Steady nonlinear diffusion-driven flow

Page, Michael A.; Johnson, E. R.

doi:10.1017/s002211200900679x

Cited by 14 publications

(22 citation statements)

References 9 publications

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“…This flow field is similar to u 0 (η) within the boundary-layer scale (γ −1 ≈ 2 mm) over most of the top and bottom sloping surfaces, with a slight (∼25%) reduction in peak velocity. The flow field diverges noticeably from the analytical form within two millimetres of the sides, front and rear of the wedge, as well as outside the boundary layer, where fore-aft-asymmetric flow structures exist to balance the rearward volume flux along the sloping surfaces 10,11 ; the same qualitative features are present in our PIV data set (Fig. 2a).…”

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confidence: 56%

Propulsion generated by diffusion-driven flow

2010

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Buoyancy-driven flow, which is flow driven by spatial variations in fluid density 1 , lies at the heart of a variety of physical processes, including mineral transport in rocks 2 , the melting of icebergs 3 and the migration of tectonic plates 4 . Here we show that buoyancy-driven flows can also generate propulsion. Specifically, we find that when a neutrally buoyant wedgeshaped object floats in a density-stratified fluid, the diffusiondriven flow at its sloping boundaries generated by molecular diffusion produces a macroscopic sideways thrust. Computer simulations reveal that thrust results from diffusion-driven flow creating a region of low pressure at the front, relative to the rear of an object. This discovery has implications for transport processes in regions of varying fluid density, such as marine snow aggregation at ocean pycnoclines 5 , and wherever there is a temperature difference between immersed objects and the surrounding fluid, such as particles in volcanic clouds 6 .A fluid system with spatially varying density, resulting from temperature and/or salinity variations, for example, is stably-stratified when increasing density is parallel to the direction of gravity. When an object is released in a quiescent, stably-stratified fluid, it is expected to settle or rise to the neutral buoyancy level at which the density of the object matches that of the surrounding fluid, and remain stationary thereafter. We carried out a control experiment in which a 19.05-mm-diameter sphere of density ρ = 1,115 kg m −3 was released in a tank of height H = 0.40 m, width W = 0.20 m and length L = 0.40 m, filled with salt-stratified water with density gradient dρ/dz = −511 ± 3 kg m −4 . As expected, the sphere settled to its neutral buoyancy height, where it remained stationary for 24 hours. A similar experiment was then carried out using a triangular wedge ( Fig. 1) of length l = 99.9 ± 0.1 mm, base h = 17.6 ± 0.10 mm (corresponding to slope angle α = 5.0 ± 0.1 • ) and width w = 25.1 ± 0.10 mm. In striking contrast to the stationary sphere, the wedge moved at a constant speed u = 10.2 ± 0.1 × 10 −3 m h −1 (2.83 ± 0.03 × 10 −6 m s −1 ) in the direction of its tip, without any obvious cause ( Fig. 1 and its top inset; also see Supplementary Movie S1).To investigate the cause of this spontaneous propulsion, we visualized the velocity fields in the horizontal and vertical midplanes of the moving wedge using particle image velocimetry (PIV; Fig. 2). Here, z is the vertical coordinate antiparallel to gravity and x and y are the coordinates in the horizontal plane, parallel and perpendicular to the long axis of the wedge, respectively. These experiments reveal that fluid is drawn in towards the wedge tip in the horizontal plane to supply up-slope flow in a thin boundary layer above the sloping surface. Furthermore, fluid immediately behind the wedge moves with the same speed as the wedge; this phenomenon, known as blocking, occurs for obstacles in stratified flow when buoyancy forces dominate inertia and viscous forces 1 . As ...

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confidence: 56%

Propulsion generated by diffusion-driven flow

2010

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“…However, all of these studies have concentrated on boundary layers over constant-slope bottom boundaries. A rare study that includes the effect of a change in bottom slope is Page & Johnson (2009), who studied the boundary-layer response in a diamond-shaped box with heated walls: a very interesting study, but not concerned with oceanographic applications.…”

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confidence: 99%

Diffusive boundary layers over varying topography

Dell

Pratt

2015

J. Fluid Mech.

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Diffusive bottom boundary layers can produce upslope flows in a stratified fluid. Accumulating observations suggest that these boundary layers may drive upwelling and mixing in mid-ocean ridge flank canyons. However, most studies of diffusive bottom boundary layers to date have concentrated on constant bottom slopes. We present a study of how diffusive boundary layers interact with various idealized topography, such as changes in bottom slope, slopes with corrugations and isolated sills. We use linear theory and numerical simulations in the regional ocean modeling system (ROMS) model to show changes in bottom slope can cause convergences and divergences within the boundary layer, in turn causing fluid exchanges that reach far into the overlying fluid and alter stratification far from the bottom. We also identify several different regimes of boundary-layer behaviour for topography with oceanographically relevant size and shape, including reversing flows and overflows, and we develop a simple theory that predicts the regime boundaries, including what topographies will generate overflows. As observations also suggest there may be overflows in deep canyons where the flow passes over isolated bumps and sills, this parameter range may be particularly significant for understanding the role of boundary layers in the deep ocean.

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“…Later, the asymptotic [9] and exact [10] solutions of the problem of formation of flows on an infinite slope, when nonlinear terms in the equations of motion are dropped due to the configuration, were constructed. The parameters of steady flows in an inclined con tainer [11] were analytically estimated recently.…”

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confidence: 99%