TY - JOUR

T1 - On the statistical properties of inertia and drag forces in nonlinear multi-directional irregular water waves

AU - Klahn, Mathias

AU - Madsen, Per A.

AU - Fuhrman, David R.

N1 - Publisher Copyright:
© 2021 Cambridge University Press. All rights reserved.

PY - 2021

Y1 - 2021

N2 - We consider nonlinear, directionally spread irregular wave fields in
deep water and study the statistical properties of the total inline
force that would be induced by the waves on a vertical circular
cylinder. Starting from the two-dimensional Morison equation, we
specifically investigate the effect of wave steepness and directionality
on the probability density functions (PDFs) of the inertia and drag
forces. To do so, we derive new analytical expressions for the PDFs of
these forces based on first-order theory and compare them with the
results of fully nonlinear numerical simulations. We show that the
inertia force for the main direction (x)
of the wave field is in general unaffected by nonlinear effects, while
the inertia force for the direction perpendicular to the main direction (y)
is subject to substantial third-order effects when the steepness is
appreciable and the wave field becomes relatively long crested.
Moreover, we show that the drag force for the x-direction is in general subject to substantial second-order effects. The drag force for the y-direction is also affected by second-order effects, but to a much smaller degree than the x-direction. It is, however, strongly affected by third-order effects under the same conditions as the inertia force in the y-direction. We conclude that the total force can be accurately approximated by first-order theory when the ratio kpD/ε is large (with kp the peak wavenumber, D the cylinder's diameter and ε
the wave steepness), while first-order theory underestimates the
probability of large forces considerably when this ratio is small.

AB - We consider nonlinear, directionally spread irregular wave fields in
deep water and study the statistical properties of the total inline
force that would be induced by the waves on a vertical circular
cylinder. Starting from the two-dimensional Morison equation, we
specifically investigate the effect of wave steepness and directionality
on the probability density functions (PDFs) of the inertia and drag
forces. To do so, we derive new analytical expressions for the PDFs of
these forces based on first-order theory and compare them with the
results of fully nonlinear numerical simulations. We show that the
inertia force for the main direction (x)
of the wave field is in general unaffected by nonlinear effects, while
the inertia force for the direction perpendicular to the main direction (y)
is subject to substantial third-order effects when the steepness is
appreciable and the wave field becomes relatively long crested.
Moreover, we show that the drag force for the x-direction is in general subject to substantial second-order effects. The drag force for the y-direction is also affected by second-order effects, but to a much smaller degree than the x-direction. It is, however, strongly affected by third-order effects under the same conditions as the inertia force in the y-direction. We conclude that the total force can be accurately approximated by first-order theory when the ratio kpD/ε is large (with kp the peak wavenumber, D the cylinder's diameter and ε
the wave steepness), while first-order theory underestimates the
probability of large forces considerably when this ratio is small.

KW - Surface gravity waves

U2 - 10.1017/jfm.2021.256

DO - 10.1017/jfm.2021.256

M3 - Journal article

AN - SCOPUS:85104492762

SN - 0022-1120

VL - 916

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

M1 - A59

ER -