Boundary layer flow and bed shear stress under a solitary wave

Abstract

Liu & Orfila (J. Fluid Mech. vol. 520, 2004, p. 83) derived analytical solutions for viscous boundary layer flows under transient long waves. Their analytical solutions were obtained with the assumption that the nonlinear inertia force was negligible in the momentum equations. In this paper, using Liu & Orfila's solution and the solutions for the nonlinear boundary layer equations, we examine the boundary layer flow characteristics under a solitary wave. It is found that while the horizontal component of the free-stream velocity outside the boundary layer always moves in the direction of wave propagation, the fluid particle velocity near the bottom inside the boundary layer reverses direction as the wave decelerates. Consequently, the bed shear stress also changes sign during the deceleration phase. Laboratory measurements, including the free-surface displacement, particle image velocimetry (PIV) resolved velocity fields of the viscous boundary layer, and the calculated bed shear stress were also collected to check the theoretical results. Excellent agreement is observed.

Linear stability of boundary layers under solitary waves

“…In the present work, the nonlinear boundary layer equations are solved. The result is compared to the linear boundary layer solution in Liu et al (2007) revealing that both profiles are disagreeing more than has been found before. A change of frame of reference has been used to allow for a classical linear stability analysis without the need to redefine the notion of stability for this otherwise unsteady flow.…”

“…The third order approximate solution by Grimshaw (1971) for the potential Φ in 1 has been used by Liu et al (2007) and Blondeaux (2008, 2011) is thereby approximated by Grimshaw (1971): …”

“…Liu and Orfila (2004), and research has focused on it. Investigation of the bottom boundary layer under a solitary wave has been initiated by Liu et al (2007) when they published theoretical and experimental results concerning the shape of the boundary layer profile. This work has led to subsequent publications by Sumer et al (2010), Blondeaux (2008, 2011) and Blondeaux et al (2012) investigating the transitions in the boundary layer.…”

“…This results in a different boundary layer flow, thereby excluding nonlinear and nonparallel effects. A justification for this uniformization was founded on the conclusion by Liu et al (2007), that the linear boundary layer flow approximates the nonlinear one very closely. This conclusion is, however, based on an erroneous formula given in Liu and Orfila (2004) and therefore not properly justified.…”

“…In general neither the frequency nor the amplitude of the perturbation have been controlled in Blondeaux (2008, 2011) and Sumer et al (2010). In the present treatise, the incorrect formulae in Liu et al (2007) are discussed and the corrected nonlinear boundary layer solution is presented. To avoid dealing with a transient boundary value problem, a simple change of frame of reference is made.…”