The effect of double diffusion on entrainment in turbulent plumes

We investigate experimentally the effect of double diffusion in the salt-fingering configuration on entrainment in turbulent plumes. Plumes over a range of source buoyancy fluxes and source density ratios are examined. When the plumes are double diffusive ( ) the entrainment coefficient is not constant, with an up to 20 % reduction from the value found for single-diffusive plumes, that is, plumes with . The scale of reduction is found to be in direct relation to the source density ratio and is inversely related to the distance travelled by the plume, indicating that double-diffusive effects decrease as the plume evolves. We propose an explanation for the observed reduction in the entrainment coefficient on the basis of differential diffusion hindering large-scale engulfment at the edge of the plume.We acknowledge funding from the EPSRC under the Programme Grant EP/K034529/1 ‘Mathematical Underpinnings of Stratified Turbulence’ (MUST), and from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme under grant no. 742480 ‘Stratified Turbulence And Mixing Processes’ (STAMP). M.D. is supported by the Gates Cambridge Scholarship

Research data supporting "Regime transitions and energetics of sustained stratified shear flows"

We provide the following data: 1. The three-component velocity and density fields in space and time (u, v, w, ρ)(x, y, z, t) for all 16 experiments listed in table 2 of the paper; 2. The MATLAB codes used to compute and plot the energetics of the above data, as explained in the paper and shown in figures 10, 11, 14, 15, 16. 3. Movies showing all the flow fields and the spanwise vorticity in a number of slices allowing for an advanced visualisation of the 4D data to complement figures 3-4; 4. Plots of the mass flux and volume flux for each experiment; 5. A README.pdf file giving more information about the data, its format and usage instructions

Regime transitions and energetics of sustained stratified shear flows

We describe the long-term dynamics of sustained stratified shear flows in the laboratory. The stratified inclined duct (SID) experiment sets up a two-layer exchange flow in an inclined duct connecting two reservoirs containing salt solutions of different densities. This flow is primarily characterised by two non-dimensional parameters: the tilt angle of the duct with respect to the horizontal, \unicode[STIX]{x1D703} (a few degrees at most), and the Reynolds number $Re$, an input parameter based on the density difference driving the flow. The flow can be sustained with constant forcing over arbitrarily long times and exhibits a wealth of dynamical behaviours representative of geophysically relevant sustained stratified shear flows. Varying \unicode[STIX]{x1D703} and $Re$ leads to four qualitatively different regimes: laminar flow; mostly laminar flow with finite-amplitude, travelling Holmboe waves; spatio-temporally intermittent turbulence with substantial interfacial mixing; and sustained, vigorous interfacial turbulence (Meyer & Linden, J. Fluid Mech., vol. 753, 2014, pp. 242–253). We seek to explain the scaling of the transitions between flow regimes in the two-dimensional plane of input parameters (\unicode[STIX]{x1D703},Re). We improve upon previous studies of this problem by providing a firm physical basis and non-dimensional scaling laws that are mutually consistent and in good agreement with the empirical transition curves we inferred from 360 experiments spanning \unicode[STIX]{x1D703}\in [-1^{\circ },6^{\circ }] and $Re\in [300,5000]$. To do so, we employ state-of-the-art simultaneous volumetric measurements of the density field and the three-component velocity field, and analyse these experimental data using time- and volume-averaged potential and kinetic energy budgets. We show that regime transitions are caused by an increase in the non-dimensional time- and volume-averaged kinetic energy dissipation within the duct, which scales with \unicode[STIX]{x1D703}Re at high enough angles. As the power input scaling with \unicode[STIX]{x1D703}Re is increased above zero, the two-dimensional, parallel-flow dissipation (power output) increases to close the budget through an increase in the magnitude of the exchange flow, incidentally triggering Holmboe waves above a certain threshold in interfacial shear. However, once the hydraulic limit of two-layer exchange flows is reached, two-dimensional dissipation plateaus and three-dimensional dissipation at small scales (turbulence) takes over, at first intermittently, and then steadily, in order to close the budget and follow the \unicode[STIX]{x1D703}Re scaling. This general understanding of regime transitions and energetics in the SID experiment may serve as a basis for the study of more complex sustained stratified shear flows found in the natural environment.EPSRC Doctoral Prize EPSRC Programme Grant EP/K034529/1 ERC Horizon 2020 Grant No 74248

A comparison of entrainment in turbulent line plumes adjacent to and distant from a vertical wall

EPSRC (R008957/1) EPSRC (K034529/1) ERC (742480

Conditional sampling of a high Péclet number turbulent plume and the implications for entrainment

We present simultaneous two-dimensional velocity and scalar measurements on a central vertical plane in an axisymmetric pure turbulent plume. We use an edge-detection algorithm to determine the edge of the plume, and compare the data obtained in both a fixed Eulerian frame and a frame relative to local coordinates defined in terms of the instantaneous plume edge. In an Eulerian frame we observe that the time-averaged distributions of vertical and horizontal velocity are self-similar, the vertical velocity being well represented by a Gaussian distribution. We condition these measurements on whether fluid is inside or outside of the plume, and whether fluid inside is mixed plume fluid or engulfed ambient fluid. We find that, on average, 5 % of the total vertical volume transport occurs outside the plume and this figure rises to nearly 14 % at heights between large-scale coherent structures. We show that the fluxes of engulfed fluid within the plume envelope are slightly larger than the vertical transport outside the plume – indicating that ambient fluid is engulfed into the plume envelope before being nibbled across the turbulent/non-turbulent interface (TNTI) and then ultimately irreversibly mixed. Our new measurements in the plume coordinate (following the meandering fluctuating plume) show the flow within the plume and in the nearby ambient fluid is strongly influenced by whether an eddy is present locally within the plume, or absent. When an eddy is present and the plume is wide, the vertical velocities near the plume edge are small and hence all vertical transport is inside the plume. In regions where the plume is narrow and there is no eddy, large vertical velocities and hence transport are observed outside the plume suggesting that pressure forces associated with the eddies accelerate ambient fluid which is then engulfed into the plume. Finally, we show that observing significant vertical velocities beyond the scalar edge of the plume does not suggest that the characteristic width of the velocity distribution is greater than that of the scalar field; on the contrary, we show our observations to be consistent with a buoyancy distribution that is up to 20 % wider than that of the velocity. Measurements in the plume coordinates show that the mixing of momentum across the plume results in a distribution for which the differential entropy is close to maximal and the mixing of momentum is uninhibited (i.e. not bounded) by the TNTI of the plume. Furthermore, our measurements suggest that the scalar mixing across the plume may also result in a distribution for which the differential entropy is close to maximal but, in contrast to the momentum, the scalar mixing is strictly bounded by the plume edge.This work was supported, in part, by the Leverhulme Trust Research Programme Grant RP2013-SL-008, the EPSRC Programme Grant EP/K034529/1, the Gulf of Mexico Research Institute and by iCASE awards from NERC and the UK Met Office (RG82562) and EPSRC and Arup (RG83017)

The structure and origin of confined Holmboe waves

Finite-amplitude manifestations of stratified shear flow instabilities and their spatio-temporal coherent structures are believed to play an important role in turbulent geophysical flows. Such shear flows commonly have layers separated by sharp density interfaces, and are therefore susceptible to the so-called Holmboe instability, and its finite-amplitude manifestation, the Holmboe wave. In this paper, we describe and elucidate the origin of an apparently previously unreported long-lived coherent structure in a sustained stratified shear flow generated in the laboratory by exchange flow through an inclined square duct connecting two reservoirs filled with fluids of different densities. Using a novel measurement technique allowing for time-resolved, near-instantaneous measurements of the three-component velocity and density fields simultaneously over a three-dimensional volume, we describe the three-dimensional geometry and spatio-temporal dynamics of this structure. We identify it as a finite-amplitude, nonlinear, asymmetric confined Holmboe wave (CHW), and highlight the importance of its spanwise (lateral) confinement by the duct boundaries. We pay particular attention to the spanwise vorticity, which exhibits a travelling, near-periodic structure of sheared, distorted, prolate spheroids with a wide ‘body’ and a narrower ‘head’. Using temporal linear stability analysis on the two-dimensional streamwise-averaged experimental flow, we solve for three-dimensional perturbations having two-dimensional, cross-sectionally confined eigenfunctions and a streamwise normal mode. We show that the dispersion relation and the three-dimensional spatial structure of the fastest-growing confined Holmboe instability are in good agreement with those of the observed confined Holmboe wave. We also compare those results with a classical linear analysis of two-dimensional perturbations (i.e. with no spanwise dependence) on a one-dimensional base flow. We conclude that the lateral confinement is an important ingredient of the confined Holmboe instability, which gives rise to the CHW, with implications for many inherently confined geophysical flows such as in valleys, estuaries, straits or deep ocean trenches. Our results suggest that the CHW is an example of an experimentally observed, inherently nonlinear, robust, long-lived coherent structure which has developed from a linear instability. We conjecture that the CHW is a promising candidate for a class of exact coherent states underpinning the dynamics of more disordered, yet continually forced stratified shear flows.</jats:p

The Fluxes and Behaviour of Plumes Inferred from Measurements of Coherent Structures within Images of the Bulk Flow

This paper describes how measurements of the movement of identifiable features at the edge of a turbulent plume can be interpreted to determine the properties of the mean flow and consequently, using plume theory, can be used to make estimates of the fluxes of volume (mass), momentum, and buoyancy in a plume. This means that video recordings of smoke rising from a chimney or buoyant material from a source on the sea bed can be used to make accurate estimates of the source conditions for the plume. At best we can estimate the volume flux and buoyancy flux to within about 5% and 15% of the actual values, respectively. Although this is restricted to the case of a plume rising in a stationary and unstratified environment, we show that the results may be of practical use in other more complex situations. In addition, we demonstrate that large-scale (turbulent) coherent structures at the plume edge form on a scale approximately 40% of the local (mean) plume half-width and travel at almost 60% of the average local (mean) velocity in the plume.The authors would like to acknowledge that the genesis of the work reported herein was a study investigating the physics of turbulent fountains, via coherent structure tracking, which was carried out by HCB and Prof. Gary R. Hunt (Burridge & Hunt, In Preparation). In addition, the authors gratefully acknowledge the skills and expertise provided by the technical staff at the G. K. Batchelor laboratory; HCB acknowledges the insightful comments of Prof. Colm-cille Caulfield. This work was supported, in part, by the Leverhulme Trust Research Programme Grant RP2013-SL-008, the EPSRC Programme Grant EP/K034529/1 and by the Royal Societ

The antiangiogenic agent ZD4190 prevents tumour outgrowth in a model of minimal residual carcinoma in deep tissues

BACKGROUND: Tumour cells may persist at the operative site after seemingly adequate surgery. Radiotherapy is often given in an attempt to prevent repopulation, but this modality cannot be relied upon to prevent locoregional recurrence. An alternative strategy is to take advantage of the requirement of tumour cells to develop an independent blood supply and block this process to prevent recurrence. METHODS: In this study, we evaluate the effect of the angiogenesis inhibitor, ZD4190, using a rodent model of residual carcinoma in deep tissues, mimicking the clinical scenario where low numbers of malignant cells persist at the operative site. RESULTS: The tumour burden that could be eliminated was dependent on the site where the cells were implanted. Immediate treatment with ZD4190 prevented outgrowth of up to 2.5 x 10(5) cells in the rectus muscle and 1 x 10(5) in the gastrocnemius, whereas control animals developed large tumours. When more than 2.5 x 10(6) cells were implanted into the rectus or 1 x 10(6) into the gastrocnemius and treatment was maintained for 3 weeks, the carcinomas that developed in ZD4190-treated animals showed a reduced microvessel density and increased necrosis when compared with the vehicle-treated controls, but an infiltrative growth pattern was common. CONCLUSION: These findings suggest that antiangiogenic agents have a role to play in preventing outgrowth of residual carcinoma and are likely to be most effective when the tumour burden is minimal

Formation and Propagation of Matter Wave Soliton Trains

Attraction between atoms in a Bose-Einstein-Condensate renders the condensate unstable to collapse. Confinement in an atom trap, however, can stabilize the condensate for a limited number of atoms, as was observed with 7Li, but beyond this number, the condensate collapses. Attractive condensates constrained to one-dimensional motion are predicted to form stable solitons for which the attractive interactions exactly compensate for the wave packet dispersion. Here we report the formation or bright solitons of 7Li atoms created in a quasi-1D optical trap. The solitons are created from a stable Bose-Einstein condensate by magnetically tuning the interactions from repulsive to attractive. We observe a soliton train, containing many solitons. The solitons are set in motion by offsetting the optical potential and are observed to propagate in the potential for many oscillatory cycles without spreading. Repulsive interactions between neighboring solitons are inferred from their motion