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

• Published in: Volume 7B: Ocean Engineering
• Main Authors: Li, Yan, Ellingsen, Simen Andreas Ådnøy
• Format: Book Part
• Language: English
• Published: ASME 2018
• Subjects: Arctic
• Online Access: http://hdl.handle.net/11250/2585675; https://doi.org/10.1115/OMAE2018-78560

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. publishedVersion Copyright © 2018 by ASME