Effects of Turbulent Flows and Superdiffusion on Reaction-Dffusion Systems

The basic question underlying the work presented in this thesis concerns the self-organization and pattern formation in inanimate media when a fluid flow is present. This thesis studies the active and passive transport in turbulent and chaotic fluid flows. Thereby the focus is mainly of experimental nature. Especial interest is placed on the experimental observation and description of new patterns emerging, when active media is subjected to a turbulent fluid flow. In particular the effect of intense mixing as can be achieved by highly chaotic or turbulent fluid flows is to be uncovered. The first goal is to characterize and explain the phenomenon of a global reactive wave in a similar experimental realization observed by Fernandez Garca et al. in 2008. One step towards this goal is the measurement of the mixing caused by the Faraday experiment. This experiment consists in the vertical forcing of a container filled with liquid. Once the velocity field had been characterized we aimed for a definition of suitable analysis methods in order to study the transport of active media on different time and length-scales. Especially for intermediate range Damkoehler numbers, i.e. where the ratio of the timescale of the fluid flow and those of the reaction timescale is similar has not been studied in an experimental system with an excitable chemical reaction before. The analysis tools applied to this experimental model system might also partly be valid for the characterization of other reaction-diffusion-advection processes as found in many natural and men-made systems, such as plankton blooms in the ocean, chemicals in the atmosphere or bioreactors. The understanding of the role of the interplay of the typical timescales of the reaction and advection processes are to be discovered. A simple model accounting partly for some of the observed characteristics, such as the local scale-free transport, is formulated. The interplay of diffusive and advective processes is further studied in detail for a numerical model flow imitating the gulf-stream current. The details of this interplay can also lead to superdiffusion and scale-free transport

How coherent structures dominate the residence time in a bubble wake: an experimental example

Mixing timescales and residence times in reactive multiphase flows can be essential for product selectivity. For instance when a gas species is consumed e.g. by a competitive consecutive reaction with moderate reaction kinetics where reaction timescales are comparable to relevant mixing timescales. To point out the importance of the details of the fluid flow, we analyze experimental velocity data from a Taylor bubble wake by means of Lagrangian methods. By adjusting the channel diameter in which the Taylor bubble rises, and thus the rise velocity, we obtain three different wake regimes. Remarkably the normalized residence times of passive particles advected in the wake velocity field show a peak for intermediate rise velocities. This fact seems unintuitive at first glance because one expects a faster removal of passive tracers for a faster overall flow rate. However, the details of the flow topology analyzed using Finite Time Lyapunov Exponent (FTLE) fields and Lagrangian Coherent Structures (LCS) reveal the existence of a very coherent vortical pattern in the bubble wake which explains the long residence times. The increased residence times within the vortical structure and the close bubble interface acting as a constant gas species source could enhance side product generation of a hypothetical competitive consecutive reaction, where the first reaction with the gas species forms the desired product and the second the side product.Comment: 13 pages, 7 figures, 1 tabl

How does filtering change the perspective on the scale-energetics of the near-wall cycle?

We investigate the flux of kinetic energy across length scales in a turbulent pipe flow. We apply explicit spatial filtering of DNS data and assess the effect of different filter kernels (Fourier, Gauss, box) on the local structure of the inter-scale energy flux ($\Pi$) and its statistics. Qualitatively, the mean energy flux at each wall-normal distance is robust with respect to the filter kernel, whereas there are significant differences in the estimated intensity and distribution of localised $\Pi$ events. We find conflicting correlations between typical flow structures in the buffer layer (streaks, vortices and different $Q$ events) and regions of forward/backward transfer in the instantaneous $\Pi$ field. In particular, cross-correlations are highly upstream-downstream symmetric for the Fourier kernel, but asymmetric for the Gauss and box kernel. We show that for the Gauss and box kernel, $\Pi$ events preferably sit on the inclined meander at the borders of streaks where strong shear layers occur, whereas they appear centred on top of the streaks for the Fourier kernel. Moreover, using the Fourier kernel we reveal a direct coincidence of backward scatter and fluid transport away from the wall ($Q_{1}$), which is absent for the Gauss and the box kernel. However, all kernels equally predict backward scatter directly downstream of $Q_{1}$ events. Our findings expand the common understanding of the wall cycle and might impact modelling and control strategies. Altogether, our results suggest that interpretations of the inter-scale energy flux relying on Fourier filters should be taken with caution, because Fourier filters act globally in physical space, whereas $\Pi$ events are strongly spatially localised. Our Python post-processing tool eFlux for scale separation and flux computations in pipe flows is freely available and can be easily adapted to other flow geometries.Comment: 22 pages, 9 figue

lcs4Foam -- An OpenFOAM Function Object to Compute Lagrangian Coherent Structures

To facilitate the understanding and to quantitatively assess the material transport in fluids, a modern characterisation method has emerged in fluid dynamics in the last decades footed in dynamical systems theory. It allows to examine the most influential material lines which are called Lagrangian Coherent Structures (LCS) and order the material transport into dynamically distinct regions at large scales which resist diffusion or mixing. LCS reveal the robust skeleton of material surfaces and are essential to assess material transport in time-dependent flows quantitatively. Candidates of LCS can be estimated and visualised from finite-time stretching and folding fields by calculating the Finite-Time Lyapunov Exponents (FTLE). In this contribution, we provide an OpenFOAM function object to compute FTLE during CFD simulation. This enables the OpenFOAM community to assess the geometry of the material transport in any flow quantitatively on-the-fly using principally any OpenFOAM flow solver

Outcome Prediction for Estrogen Receptor-Positive Breast Cancer Based on Postneoadjuvant Endocrine Therapy Tumor Characteristics

Background Understanding how tumor response is related to relapse risk would help clinicians make decisions about additional treatment options for patients who have received neoadjuvant endocrine treatment for estrogen receptor-positive (ER+) breast cancer. Methods Tumors from 228 postmenopausal women with confirmed ER+ stage 2 and 3 breast cancers in the P024 neoadjuvant endocrine therapy trial, which compared letrozole and tamoxifen for 4 months before surgery, were analyzed for posttreatment ER status, Ki67 proliferation index, histological grade, pathological tumor size, node status, and treatment response. Cox proportional hazards were used to identify factors associated with relapse-free survival (RFS) and breast cancer-specific survival (BCSS) in 158 women. A preoperative endocrine prognostic index (PEPI) for RFS was developed from these data and validated in an independent study of 203 postmenopausal women in the IMPACT trial, which compared treatment with anastrozole, tamoxifen, or the combination 3 months before surgery. Statistical tests were two-sided. Results Median follow-up in P024 was 61.2 months. Patients with confirmed baseline ER+ clinical stage 2 and 3 tumors that were downstaged to stage 1 or 0 at surgery had 100% RFS (compared with higher stages, P < .001). Multivariable testing of posttreatment tumor characteristics revealed that pathological tumor size, node status, Ki67 level, and ER status were independently associated with both RFS and BCSS. The PEPI model based on these factors predicted RFS in the IMPACT trial (P = .002). Conclusions Breast cancer patients with pathological stage 1 or 0 disease after neoadjuvant endocrine therapy and a low-risk biomarker profile in the surgical specimen (PEPI score 0) have an extremely low risk of relapse and are therefore unlikely to benefit from adjuvant chemotherap

Outcome prediction for estrogen receptor-positive breast cancer based on postneoadjuvant endocrine therapy tumor characteristics

BACKGROUND: Understanding how tumor response is related to relapse risk would help clinicians make decisions about additional treatment options for patients who have received neoadjuvant endocrine treatment for estrogen receptor–positive (ER+) breast cancer. METHODS: Tumors from 228 postmenopausal women with confirmed ER+ stage 2 and 3 breast cancers in the P024 neoadjuvant endocrine therapy trial, which compared letrozole and tamoxifen for 4 months before surgery, were analyzed for posttreatment ER status, Ki67 proliferation index, histological grade, pathological tumor size, node status, and treatment response. Cox proportional hazards were used to identify factors associated with relapse-free survival (RFS) and breast cancer–specific survival (BCSS) in 158 women. A preoperative endocrine prognostic index (PEPI) for RFS was developed from these data and validated in an independent study of 203 postmenopausal women in the IMPACT trial, which compared treatment with anastrozole, tamoxifen, or the combination 3 months before surgery. Statistical tests were two-sided. RESULTS: Median follow-up in P024 was 61.2 months. Patients with confirmed baseline ER+ clinical stage 2 and 3 tumors that were downstaged to stage 1 or 0 at surgery had 100% RFS (compared with higher stages, P < .001). Multivariable testing of posttreatment tumor characteristics revealed that pathological tumor size, node status, Ki67 level, and ER status were independently associated with both RFS and BCSS. The PEPI model based on these factors predicted RFS in the IMPACT trial (P = .002). CONCLUSIONS: Breast cancer patients with pathological stage 1 or 0 disease after neoadjuvant endocrine therapy and a low-risk biomarker profile in the surgical specimen (PEPI score 0) have an extremely low risk of relapse and are therefore unlikely to benefit from adjuvant chemotherapy

Eddy-induced particle dispersion in the near-surface North Atlantic

Author Posting. © American Meteorological Society, 2012. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 42 (2012): 2206–2228, doi:10.1175/JPO-D-11-0191.1.This study investigates the anisotropic properties of the eddy-induced material transport in the near-surface North Atlantic from two independent datasets, one simulated from the sea surface height altimetry and one derived from real-ocean surface drifters, and systematically examines the interactions between the mean- and eddy-induced material transport in the region. The Lagrangian particle dispersion, which is widely used to characterize the eddy-induced tracer fluxes, is quantified by constructing the “spreading ellipses.” The analysis consistently demonstrates that this dispersion is spatially inhomogeneous and strongly anisotropic. The spreading is larger and more anisotropic in the subtropical than in the subpolar gyre, and the largest ellipses occur in the Gulf Stream vicinity. Even at times longer than half a year, the spreading exhibits significant nondiffusive behavior in some parts of the domain. The eddies in this study are defined as deviations from the long-term time-mean. The contributions from the climatological annual cycle, interannual, and subannual (shorter than one year) variability are investigated, and the latter is shown to have the strongest effect on the anisotropy of particle spreading. The influence of the mean advection on the eddy-induced particle spreading is investigated using the “eddy-following-full-trajectories” technique and is found to be significant. The role of the Ekman advection is, however, secondary. The pronounced anisotropy of particle dispersion is expected to have important implications for distributing oceanic tracers, and for parameterizing eddy-induced tracer transfer in non-eddy-resolving models.IR was supported by Grant NSF-OCE-0725796. IK would like to acknowledge support by the National Science foundation Grant OCE-0842834.2013-06-0