A turbulent patch arising from a breaking internal wave

Yakovenko, S. N.; Thomas, T.G.; Castro, Ian P.

doi:10.1017/s0022112011000644

Cited by 3 publications

(16 citation statements)

References 39 publications

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“…This leads to a local vortex form with an associated updraft current quite similar to a hydraulic jump: a significant positive vertical velocity can be observed in the middle of the instability region as well as stronger values of turbulent kinetic energy. In agreement with Yu & Cai [59], waves are observed downstream of the jump (see also [52]). …”

Section: Interfaces With Turbulent Flowssupporting

confidence: 85%

Interfaces and inhomogeneous turbulence

Hunt

Eames

Silva

et al. 2011

Phil. Trans. R. Soc. A.

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A Euromech colloquium, on interfacial processes and inhomogeneous turbulence, was held in London on 28-30 June 2010. Papers were presented describing and analysing the influence of interfaces that separate turbulent/non-turbulent regions, between regions of contrasting fluid properties, or at the edge of boundaries. This paper describes a summary of the work presented, giving a snapshot of the current progress in this area, along with discussions about future research directions.

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Section: Interfaces With Turbulent Flowssupporting

confidence: 85%

Interfaces and inhomogeneous turbulence

Hunt

Eames

Silva

et al. 2011

Phil. Trans. R. Soc. A.

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“…The earliest version of the code is described by Thomas & Williams (1997), and for density-stratified flows it was modified (when starting the work for Yakovenko et al (2011)) to include simultaneous solution of the density equation, making the usual Boussinesq assumption. Using coordinates x, y, z, t appropriately non-dimensionalised by the obstacle height h and, for time, free-stream velocity U, the continuity, Navier-Stokes and density equations therefore become…”

Section: Methodsmentioning

confidence: 99%

“…The last term in (2.2) is the buoyancy term, and the only non-zero contribution appears in the vertical momentum equation, of course, through the gravitational vector. Full details of the numerical methods used are provided in the companion paper (Yakovenko et al 2011), so here only a brief summary is given. Second-order central differencing on a uniform Cartesian mesh was applied to all spatial derivatives and a second-order Adams-Bashforth scheme was used for time advancement, with a projection method for pressure computations.…”

Section: Methodsmentioning

confidence: 99%

“…A straightforward sponge zone technique was used to prevent long-wave reflections from the two ends of the computational domain. These are fully described and validated by Yakovenko et al (2011), but their use was less crucial for the current work because transition in the breaking wave occurred at relatively early times. Periodicity was used for the spanwise boundary conditions.…”

Section: Methodsmentioning

confidence: 99%

“…Once transition is complete, a fully turbulent and essentially steady 'patch' (a fully mixed region having largely uniform density) emerges, and the nature of this patch was explored in our previous paper (Yakovenko, Thomas & Castro 2011). The hill is 2D but the computation was a full direct numerical simulation (DNS) at Re = Uh/ν = 4000, Pr ≡ ν/κ = 1 and F h = U/Nh = 0.6, where N is the Brunt-Väisälä frequency defined by N = [−(g/ρ)(dρ/dz)] 1/2 .…”

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confidence: 99%

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Transition through Rayleigh–Taylor instabilities in a breaking internal lee wave

2014

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Results of direct numerical simulations of the transitional processes that characterise the evolution of a breaking internal gravity wave to a fully developed and essentially steady turbulent patch are presented. The stationary lee wave was forced by the imposition of an appropriate bottom boundary shape within a density-stratified domain having a uniform upstream velocity and density gradient, and with the ratio of momentum to thermal (or other) diffusivity defined by Pr = 1. An earlier paper considered the eventual, fully developed turbulent patch arising after the breaking process is complete (Yakovenko et al., J. Fluid Mech., vol. 677, 2011, pp. 103-133); the focus in this paper is on the instabilities in the breaking process itself. The flow is analysed using streamlines, density contours and temporal and spatial spectra, as well as second moments of the velocity and density fluctuations, for a Reynolds number of 4000 based on the height of the bottom topography and the upstream velocity. The computations (on a grid using in excess of 10 9 mesh points) yielded sufficient resolution to capture the fine-scale transition processes as well as the subsequent fully developed turbulence discussed earlier. It is shown that the major instability is of Rayleigh-Taylor type (RTI) with a resulting mixing region depth growing in a manner consistent with more classical RTI studies, despite the much more complicated environment. The resolution was sufficient to capture secondary Kelvin-Helmholtz-type instabilities on the developing RTI structures. Overall evolution towards the fully turbulent state characterised by a significant region of − 5 3 subrange in both velocity and density spectra is very rapid. It is much faster than the long time scale characterising the subsequent evolution of the turbulent patch; this latter time scale is sufficiently large that the turbulent patch can itself be viewed as essentially steady.

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Tidal flow over topography: effect of excursion number on wave energetics and turbulence

2014

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The excursion number, Ex = U 0 /Ωl, is a parameter that characterizes the ratio of streamwise fluid advection during a tidal oscillation of amplitude U 0 and frequency Ω to the streamwise topographic length scale l. Direct numerical simulations are performed to study how internal gravity waves and turbulence change when Ex is varied from a low value (typical of a ridge in the deep ocean) to a value of unity (corresponding to energetic tides over a small topographic feature). An isolated obstacle having a smoothed triangular shape and 20 % of the streamwise length at critical slope is considered. With increasing values of Ex, the near field of the internal waves loses its beam-like character, the wave response becomes asymmetric with respect to the ridge centre, and transient lee waves form. Analysis of the baroclinic energy balance shows significant reduction in the radiated wave flux in the cases with higher Ex owing to a substantial rise in advection and baroclinic dissipation as well as a decrease in conversion. Turbulence changes qualitatively with increasing Ex. In the situation with Ex ∼ 0.1, turbulence is intensified at the near-critical regions of the slope, and is also significant in the internal wave beams above the ridge where there is intensified shear. At Ex = O(1), the transient lee waves overturn adjacent to the ridge flanks and, owing to convective instability, buoyancy acts as a source for turbulent kinetic energy. The size of the turbulent overturns has a non-monotonic dependence on excursion number: the largest overturns, as tall as twice the obstacle height, occur in the Ex = 0.4 case, but there is a substantial decrease of overturn size at larger values of Ex simulated here.

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A turbulent patch arising from a breaking internal wave

Cited by 3 publications

References 39 publications

Interfaces and inhomogeneous turbulence

Interfaces and inhomogeneous turbulence

Transition through Rayleigh–Taylor instabilities in a breaking internal lee wave

Tidal flow over topography: effect of excursion number on wave energetics and turbulence

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