
two barges in different water depth. Close agreement is found for the tanker case. Some discrepancies are observed for the two barges.
Although the theoretical foundations of the Aranha formula are not completely understood, it nevertheless provides reasonable estimates,
which are quite valuable for engineering applications in the offshore industry. 䉷 1999 Elsevier Science Ltd. All rights reserved.
Keywords: Wave drift damping; Floating bodies; Heuristic approach
1. Introduction
It is well known that weakly moored floating bodies are
prone to large-amplitude, low-frequency resonant motions
owing to wind and difference frequency second-order wave
forces. The amplitude of these resonant motions is dictated
by the amount of damping, which therefore dictates, to a
large extent, the size of the mooring system. Consequently,
the development of accurate numerical tools to quantify
damping processes is of the utmost importance. One such
process is wave drift damping, so called due to the depen-
dency of drift coefficients upon the floating body’s own drift
velocity.
A heuristic approach to wave drift damping was intro-
duced by Aranha [1] and Clark et al. [2]. The purpose of this
note is to compare results derived by this heuristic approach
with experimental results obtained during model tests [3,4].
2. Brief literature review
It has long been known that second-order drift forces on a
hull are influenced by its speed. A Taylor expansion of these
forces yields to a leading order in speed:
F
d
v
; UF
d
v
; 0 ⫹ U
2
F
d
2
U
⫹ OU
2
1
The 2F
d
/2U term is equivalent to a damping term, and Eq.
(1) may be rewritten using wave drift damping B(
v
), so
called after Wichers [5]
F
d
v
; UF
d
v
; 0 ⫺ B
v
U ⫹ OU
2
2
The determination of the wave drift damping coefficient
B(
v
) amounts to the calculation of drift forces for small
increments of forward speed.
Until a few years ago, no complete rigorous solutions to
the forward speed problem were available, especially for
hulls violating the slender body assumption. The reader
will find in Clark et al. [2] references to several papers
dealing with this issue. This made the determination of
wave drift damping quadratic transfer functions a tedious
numerical exercise, if possible at all numerically, in view of
the lack of a rigorous theory. Experimental results were used
instead.
The heuristic approach of Aranha [1] and Clark et al. [2]
to wave drift damping is a modified version of the gradient
method whereby the damping quadratic transfer function
B(
v
) in deep water is the sum of two terms, one proportional
to the drift force derivative with respect to the radial
frequency 2F
d
/2
v
, and a second term proportional to the
drift force F
d
itself:
B
v
⫺
2
F
d
2
U
v
2
g
2
F
d
2v
⫹
4
v
g
F
d
3
where U refers to the floating body drift velocity and F
d
Applied Ocean Research 21 (1999) 93–97
0141-1187/99/$ - see front matter 䉷 1999 Elsevier Science Ltd. All rights reserved.
PII: S0141-1187(98)00041-8
* Corresponding author.