Richard J. Munro

Sediment resuspension and erosion by vortex rings

Particle resuspension and erosion induced by a vortex ring interacting with a sediment layer was investigated experimentally using flow visualization (particle image velocimetry), high-speed video, and a recently developed light attenuation method for measuring displacements in bed level. Near-spherical sediment particles were used throughout with relative densities of 1.2–7 and diameters (d) ranging between 90 and 1600 μm. Attention was focused on initially smooth, horizontal bedforms with the vortex ring aligned to approach the bed vertically. Interaction characteristics were investigated in terms of the dimensionless Shields parameter, defined using the vortex-ring propagation speed. The critical conditions for resuspension (whereby particles are only just resuspended) were determined as a function of particle Reynolds number (based on the particle settling velocity and d). The effects of viscous damping were found to be significant for d/δ<15, where δ denotes the viscous sublayer thickness. Measuremen...

A Concentration pdf for the Relative Dispersion of a Contaminant Plume in the Atmosphere

Observations of the dispersion of a contaminant plume in theatmospheric boundary layer, obtained using a Lidar, are analysedin a coordinate frame relative to the instantaneous centre of massof the plume. To improve the estimates of relative dispersionstatistics, maximum entropy inversion is used to remove noise fromthe Lidar concentration profiles before carrying out the analysis.A parametric form is proposed for the probability density function(pdf) of concentration, consisting of a mixture of a betadistribution and of a generalised Pareto distribution (GPD). Thispdf allows for the possibility of a unimodal or bimodaldistribution, and is shown to give a satisfactory fit toobservations from a range of positions relative to the source. Thevariation of the fitted parameters with crossplume location isanalysed, and the maximum possible concentration is found todecrease away from the plume centre.

The High Concentration Tails Of The Probability Density Function Of A Dispersing Scalar In The Atmosphere

The distribution function for concentrations of a scalar pollutant dispersing in the turbulent atmosphere has a finite domain that is bounded above and below. Three methods, based on extreme value statistics, are used to obtainestimates for the upper bound and to describe the high concentration tailbehaviour of the distribution; all three methods are applied to concentrationdata obtained from experimental atmospheric releases. Quantile quantile (QQ)plots are used to assess the goodness of fit of the resulting estimates of thedistribution, and also to compare the performance of the three methods. Thepredicted values for the upper bound are orders of magnitude less than thesource concentration, illustrating that molecular diffusion has a large effecton the high concentrations.

Threshold criteria for incipient sediment motion on an inclined bedform in the presence of oscillating-grid turbulence

Here, we report laboratory experiments to investigate the threshold criteria for incipient sediment motion in the presence of oscillating-grid turbulence, with the bed slope inclined at angles between the horizontal and the repose limit for the sediment. A set of nine mono-disperse sediment types was used with size ranges normally associated with either the hydraulically-smooth or transitional regimes. Measurements of the (turbulent) fluid velocity field, in the region between the grid and bedforms surface, were obtained using two-dimensional particle imaging velocimetry. Statistical analysis of the velocity data showed that the turbulence had a anisotropic structure, due to the net transfer of energy from the normal to the tangential velocity components in the near-bed region, and that the fluctuations were dominant compared to the secondary mean flow. The sediment threshold criteria for horizontal bedforms were compared with, and found to be in good qualitative agreement with the standard Shields curve. For non-horizontal bedforms, the bed mobility was found to increase with increasing bed slope, and the threshold criteria were compared with previously-reported theoretical models, based on simple force-balance arguments.

Instabilities in the spin-up of a rotating, stratified fluid

Theoretical analyses and laboratory experiments have been performed on the stability of a flow generated by the differential cyclonic corotation of a flat, rigid disk in a uniformly rotating, linearly stratified fluid contained within a cylindrical tank. The undisturbed fluid is stably stratified with salt (Schmidt number σ≈670) and the (vertical) axes of rotation of the disk and the fluid container are coincident. The theoretical analysis shows that when the interior flow satisfies gradient wind balance (or, alternatively, thermal wind balance), it is destabilized by the action of viscosity. In the experiments, the manifestation of the viscous overturning instability is seen to be the formation of steplike internal microstructures in the density field, observed as regularly spaced, curved ring-shaped sheets with associated localized sharp, vertical density gradients. A stability analysis of the flow shows that the instability criterion is dependent on local values of the vertical and radial gradients of ...

Some Simple Statistical Models For Relative And Absolute Dispersion

Observations of the dispersion of a contaminant plume in the atmospheric boundary layer, obtained using a Lidar, are analysed in the coordinate frame relative to the instantaneous centre of mass of the plume, as well as the absolute (or fixed) coordinate frame. The study extends the work presented in a previous article, which analysed the structure of the probability density function (pdf) of concentration within the relative coordinate frame. Firstly, the plume displacement component, or plume meander, is analysed and a simple parametric form for the pdf of the plume centreline position is suggested. This is then used to analyse the accuracy and applicability of absolute framework statistical quantities obtained by a convolution of the relative frame statistical quantity with the plume centreline pdf.

The interaction of a vortex ring with a sloped sediment layer: Critical criteria for incipient grain motion

Experiments were performed to analyse the interaction between a vortex ring and a sloped sediment layer. Attention focussed on interactions under “critical” conditions, in which sediment motion was only just induced by the rings flow field. Both hydraulically smooth and hydraulically rough bedforms were analysed, using near-spherical monodisperse sediments with relative densities of 1.2 and 2.5 and mean diameters (d p ) ranging between 80 and 1087 μm. Measurements of the vortex-ring flow field were obtained, during the interaction, using two-dimensional particle imaging velocimetry. The threshold conditions for incipient sediment motion were analysed in terms of the critical Shields parameter (N c ), defined in terms of the peak tangential velocitymeasured adjacent to the bed surface. Bed-slope effects were investigated by tilting the sediment layer at various angles between the horizontal and the repose limit for the sediment. In all cases, the propagation axis of the vortex ring was aligned normal to the bed surface. The measured values of N c were compared with a force-balance model based on the conditions for incipient grain motion on a sloping bed. For hydraulically smooth bedforms, where the bed roughness is small compared to the boundary-layer depth, the model was derived to account for how viscous stresses affect the drag and lift forces acting on the near surface sediment. For hydraulically rough bedforms, where this viscous-damping effect is not present, the model assumes the drag and lift forces scale with the square of the near-bed (inviscid) velocity scale. In both cases, the model predicts that bedforms become more mobile as the bed slope is increased. However, the damping effect of the viscous sublayer acts as a stabilizing influence for hydraulically smooth bedforms, to reduce the rate at which the bed mobility increases with bed slope. The measured values of N c were in agreement with the trends predicted by this model, and exhibit a transition in behaviour between the smooth-bed and rough-bed cases when d p /δ s ≈ 20 (where δ s is the viscous-sublayer length scale).

Stratified spin-up in a sliced, square cylinder

We previously reported experimental and theoretical results on the linear spin-up of a linearly stratified, rotating fluid in a uniform-depth square cylinder [M. R. Foster and R. J. Munro, “The linear spin-up of a stratified, rotating fluid in a square cylinder,” J. Fluid Mech.712, 7–40 (2012)]. Here we extend that analysis to a “sliced” square cylinder, which has a base-plane inclined at a shallow angle α. Asymptotic results are derived that show the spin-up phase is achieved by a combination of the Ekman-layer eruptions (from the perimeter region of the cylinders lid and base) and cross-slope-propagating stratified Rossby waves. The final, steady state limit for this spin-up phase is identical to that found previously for the uniform depth cylinder, but is reached somewhat more rapidly on a time scale of order E −1/2Ω−1/log (α/E 1/2) (compared to E −1/2Ω−1 for the uniform-depth cylinder), where Ω is the rotation rate and E the Ekman number. Experiments were performed for Burger numbers, S, between 0.4 and 16, and showed that for S≳O(1)S≳O1 , the Rossby modes are severely damped, and it is only at small S, and during the early stages, that the presence of these wave modes was evident. These observations are supported by the theory, which shows the damping factors increase with S and are numerically large for S≳O(1)S≳O1 .

Analysis of intercomponent energy transfer in the interaction of oscillating-grid turbulence with an impermeable boundary

New experimental results are presented that investigate the nature of the intercomponent energy transfer that occurs in the interaction between oscillating-grid turbulence and a solid impermeable boundary, using instantaneous velocity measurements obtained from two-dimensional particle imaging velocimetry (PIV). Estimates of the pressure-strain correlation term (Πsij) of the transport equation of the Reynolds stress tensor, which represents intercomponent energy transfer, are obtained using the PIV data from a balance of the remaining terms of the transport equation. The influence of Πsij on the flow is examined by computing the energy spectra and conditional turbulent statistics associated with events in which intercomponent energy transfer is thought to be concentrated. Data reported here are in support of viscous and “return-to-isotropy” mechanisms governing the intercomponent energy transfer previously proposed, respectively, by Perot and Moin [J. Fluid Mech. 295, 199–227 (1995)] and Walker et al. [J. Fluid Mech. 320, 19–51 (1996)]. However, the data reported also indicate the presence of a weak net intercomponent energy transfer from the boundary-normal velocity components to the boundary-tangential velocity components over a thin region outside the viscous sublayer which is not captured within existing models of intercomponent energy transfer at the boundary.