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research-article

A Note on the Second-order Contribution to Extreme Waves Generated During Hurricanes

[+] Author and Article Information
Mark McAllister

Department of Engineering Science, University of Oxford, Oxford OX1 3PJ, United Kingdom
mark.mcallister@eng.ox.ac.uk

Thomas AA Adcock

Department of Engineering Science, University of Oxford, Oxford OX1 3PJ, United Kingdom
thomas.adcock@eng.ox.ac.uk

Paul H. Taylor

Faculty of Engineering and Mathematical Sciences, University of Western Australia, Crawley WA 6009, Australia
paul.taylor@eng.ox.ac.uk

Ton van den Bremer

Department of Engineering Science, University of Oxford, Oxford OX1 3PJ, United Kingdom
ton.vandenbremer@eng.ox.ac.uk

1Corresponding author.

ASME doi:10.1115/1.4042540 History: Received September 26, 2018; Revised January 11, 2019

Abstract

High wind speeds generated during hurricanes result in the formation of extreme waves. Extreme waves by nature are steep meaning that linear wave theory alone is insufficient in understanding and predicting their occurrence. The complex, highly transient nature of the direction of wind and hence of waves generated during hurricanes affects this nonlinear behaviour. Herein, we examine how this directionality can affect the second-order nonlinearity of extreme waves generated during hurricanes. This is achieved through both deterministic calculations and experiments based on the observations of Young (J. Geophys. Res. Oceans vol. 111, 2006). Our calculations show that interactions between the tail and peak of the spectrum can become significant when they travel in different directions, resulting in second-order difference components that exist in the linear range of frequencies. These calculations are supported by experimental observations. Bound second-order difference components or subharmonics typically exist as low frequency infra-gravity waves. Components that exist in the linear range of frequencies may be missed by conventional methods of processing field data where low-pass filtering is used and hence overlooked. In this note, we show that in idealised directional spreading conditions representative of a hurricane, failing to account for second-order difference components may lead to underestimation of extreme wave height.

Copyright (c) 2019 by ASME
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