Abstract
In this paper we highlight that extreme events such as freak waves are a transient phenomenon in keeping with the old fisherman tale that these extreme events seem to appear out of nowhere. Janssen (J. Phys. Oceanogr., vol. 33, 2003, pp. 863-884) obtained an evolution equation for the ensemble average of the excess kurtosis, which is a measure for the deviation from normality and an indicator for nonlinear focusing resulting in extreme events. In the limit of a narrow-band wave train, whose dynamics is governed by the two-dimensional nonlinear Schrödinger (NLS) equation, the excess kurtosis is under certain conditions seen to grow to a maximum after which it decays to zero for large times. This follows from a numerical solution of the problem and also from an analytical solution presented by Fedele (J. Fluid Mech., vol. 782, 2015, pp. 25-36). The analytical solution is not explicit because it involves an integral from initial time to actual time. We therefore study a number of properties of the integral expression in order to better understand some interesting features of the time-dependent excess kurtosis and the generation of extreme events.
| Language | English |
|---|---|
| Pages | 790-818 |
| Number of pages | 29 |
| Journal | Journal of Fluid Mechanics |
| Volume | 859 |
| DOIs | |
| State | Published - 25 Jan 2019 |
Fingerprint
Keywords
- surface gravity waves
- waves/free-surface flows
Cite this
}
Asymptotics for the long-time evolution of kurtosis of narrow-band ocean waves. / Janssen, Peter A.E.M. (Corresponding author); Janssen, Augustus J.E.M.
In: Journal of Fluid Mechanics, Vol. 859, 25.01.2019, p. 790-818.Research output: Contribution to journal › Article › Academic › peer-review
TY - JOUR
T1 - Asymptotics for the long-time evolution of kurtosis of narrow-band ocean waves
AU - Janssen,Peter A.E.M.
AU - Janssen,Augustus J.E.M.
PY - 2019/1/25
Y1 - 2019/1/25
N2 - In this paper we highlight that extreme events such as freak waves are a transient phenomenon in keeping with the old fisherman tale that these extreme events seem to appear out of nowhere. Janssen (J. Phys. Oceanogr., vol. 33, 2003, pp. 863-884) obtained an evolution equation for the ensemble average of the excess kurtosis, which is a measure for the deviation from normality and an indicator for nonlinear focusing resulting in extreme events. In the limit of a narrow-band wave train, whose dynamics is governed by the two-dimensional nonlinear Schrödinger (NLS) equation, the excess kurtosis is under certain conditions seen to grow to a maximum after which it decays to zero for large times. This follows from a numerical solution of the problem and also from an analytical solution presented by Fedele (J. Fluid Mech., vol. 782, 2015, pp. 25-36). The analytical solution is not explicit because it involves an integral from initial time to actual time. We therefore study a number of properties of the integral expression in order to better understand some interesting features of the time-dependent excess kurtosis and the generation of extreme events.
AB - In this paper we highlight that extreme events such as freak waves are a transient phenomenon in keeping with the old fisherman tale that these extreme events seem to appear out of nowhere. Janssen (J. Phys. Oceanogr., vol. 33, 2003, pp. 863-884) obtained an evolution equation for the ensemble average of the excess kurtosis, which is a measure for the deviation from normality and an indicator for nonlinear focusing resulting in extreme events. In the limit of a narrow-band wave train, whose dynamics is governed by the two-dimensional nonlinear Schrödinger (NLS) equation, the excess kurtosis is under certain conditions seen to grow to a maximum after which it decays to zero for large times. This follows from a numerical solution of the problem and also from an analytical solution presented by Fedele (J. Fluid Mech., vol. 782, 2015, pp. 25-36). The analytical solution is not explicit because it involves an integral from initial time to actual time. We therefore study a number of properties of the integral expression in order to better understand some interesting features of the time-dependent excess kurtosis and the generation of extreme events.
KW - surface gravity waves
KW - waves/free-surface flows
UR - http://www.scopus.com/inward/record.url?scp=85057374937&partnerID=8YFLogxK
U2 - 10.1017/jfm.2018.844
DO - 10.1017/jfm.2018.844
M3 - Article
VL - 859
SP - 790
EP - 818
JO - Journal of Fluid Mechanics
T2 - Journal of Fluid Mechanics
JF - Journal of Fluid Mechanics
SN - 0022-1120
ER -