Lagrangian flows within reflecting internal waves at a horizontal free-slip surface

Zhou, Qi; Diamessis, Peter

doi:10.1063/1.4936578

Cited by 6 publications

(5 citation statements)

References 46 publications

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“…Both Hazewinkel (2010) and Horne (2015) assumed < u >= 0, an assumption that is not true at O(ǫ), the leading order of the Stokes Drift. It is well known (Wunsch 1971;Ou & Maas 1986;Zhou & Diamessis 2015;Beckebanze et al 2018b) and straight forward to determine from Eq. 7.1 that the vertical Stokes Drift component is identical (with opposite sign) to the vertical induced mean velocity, w, given by (4.8), such that the Lagrangian mean flow in the vertical direction vanishes at its leading order:…”

Section: Misconceptions Concerning Stokes Driftmentioning

confidence: 99%

“…Here, 'strong' refers to persistent, cumulative transfer of energy from the wave field into the mean flow. Strong mean flow generation is known to occur due to horizontal cross-beam variation (Bordes et al 2012;Kataoka & Akylas 2015;Semin et al 2016;Beckebanze et al 2018b), with important modifications by planetary rotation (Grisouard & Bühler 2012;Fan et al 2018), and upon reflection where incident and reflected beams interact (Thorpe 1997;Grisouard et al 2013;Zhou & Diamessis 2015;Raja 2018). Renaud & Venaille (2018) recently also found strong mean flow generation in a flat bottom boundary layer.…”

Section: Introductionmentioning

confidence: 99%

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Particle transport induced by internal wave beam streaming in lateral boundary layers

et al. 2019

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Quantifying the physical mechanisms responsible for the transport of sediments, nutrients and pollutants in the abyssal sea is a long-standing problem, with internal waves regularly invoked as the relevant mechanism for particle advection near the sea bottom. This study focuses on internalwave induced particle transport in the vicinity of (almost) vertical walls. We report a series of laboratory experiments revealing that particles sinking slowly through a monochromatic internal wave beam experience significant horizontal advection. Extending the theoretical analysis by Beckebanze et al. (2018a), we attribute the observed particle advection to a peculiar and previously unrecognized streaming mechanism originating at the lateral walls. This vertical boundarylayer streaming mechanism is most efficient for strongly inclined wave beams, when vertical and horizontal velocity components are of comparable magnitude. We find good agreement between our theoretical prediction and experimental results. †

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Section: Misconceptions Concerning Stokes Driftmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Particle transport induced by internal wave beam streaming in lateral boundary layers

et al. 2019

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“…However, we are not able to perform the same comparison at Fr ∈ {16, 64}, for which the wave amplitudes are higher, due to the prohibitive computational cost. Moreover, it is found in § 5.3 that wave-induced Lagrangian transport, which is expected to be a second-order nonlinear effect in the wave's amplitude (Zhou & Diamessis 2015), scales strongly with Fr. In summary, while the nonlinear effects found in the wave-reflecting subsurface are not very strong in the cases examined here, it is still premature to reject their importance in the real oceanic parameter range (see more in § 6.5), where the wave amplitudes might be higher.…”

Section: Discussionmentioning

confidence: 98%

“…We focus on the lateral transport due to the nonlinear effects of the waves during reflection (Zhou & Diamessis 2015). This transport is found to be more significant at the higher Re = 10 5 with IWs of higher amplitude interacting with the surface, and the results are shown for R100F4 and R100F16 in figure 16.…”

Section: Wave-driven Lagrangian Flowsmentioning

confidence: 97%

Surface manifestation of internal waves emitted by submerged localized stratified turbulence

Zhou

Diamessis

2016

J. Fluid Mech.

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The internal waves (IWs) radiated by the turbulent wake of a sphere of diameter $D$ towed at speed $U$ are investigated using three-dimensional fully nonlinear simulations performed in a linearly stratified Boussinesq fluid with buoyancy frequency $N$. The study focuses on a broad range of wave characteristics in the far field of the turbulent wave source, specifically at the sea surface (as modelled by a free-slip rigid lid) where the IWs reflect. Six simulations are performed at Reynolds number $Re\equiv UD/{\it\nu}\in \{5\times 10^{3},10^{5}\}$ and Froude number $Fr\equiv 2U/(ND)\in \{4,16,64\}$, where ${\it\nu}$ is viscosity. The wave-emitting wake is located at a fixed distance of $9D$ below the surface. As the wake evolves for up to $O(300)$ units of buoyancy time scale $1/N$, IW characteristics, such as horizontal wavelength ${\it\lambda}_{H}$ and wave period $T$, are sampled at the sea surface via wavelet transforms of horizontal divergence signals. The statistics of amplitudes and orientations of IW-induced surface strains are also reported. The mean dimensionless observable wavelength $\overline{{\it\lambda}}_{H}/D$ at the sea surface decays in time as $(Nt)^{-1}$, which is due to the waves’ dispersion. This observation is in agreement with a linear propagation model that is independent of the wake $Re$ and $Fr$. This agreement further suggests that the most energetic waves impacting the surface originate from the early-time wake that is adjusting to buoyancy. The most energetic dimensionless wavelength $\hat{{\it\lambda}}_{H}/D$ is found to scale as $Fr^{1/3}$ and decrease with $Re$, which causes the arrival time (in $Nt$ units) of the strongest waves at the surface to scale as $Fr^{-1/3}$ and increase with $Re$. This wavelength $\hat{{\it\lambda}}_{H}$ is also found to correlate with the vertical Taylor scale of the wake turbulence. IW-driven phenomena at the surface that are of interest to an observer, such as the local enrichment of surfactant and the transport of ocean surface tracers, are also examined. The local enrichment ratio of surface scalar scales linearly with the steepness of IWs that reach the surface, and the ratio often exceeds a possible visibility threshold. The Lagrangian drifts of ocean tracers, which are linked to the nonlinear interaction between incident and reflecting IW packets, create a local divergence in lateral mass transport right above the wake centreline, an effect that intensifies strongly with increasing $Fr$. The findings of this study may serve as a platform to investigate the generation and surface manifestation of IWs radiated by other canonical submerged stratified turbulent flows.

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“…Key ingredients for mean vertical vorticity production through streaming by internal waves beams -and hence vortical mean flow generation -are both viscous attenuation and horizontal-cross-beam variations of the wave beam amplitude. Several recent studies investigate vortical mean flow generation through streaming in truly three-dimensional settings, both numerically (King et al 2010;Grisouard & Bühler 2012;van den Bremer 2014;Zhou & Diamessis 2015;Raja 2018) and experimentally (Grisouard 2010;Bordes et al 2012;Grisouard et al 2013;Semin et al 2016;Kataoka et al 2017). Over long time scales, the vortical induced mean flow may become sufficiently energetic such that wave-mean flow interactions eventually lead to a breakdown of the internal wave itself.…”

Section: Introductionmentioning

confidence: 99%

Mean flow generation by three-dimensional nonlinear internal wave beams

2019

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We study the generation of resonantly growing mean flow by weakly non-linear internal wave beams. With a perturbational expansion, we construct analytic solutions for 3D internal wave beams, exact up to first order accuracy in the viscosity parameter. We specifically focus on the subtleties of wave beam generation by oscillating boundaries, such as wave makers in laboratory set-ups. The exact solutions to the linearized equations allow us to derive an analytic expression for the mean vertical vorticity production term, which induces a horizontal mean flow. Whereas mean flow generation associated with viscous beam attenuation -known as streaming -has been described before, we are the first to also include a peculiar inviscid mean flow generation in the vicinity of the oscillating wall, resulting from line vortices at the lateral edges of the oscillating boundary. Our theoretical expression for the mean vertical vorticity production is in good agreement with earlier laboratory experiments, for which the previously unrecognized inviscid mean flow generation mechanism turns out to be significant. † Email address for correspondence: f.beckebanze@uu.nl arXiv:1805.12356v2 [physics.flu-dyn]

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Lagrangian flows within reflecting internal waves at a horizontal free-slip surface

Cited by 6 publications

References 46 publications

Particle transport induced by internal wave beam streaming in lateral boundary layers

Particle transport induced by internal wave beam streaming in lateral boundary layers

Surface manifestation of internal waves emitted by submerged localized stratified turbulence

Mean flow generation by three-dimensional nonlinear internal wave beams

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