Large eddy simulation of a turbulent submerged jet interacting with a wave environment

Abstract We use numerical simulations to study the interaction between a turbulent jet, discharged vertically from a circular nozzle at the bottom of a horizontal liquid layer of height $$h_0=0.35$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>h</mml:mi> <mml:mn>0</mml:mn> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>0.35</mml:mn> </mml:mrow> </mml:math> m, and surface waves. All simulations are run at a fixed value of the jet Reynolds number ( $$ \textrm{Re}_{j}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mtext>Re</mml:mtext> <mml:mi>j</mml:mi> </mml:msub> </mml:math> = 20,000, based on the nozzle diameter) and for two different values of the surface waves elevation, $$H=0.02$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>H</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0.02</mml:mn> </mml:mrow> </mml:math> m (simulation R 1) and $$H=0.03$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>H</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0.03</mml:mn> </mml:mrow> </mml:math> m (simulation R 2). A reference simulation, assuming a free surface without waves, is also performed for comparison purposes (simulation R 0). We focus on the influence of the surface waves on the jet flow field, considering in particular the behavior of the jet width and of the mean jet velocity—which we analyze applying a phase-averaged technique. Our results show that surface waves induce a reduction of the vertical component of the jet velocity, and a corresponding increase of the horizontal components of the jet velocity. In particular, we observe that the reduction of the centerline mean vertical velocity (along the vertical direction z ) is linear in the region close to the jet nozzle, $$W_0/W_m\sim z$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>W</mml:mi> <mml:mn>0</mml:mn> </mml:msub> <mml:mo>/</mml:mo> <mml:msub> <mml:mi>W</mml:mi> <mml:mi>m</mml:mi> </mml:msub> <mml:mo>∼</mml:mo> <mml:mi>z</mml:mi> </mml:mrow> </mml:math> , but can be faster than linear (superlinear) in the region close to the liquid surface, for the larger amplitude waves. Correspondingly, the jet width increases linearly with z , $$b \sim C \left( z/d_0 \right) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>b</mml:mi> <mml:mo>∼</mml:mo> <mml:mi>C</mml:mi> <mml:mfenced> <mml:mi>z</mml:mi> <mml:mo>/</mml:mo> <mml:msub> <mml:mi>d</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:mfenced> </mml:mrow> </mml:math> , but at a slope C that does depend on the distance from the liquid surface. These findings suggest that surface waves enhance entrainment and dilution, offering insights for improving jet–wave interaction models and parameterizations.