Reconfiguration and dynamics of clamped fibers under finite-amplitude surface gravity waves

We investigate the behavior of a flexible stem completely submerged under a surface gravity wave of finite amplitude using fully resolved direct numerical simulations. By varying the rigidity of the stem over ten orders of magnitude, we explore its motion in the drag-dominated regime with realistic air and water properties. Our findings reveal two distinct structural responses of the stem depending on the ratio between its natural frequency (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:msub><a:mi>f</a:mi><a:mi>nat</a:mi></a:msub></a:math>) and the wave frequency (<b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:msub><b:mi>f</b:mi><b:mi>wave</b:mi></b:msub></b:math>). For <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:msub><c:mi>f</c:mi><c:mi>nat</c:mi></c:msub><c:mo>/</c:mo><c:msub><c:mi>f</c:mi><c:mi>wave</c:mi></c:msub><c:mo>≫</c:mo><c:mn>1</c:mn></c:mrow></c:math>, the stem maintains on average a straight configuration and exhibits streamwise oscillations in phase opposition with the wave, moving symmetrically with respect to the vertical direction. Conversely, for <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mrow><d:msub><d:mi>f</d:mi><d:mi>nat</d:mi></d:msub><d:mo>/</d:mo><d:msub><d:mi>f</d:mi><d:mi>wave</d:mi></d:msub><d:mo>≪</d:mo><d:mn>1</d:mn></d:mrow></d:math>, the stem reconfigures under the influence of the Stokes drift, bending forward and breaking the symmetry, and exhibits oscillations that are more coherent with the surrounding flow field. Resonance is observed when <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mrow><e:msub><e:mi>f</e:mi><e:mi>nat</e:mi></e:msub><e:mo>≈</e:mo><e:msub><e:mi>f</e:mi><e:mi>wave</e:mi></e:msub></e:mrow></e:math>. These results provide insights into the dynamics of slender vegetation and manmade structures in wave fields, offering valuable implications for marine biology and engineering.