Laboratory evidence of modifications to the Benjamin-Feir instability by shear flow

<p>Modulational or Benjamin-Feir instability (BFI) causes trains of Stokes waves to form groups through energy transfer to specific side-bands in the frequency spectrum. The groupiness developing as the wave propagates is believed to be a candidate mechanism for the formation of extreme rogue waves.&#160;</p> <p>Theoretical [1,2] and experimental [3] studies have shown that the presence of a vertically sheared current can either stabilise or destabilise the wave train depending on the sign of the associated vorticity. A recent theory from a Lagrangian reference system shows that, if an Eulerian current is present which is equal and opposite to the Stokes drift velocity profile, the BFI can vanish altogether [4].&#160;</p> <p>We conduct an experimental study of the groupiness and sideband growth of regular waves travelling on velocity profiles of different shear. The experiments are conducted in the recirculating, open water channel at NTNU where an active grid at the inlet allows us to tailor the velocity profile to nearly cancel the Stokes drift profile. We demonstrate how the groupiness is drastically reduced in this case. The sideband growth and, for steep waves, the distance travelled before breaking occurs is investigated for different velocity profiles and steepnesses while keeping the wavelength constant.&#160;</p> <p>[1] Baumstein A 1998 &#8220;Modulation of gravity waves with shear in water&#8221; <em>Stud. Appl. Math. </em><strong>100&#160;</strong>365-390.<br />[2] Thomas R., Kharif C and Manna M 2012 &#8220;A nonlinear Schr&#246;dinger equation for water waves on finite depth with constant vorticity&#8221; <em>Phys. Fluids </em><strong>24&#160;</strong>127102.<br />[3] Steer JN, Borthwich AG, Stagonas D, Buldakov E and van den Bremer, T 2020 &#8220;Experimental study of dispersion and modulational instability of surface gravity waves on constant vorticity currents&#8221; <em>J. Fluid Mech. </em><strong>884&#160;</strong>A40.<br />[4] Pizzo N, Lenain L, R&#248;mcke O, Ellingsen S&#197;, Smeltzer BK 2023 "The role of Lagrangian drift in the geometry, kinematics and dynamics of surface waves"&#160; <em>J. Fluid Mech.</em> <strong>954 </strong>R4.</p>