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

2018 ◽  
Author(s):  
Yan Li ◽  
Simen Å. Ellingsen
Keyword(s):  
Surface Waves ◽  
River Estuary ◽  
Dimensionless Frequency ◽  
Gravitational Acceleration ◽  
Columbia River Estuary ◽  
Depth Dependence ◽  
Shear Current ◽  
Surface Disturbance ◽  
Numerical Tools ◽  
A Current

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.

scholarly journals Multiple resonances of a moving oscillating surface disturbance on a shear current

2016 ◽  
Vol 808 ◽  
pp. 668-689 ◽  
Author(s):  
Yan Li ◽  
Simen Å. Ellingsen
Keyword(s):  
Free Surface ◽  
Dispersion Relation ◽  
Constant Velocity ◽  
Critical Value ◽  
Far Field ◽  
Gravitational Acceleration ◽  
Ship Waves ◽  
Infinite Depth ◽  
Shear Current ◽  
Surface Disturbance

We consider waves radiated by a disturbance of oscillating strength moving at constant velocity along the free surface of a shear flow, which, when undisturbed, has uniform horizontal vorticity of magnitude $S$. When no current is present the problem is a classical one and much studied, and in deep water a resonance is known to occur when $\unicode[STIX]{x1D70F}=|\boldsymbol{V}|\unicode[STIX]{x1D714}_{0}/g$ equals the critical value $1/4$ ($\boldsymbol{V}$: velocity of disturbance, $\unicode[STIX]{x1D714}_{0}$: oscillation frequency, $g$: gravitational acceleration). We show that the presence of a subsurface shear current can change this picture radically. Not only does the resonant value of $\unicode[STIX]{x1D70F}$ depend strongly on the angle between $\boldsymbol{V}$ and the current’s direction and the ‘shear-Froude number’ $\mathit{Fr}_{s}=|\boldsymbol{V}|S/g$; when $\mathit{Fr}_{s}>1/3$, multiple resonant values – as many as four – can occur for some directions of motion. At sufficiently large values of $\mathit{Fr}_{s}$, the smallest resonance frequency tends to zero, representing the phenomenon of critical velocity for ship waves. We provide a detailed analysis of the dispersion relation for the moving oscillating disturbance, in both finite and infinite water depth, including for the latter case an overview of the different far-field waves which exist in different sectors of wave-vector space under different conditions. Owing to the large number of parameters, a detailed discussion of the structure of resonances is provided for infinite depth only, where analytical results are available.

Latest Pleistocene and Holocene (2–16ka) sedimentation in the Columbia River Estuary, Oregon, USA

2010 ◽  
Vol 273 (1-4) ◽  
pp. 83-95 ◽  
Author(s):  
Diana Baker ◽  
Curt Peterson ◽  
Eileen Hemphill-Haley ◽  
David Twichell
Keyword(s):  
River Estuary ◽  
Columbia River ◽  
Columbia River Estuary

Using Landscape Ecology Principles to Prioritize Habitat Restoration Projects Across the Columbia River Estuary

2021 ◽  
Author(s):  
W.G. Hood ◽  
K. Blauvelt ◽  
D.L. Bottom ◽  
J.M. Castro ◽  
G.E. Johnson ◽  
...  
Keyword(s):  
Landscape Ecology ◽  
Habitat Restoration ◽  
River Estuary ◽  
Columbia River ◽  
Columbia River Estuary
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