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Surface Waves Generated by a Translating and Oscillating Source Atop Realistic Shear Flows

[+] Author Affiliations
Yan Li, Simen Å. Ellingsen

Norwegian University of Science and Technology, Trondheim, Norway

Paper No. OMAE2018-78560, pp. V07BT06A056; 8 pages
doi:10.1115/OMAE2018-78560
From:
  • ASME 2018 37th International Conference on Ocean, Offshore and Arctic Engineering
  • Volume 7B: Ocean Engineering
  • Madrid, Spain, June 17–22, 2018
  • Conference Sponsors: Ocean, Offshore and Arctic Engineering Division
  • ISBN: 978-0-7918-5127-2
  • Copyright © 2018 by ASME

abstract

We analyze surface waves generated by a translating, oscillating surface disturbance atop a horizontal background flow of arbitrary depth dependence, with a focus on determining the Doppler resonance. For a critical value of the dimensionless frequency τ = ωV/g (ω: oscillation frequency, V: source velocity, g: gravitational acceleration) at which generated waves cannot escape. In the absence of shear the resonant value is famously 1/4; the presence of a shear current modifies this. We derive the theoretical and numerical tools for studying this problem, and present the first calculation of the Doppler resonance for a source atop a real, measured shear current to our knowledge. Studying graphical solutions to the (numerically obtained) dispersion relation allows derivation of criteria determining the number of far-field waves that exist in different sectors of propagation directions, from which the criteria for Doppler resonance follow. As example flows we study a typical wind-driven current, and a current measured in the Columbia River estuary. We show that modeling these currents as uniform or with a linear depth dependence based on surface measures may lead to large discrepancies, in particular for long and moderate wavelengths.

Copyright © 2018 by ASME

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