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

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 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

Continuous Requirement for the Clr4 Complex But Not RNAi for Centromeric Heterochromatin Assembly in Fission Yeast Harboring a Disrupted RITS Complex

Formation of centromeric heterochromatin in fission yeast requires the combined action of chromatin modifying enzymes and small RNAs derived from centromeric transcripts. Positive feedback mechanisms that link the RNAi pathway and the Clr4/Suv39h1 histone H3K9 methyltransferase complex (Clr-C) result in requirements for H3K9 methylation for full siRNA production and for siRNA production to achieve full histone methylation. Nonetheless, it has been proposed that the Argonaute protein, Ago1, is the key initial trigger for heterochromatin assembly via its association with Dicer-independent “priRNAs.” The RITS complex physically links Ago1 and the H3-K9me binding protein Chp1. Here we exploit an assay for heterochromatin assembly in which loss of silencing by deletion of RNAi or Clr-C components can be reversed by re-introduction of the deleted gene. We showed previously that a mutant version of the RITS complex (Tas3WG) that biochemically separates Ago1 from Chp1 and Tas3 proteins permits maintenance of heterochromatin, but prevents its formation when Clr4 is removed and re-introduced. Here we show that the block occurs with mutants in Clr-C, but not mutants in the RNAi pathway. Thus, Clr-C components, but not RNAi factors, play a more critical role in assembly when the integrity of RITS is disrupted. Consistent with previous reports, cells lacking Clr-C components completely lack H3K9me2 on centromeric DNA repeats, whereas RNAi pathway mutants accumulate low levels of H3K9me2. Further supporting the existence of RNAi–independent mechanisms for establishment of centromeric heterochromatin, overexpression of clr4+ in clr4Δago1Δ cells results in some de novo H3K9me2 accumulation at centromeres. These findings and our observation that ago1Δ and dcr1Δ mutants display indistinguishable low levels of H3K9me2 (in contrast to a previous report) challenge the model that priRNAs trigger heterochromatin formation. Instead, our results indicate that RNAi cooperates with RNAi–independent factors in the assembly of heterochromatin