AUTHOR=Christensen Kai Håkon , Weber Jan Erik Hobæk 

TITLE=Application of a Robin boundary condition to surface waves

JOURNAL=Frontiers in Marine Science

VOLUME=10

YEAR=2023

URL=https://www.frontiersin.org/journals/marine-science/articles/10.3389/fmars.2023.1129643

DOI=10.3389/fmars.2023.1129643

ISSN=2296-7745

ABSTRACT=<p>Surface effects on deep-water gravity waves are investigated theoretically by the application of a Robin boundary condition with a complex Robin parameter, <inline-formula><mml:math display="inline" id="im1" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>R</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mi>R</mml:mi><mml:mi>r</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:mi>i</mml:mi><mml:msub><mml:mi>R</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>. The Robin condition combines the shear stress and the horizontal velocity at the ocean surface. We show that this condition describes wave damping related to surface phenomena like elastic films or thin viscous fluid layers. It may also model wave generation by oscillating surface stresses depending on the signs and magnitudes of <inline-formula><mml:math display="inline" id="im2" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mi>r</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math display="inline" id="im3" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>.</p>