Stability of the solitary wave boundary layer subject to finite-amplitude disturbances

Abstract

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Receptivity and transition in a solitary wave boundary layer over random bottom topography

“…These peaks indicate that the average spanwise spacing between adjacent streak pairs is l * s ≈ 2π/1.5δ * s ≈ 4.2δ * s . Using a linear non-normal analysis based on a body forcing model, Önder & Liu (2020) also observed a high amplification in the range k y ≈ 1.5. This suggests that a similar non-normal amplification mechanism (lift-up mechanism) becomes prominent for t ≥ −π/3 in the present problem.…”

“…This mapping transforms the physical domain with undulated bottom to a rectangular box, which is suitable for a mixed discretization, where a bi-dimensional spectral-element discretization (Karniadakis & Sherwin 2005) can be combined with Fourier expansions (Karniadakis 1990). The mixed representation allows significant cost reduction and was employed in previous DNS works on bottom boundary layers (Önder & Yuan 2019;Önder & Liu 2020;Xiong et al 2020). We employ a bi-dimensional modified Legendre basis (Karniadakis & Sherwin 2005) in the streamwise-wall normal (x-z) plane, and Fourier expansions are defined in the spanwise (ȳ) direction.…”

“…The computational domain is sufficiently large to allow the transition modes and their secondary instabilities to develop, e.g. the vortex rollers have a streamwise spacing of approximately x ≈ 15 (Vittori & Blondeaux 2008) and the linear non-normal theory predicts a spanwise streak spacing y ≈ 4-5 (Verschaeve et al 2017;Önder & Liu 2020). Periodic boundaries are employed in the streamwise and spanwise directions.…”

“…These streaks are accompanied by counter-rotating vortices (figure 6b), which are arranged to transport low-momentum fluid upwards and high-momentum fluid downwards. This is the lift-up mechanism (Landahl 1980), which is discussed in detail in Önder & Liu (2020) for SWBLs. As the cross-stream velocity components building the vortices are of the same order (figure 6b), we will consider hereafter only the vertical velocity to discuss the dynamics of vortices.…”

“…Later in the APG stage, the non-normal growth of streaks is dominated by the non-normal growth of two-dimensional instability waves, which grow exponentially in Reynolds number. Önder & Liu (2020) modelled external perturbations as distributed body forces and analysed the receptivity of the SWBL to these perturbations in a linear framework. They also identified streamwise-constant vortices as the most effective perturbations to generate streaks.…”