Linear instability of Poiseuille flows with highly non-ideal fluids

The objective of this work is to investigate linear modal and algebraic instability in Poiseuille flows with fluids close to their vapour-liquid critical point. Close to this critical point, the ideal gas assumption does not hold and large non-ideal fluid behaviours occur. As a representative non-ideal fluid, we consider supercritical carbon dioxide (CO$_2$) at pressure of 80 bar, which is above its critical pressure of 73.9 bar. The Poiseuille flow is characterized by the Reynolds number ($Re=\rho_{w}^{*}u_{r}^{*}h^{*}/\mu_{w}^{*}$), the product of Prandtl ($Pr=\mu_{w}^{*}C_{pw}^{*}/\kappa_{w}^{*}$) and Eckert number ($Ec=u_{r}^{*2}/C_{pw}^{*}T_{w}^{*}$), and the wall temperature that in addition to pressure determines the thermodynamic reference condition. For low Eckert numbers, the flow is essentially isothermal and no difference with the well-known stability behaviour of incompressible flows is observed. However, if the Eckert number increases, the viscous heating causes gradients of thermodynamic and transport properties, and non-ideal gas effects become significant. Three regimes of the laminar base flow can be considered, subcritical (temperature in the channel is entirely below its pseudo-critical value), transcritical, and supercritical temperature regime. If compared to the linear stability of an ideal gas Poiseuille flow, we show that the base flow is more unstable in the subcritical regime, inviscid unstable in the transcritical regime, while significantly more stable in the supercritical regime. Following the corresponding states principle, we expect that qualitatively similar results will be obtained for other fluids at equivalent thermodynamic states.Comment: 34 pages, 22 figure

Inference of Markovian Properties of Molecular Sequences from NGS Data and Applications to Comparative Genomics

Next Generation Sequencing (NGS) technologies generate large amounts of short read data for many different organisms. The fact that NGS reads are generally short makes it challenging to assemble the reads and reconstruct the original genome sequence. For clustering genomes using such NGS data, word-count based alignment-free sequence comparison is a promising approach, but for this approach, the underlying expected word counts are essential. A plausible model for this underlying distribution of word counts is given through modelling the DNA sequence as a Markov chain (MC). For single long sequences, efficient statistics are available to estimate the order of MCs and the transition probability matrix for the sequences. As NGS data do not provide a single long sequence, inference methods on Markovian properties of sequences based on single long sequences cannot be directly used for NGS short read data. Here we derive a normal approximation for such word counts. We also show that the traditional Chi-square statistic has an approximate gamma distribution, using the Lander-Waterman model for physical mapping. We propose several methods to estimate the order of the MC based on NGS reads and evaluate them using simulations. We illustrate the applications of our results by clustering genomic sequences of several vertebrate and tree species based on NGS reads using alignment-free sequence dissimilarity measures. We find that the estimated order of the MC has a considerable effect on the clustering results, and that the clustering results that use a MC of the estimated order give a plausible clustering of the species.Comment: accepted by RECOMB-SEQ 201

Image-based flow decomposition using empirical wavelet transform

We propose an image-based flow decomposition developed from the two-dimensional (2D) tensor empirical wavelet transform (EWT) (Gilles 2013). The idea is to decompose the instantaneous flow data, or its visualisation, adaptively according to the averaged Fourier supports for the identification of spatially localised structures. The resulting EWT modes stand for the decomposed flows, and each accounts for part of the spectrum, illustrating fluid physics with different scales superimposed in the original flow. With the proposed method, decomposition of an instantaneous 3D flow becomes feasible without resorting to its time series. Examples first focus on the interaction between a jet plume and 2D wake, where only experimental visualisations are available. The proposed method is capable of separating the jet/wake flows and their instabilities. Then the decomposition is applied to an early stage boundary layer transition, where direct numerical simulations provided a full data-set. The tested inputs are the 3D flow data and its visualisation using streamwise velocity & λ 2 vortex identification criterion. With both types of inputs, EWT modes robustly extract the streamwise-elongated streaks, multiple secondary instabilities and helical vortex filaments. Results from 2D stability analysis justify the EWT modes that represent the streak instabilities. In contrast to proper orthogonal decomposition or dynamic modal decomposition that extract spatial modes according to energy or frequency, EWT provides a new strategy as to decompose an instantaneous flow from its spatial scales