Nonlinear softening as a predictive precursor to climate tipping

Approaching a dangerous bifurcation, from which a dynamical system such as the Earth's climate will jump (tip) to a different state, the current stable state lies within a shrinking basin of attraction. Persistence of the state becomes increasingly precarious in the presence of noisy disturbances. We consider an underlying potential, as defined theoretically for a saddle-node fold and (via averaging) for a Hopf bifurcation. Close to a stable state, this potential has a parabolic form; but approaching a jump it becomes increasingly dominated by softening nonlinearities. If we have already detected a decrease in the linear decay rate, nonlinear information allows us to estimate the propensity for early tipping due to noise. We argue that one needs to extract information about the nonlinear features (a "softening") of the underlying potential from the time series to judge the probability and timing of tipping. This analysis is the logical next step if one has detected a decrease of the linear decay rate. If there is no discernable trend in the linear analysis, nonlinear softening is even more important in showing the proximity to tipping. After extensive normal form calibration studies, we check two geological time series from paleo-climate tipping events for softening of the underlying well. For the ending of the last ice age, where we find no convincing linear precursor, we identify a statistically significant nonlinear softening towards increasing temperature. The analysis has thus successfully detected a warning of the imminent tipping event.Comment: 22 pages, 11 figures, changed title back, corrected smaller mistakes, updated reference

Backflow air and pressure analysis in emptying a pipeline containing an entrapped air pocket

[EN] The prediction of the pressure inside the air pocket in water pipelines has been the topic for a lot of research works. Several aspects in this field have been discussed, such as the filling and the emptying procedures. The emptying process can affect the safety and the efficiency of water systems. Current research presents an analysis of the emptying process using experimental and computational results. The phenomenon is simulated using the two-dimensional computational fluid dynamics (2D CFD) and the one-dimensional mathematical (1D) models. A backflow air analysis is also provided based on CFD simulations. The developed models show good ability in the prediction of the sub-atmospheric pressure and the flow velocity in the system. In most of the cases, the 1D and 2D CFD models show similar performance in the prediction of the pressure and the velocity results. The backflow air development can be accurately explained using the CFD model.This work was supported by the Fundação para a Ciência e a Tecnologia (FCT), Portugal under grant number PD/BD/114459/2016.Besharat, M.; Coronado-Hernández, OE.; Fuertes-Miquel, VS.; Viseu, MT.; Ramos, HM. (2018). Backflow air and pressure analysis in emptying a pipeline containing an entrapped air pocket. Urban Water Journal. 15(8):769-779. https://doi.org/10.1080/1573062X.2018.1540711S769779158Benjamin, T. B. (1968). Gravity currents and related phenomena. Journal of Fluid Mechanics, 31(2), 209-248. doi:10.1017/s0022112068000133Besharat, M., Teresa Viseu, M., & Ramos, H. (2017). Experimental Study of Air Vessel Behavior for Energy Storage or System Protection in Water Hammer Events. Water, 9(1), 63. doi:10.3390/w9010063Besharat, M., Tarinejad, R., & Ramos, H. M. (2015). The effect of water hammer on a confined air pocket towards flow energy storage system. Journal of Water Supply: Research and Technology-Aqua, 65(2), 116-126. doi:10.2166/aqua.2015.081Besharat, M., Tarinejad, R., Aalami, M. T., & Ramos, H. M. (2016). Study of a Compressed Air Vessel for Controlling the Pressure Surge in Water Networks: CFD and Experimental Analysis. Water Resources Management, 30(8), 2687-2702. doi:10.1007/s11269-016-1310-1Coronado-Hernández, O., Fuertes-Miquel, V., Besharat, M., & Ramos, H. (2017). Experimental and Numerical Analysis of a Water Emptying Pipeline Using Different Air Valves. Water, 9(2), 98. doi:10.3390/w9020098Coronado-Hernández, O. E., Fuertes-Miquel, V. S., Besharat, M., & Ramos, H. M. (2018). Subatmospheric pressure in a water draining pipeline with an air pocket. Urban Water Journal, 15(4), 346-352. doi:10.1080/1573062x.2018.1475578Edmunds, R. C. (1979). Air Binding in Pipes. Journal - American Water Works Association, 71(5), 272-277. doi:10.1002/j.1551-8833.1979.tb04348.xEscarameia, M. (2007). Investigating hydraulic removal of air from water pipelines. Proceedings of the Institution of Civil Engineers - Water Management, 160(1), 25-34. doi:10.1680/wama.2007.160.1.25Izquierdo, J., Fuertes, V. S., Cabrera, E., Iglesias, P. L., & Garcia-Serra, J. (1999). Pipeline start-up with entrapped air. Journal of Hydraulic Research, 37(5), 579-590. doi:10.1080/00221689909498518Kader, B. A. (1981). Temperature and concentration profiles in fully turbulent boundary layers. International Journal of Heat and Mass Transfer, 24(9), 1541-1544. doi:10.1016/0017-9310(81)90220-9Laanearu, J., Annus, I., Koppel, T., Bergant, A., Vučković, S., Hou, Q., … van’t Westende, J. M. C. (2012). Emptying of Large-Scale Pipeline by Pressurized Air. Journal of Hydraulic Engineering, 138(12), 1090-1100. doi:10.1061/(asce)hy.1943-7900.0000631Leon, A. S., Ghidaoui, M. S., Schmidt, A. R., & Garcia, M. H. (2010). A robust two-equation model for transient-mixed flows. Journal of Hydraulic Research, 48(1), 44-56. doi:10.1080/00221680903565911Martins, N. M. C., Delgado, J. N., Ramos, H. M., & Covas, D. I. C. (2017). Maximum transient pressures in a rapidly filling pipeline with entrapped air using a CFD model. Journal of Hydraulic Research, 55(4), 506-519. doi:10.1080/00221686.2016.1275046Martins, S. C., Ramos, H. M., & Almeida, A. B. (2015). Conceptual analogy for modelling entrapped air action in hydraulic systems. Journal of Hydraulic Research, 53(5), 678-686. doi:10.1080/00221686.2015.1077353Pozos, O., Gonzalez, C. A., Giesecke, J., Marx, W., & Rodal, E. A. (2010). Air entrapped in gravity pipeline systems. Journal of Hydraulic Research, 48(3), 338-347. doi:10.1080/00221686.2010.481839Ramezani, L., Karney, B., & Malekpour, A. (2016). Encouraging Effective Air Management in Water Pipelines: A Critical Review. Journal of Water Resources Planning and Management, 142(12), 04016055. doi:10.1061/(asce)wr.1943-5452.0000695Richards, R. T. (1962). Air Binding in Water Pipelines. Journal - American Water Works Association, 54(6), 719-730. doi:10.1002/j.1551-8833.1962.tb00883.xTijsseling, A. S., Hou, Q., Bozkuş, Z., & Laanearu, J. (2015). Improved One-Dimensional Models for Rapid Emptying and Filling of Pipelines. Journal of Pressure Vessel Technology, 138(3). doi:10.1115/1.4031508Triki, A. (2015). Water-hammer control in pressurized-pipe flow using an in-line polymeric short-section. Acta Mechanica, 227(3), 777-793. doi:10.1007/s00707-015-1493-1Vasconcelos, J. G., & Wright, S. J. (2008). Rapid Flow Startup in Filled Horizontal Pipelines. Journal of Hydraulic Engineering, 134(7), 984-992. doi:10.1061/(asce)0733-9429(2008)134:7(984)Wang, H., Zhou, L., Liu, D., Karney, B., Wang, P., Xia, L., … Xu, C. (2016). CFD Approach for Column Separation in Water Pipelines. Journal of Hydraulic Engineering, 142(10), 04016036. doi:10.1061/(asce)hy.1943-7900.0001171Zhou, F., Hicks, F. E., & Steffler, P. M. (2002). Transient Flow in a Rapidly Filling Horizontal Pipe Containing Trapped Air. Journal of Hydraulic Engineering, 128(6), 625-634. doi:10.1061/(asce)0733-9429(2002)128:6(625)Zhou, L., Liu, D., & Karney, B. (2013). Investigation of Hydraulic Transients of Two Entrapped Air Pockets in a Water Pipeline. Journal of Hydraulic Engineering, 139(9), 949-959. doi:10.1061/(asce)hy.1943-7900.0000750Zhou, L., Liu, D., & Ou, C. (2011). Simulation of Flow Transients in a Water Filling Pipe Containing Entrapped Air Pocket with VOF Model. Engineering Applications of Computational Fluid Mechanics, 5(1), 127-140. doi:10.1080/19942060.2011.11015357Zhou, L., Wang, H., Karney, B., Liu, D., Wang, P., & Guo, S. (2018). Dynamic Behavior of Entrapped Air Pocket in a Water Filling Pipeline. Journal of Hydraulic Engineering, 144(8), 04018045. doi:10.1061/(asce)hy.1943-7900.0001491Zukoski, E. E. (1966). Influence of viscosity, surface tension, and inclination angle on motion of long bubbles in closed tubes. Journal of Fluid Mechanics, 25(4), 821-837. doi:10.1017/s002211206600044

Experiments performed with bubbly flow in vertical pipes at different flow conditions covering the transition region: Simulation by coupling Eulerian, Lagrangian and 3D random walks models

[EN] Two phase flow experiments with different superficial velocities of gas and water were performed in a vertical upward isothermal cocurrent air-water flow column with conditions ranging from bubbly flow, with very low void fraction, to transition flow with some cap and slug bubbles and void fractions around 25%. The superficial velocities of the liquid and the gas phases were varied from 0.5 to 3 m/s and from 0 to 0.6 m/s, respectively. Also to check the effect of changing the surface tension on the previous experiments small amounts of 1-butanol were added to the water. These amounts range from 9 to 75 ppm and change the surface tension. This study is interesting because in real cases the surface tension of the water diminishes with temperature, and with this kind of experiments we can study indirectly the effect of changing the temperature on the void fraction distribution. The following axial and radial distributions were measured in all these experiments: void fraction, interfacial area concentration, interfacial velocity, Sauter mean diameter and turbulence intensity. The range of values of the gas superficial velocities in these experiments covered the range from bubbly flow to the transition to cap/slug flow. Also with transition flow conditions we distinguish two groups of bubbles in the experiments, the small spherical bubbles and the cap/slug bubbles. Special interest was devoted to the transition region from bubbly to cap/slug flow; the goal was to understand the physical phenomena that take place during this transition A set of numerical simulations of some of these experiments for bubbly flow conditions has been performed by coupling a Lagrangian code, that tracks the three dimensional motion of the individual bubbles in cylindrical coordinates inside the field of the carrier liquid, to an Eulerian model that computes the magnitudes of continuous phase and to a 3D random walk model that takes on account the fluctuation in the velocity field of the carrier fluid that are seen by the bubbles due to turbulence fluctuations. Also we have included in the model the deformation that suffers the bubble when it touches the wall and it is compressed by the forces that pushes it toward the wall, provoking that the bubble rebound like a ball.The authors of this paper are indebted to the National Plan of I+D by the support of the coordinated projects REMOD-ERN ENE2010-21368-C02-01/CON and ENE2010-21368-C02-02/CON to perform the experiments.Muñoz-Cobo, JL.; Chiva, S.; Ali Abdelaziz Essa, M.; Mendez, S. (2012). Experiments performed with bubbly flow in vertical pipes at different flow conditions covering the transition region: Simulation by coupling Eulerian, Lagrangian and 3D random walks models. Archives of Thermodynamics. 33(1):3-39. https://doi.org/10.2478/v10173-012-0001-4S33933

Random field sampling for a simplified model of melt-blowing considering turbulent velocity fluctuations

In melt-blowing very thin liquid fiber jets are spun due to high-velocity air streams. In literature there is a clear, unsolved discrepancy between the measured and computed jet attenuation. In this paper we will verify numerically that the turbulent velocity fluctuations causing a random aerodynamic drag on the fiber jets -- that has been neglected so far -- are the crucial effect to close this gap. For this purpose, we model the velocity fluctuations as vector Gaussian random fields on top of a k-epsilon turbulence description and develop an efficient sampling procedure. Taking advantage of the special covariance structure the effort of the sampling is linear in the discretization and makes the realization possible

A comparative study of turbulence models in a transient channel flow

Open Access funded by Engineering and Physical Sciences Research Council Under a Creative Commons license The authors would like to acknowledge the financial support provided by the Engineering and Physical Sciences Research Council (EPSRC) through the Grant No. EP/G068925/1.Peer reviewedPublisher PD

A qualitative exploration of men's experiences of an integrated exercise/CBT mental health promotion programme

This study investigated qualitatively the experiences of men who took part in a 10 week integrated exercise/psychosocial mental health promotion programme, "Back of the Net" (BTN). 15 participants who completed the BTN programme were recruited to participate in either a focus group discussion (N = 9) or individual interview (N = 6). A thematic analytic approach was employed to identify key themes in the data. Results indicated that participants felt that football was a positive means of engaging men in a mental health promotion program. Perceived benefits experienced included perceptions of mastery, social support, positive affect and changes in daily behaviour. The findings support the value of developing gender specific mental health interventions to both access and engage young men. © 2012 by the Men's Studies Press

Boundary-layer turbulence as a kangaroo process

A nonlocal mixing-length theory of turbulence transport by finite size eddies is developed by means of a novel evaluation of the Reynolds stress. The analysis involves the contruct of a sample path space and a stochastic closure hypothesis. The simplifying property of exhange (strong eddies) is satisfied by an analytical sampling rate model. A nonlinear scaling relation maps the path space onto the semi-infinite boundary layer. The underlying near-wall behavior of fluctuating velocities perfectly agrees with recent direct numerical simulations. The resulting integro-differential equation for the mixing of scalar densities represents fully developed boundary-layer turbulence as a nondiffusive (Kubo-Anderson or kangaroo) type of stochastic process. The model involves a scaling exponent (with → in the diffusion limit). For the (partly analytical) solution for the mean velocity profile, excellent agreement with the experimental data yields 0.58. © 1995 The American Physical Society

CFD study of fluid flow changes with erosion

For the first time, a three dimensional mesh deformation algorithm is used to assess fluid flow changes with erosion. The validation case chosen is the Jet Impingement Test, which was thoroughly analysed in previous works by Hattori et al. (Kenichi Sugiyama and Harada, 2008), Gnanavelu et al. in (Gnanavelu et al., 2009, 2011), Lopez et al. in (Lopez et al., 2015) and Mackenzie et al. in (Mackenzie et al., 2015). Nguyen et al. (2014) showed the formation of a new stagnation area when the wear scar is deep enough by performing a three-dimensional scan of the wear scar after 30 min of jet impingement test. However, in the work developed here, this stagnation area was obtained solely by computational means. The procedure consisted of applying an erosion model in order to obtain a deformed geometry, which, due to the changes in the flow pattern lead to the formation of a new stagnation area. The results as well as the wear scar were compared to the results by Nguyen et al. (2014) showing the same trend. OpenFOAM⃝R was the software chosen for the implementation of the deforming mesh algorithm as well as remeshing of the computational domain after deformation. Different techniques for mesh deformation and approaches to erosion modelling are discussed and a new methodology for erosion calculation including mesh deformation is developed. This new approach is independent of the erosion modelling approach, being applicable to both Eulerian and Lagrangian based equations for erosion calculation. Its different applications such as performance decay in machinery subjected to erosion as well as modelling of natural erosion processes are discussed here