Transient linear stability of pulsating Poiseuille flow using optimally time-dependent modes

Time-dependent flows are notoriously challenging for classical linear stability analysis. Most progress in understanding the linear stability of these flows has been made for time-periodic flows via Floquet theory focusing on time-asymptotic stability. However, little attention has been given to the transient intracyclic linear stability of periodic flows since no general tools exist for its analysis. In this work, we explore the potential of using the recent framework of the optimally time-dependent (OTD) modes (Babaee & Sapsis, Proc. R. Soc. Lond. A, vol. 472, 2016, 20150779) to extract information about both the transient and the time-asymptotic linear stability of pulsating Poiseuille flow. The analysis of the instantaneous OTD modes in the limit cycle leads to the identification of the dominant instability mechanism of pulsating Poiseuille flow by comparing them with the spectrum and the eigenmodes of the Orr–Sommerfeld operator. In accordance with evidence from recent direct numerical simulations, it is found that structures akin to Tollmien–Schlichting waves are the dominant feature over a large range of pulsation amplitudes and frequencies but that for low pulsation frequencies these modes disappear during the damping phase of the pulsation cycle as the pulsation amplitude is increased beyond a threshold value. The maximum achievable non-normal growth rate during the limit cycle was found to be nearly identical to that in plane Poiseuille flow. The existence of subharmonic perturbation cycles compared with the base flow pulsation is documented for the first time in pulsating Poiseuille flow.

Modeling of Fluid Flow in a Flexible Vessel with Elastic Walls

We exploit a two-dimensional model (Ghosh et al. in Q J Mech Appl Math 71(3):349–367, 2018; Kozlov and Nazarov in Dokl Phys 56(11):560–566, 2011, J Math Sci 207(2):249–269, 2015) describing the elastic behavior of the wall of a flexible blood vessel which takes interaction with surrounding muscle tissue and the 3D fluid flow into account. We study time periodic flows in an infinite cylinder with such intricate boundary conditions. The main result is that solutions of this problem do not depend on the period and they are nothing else but the time independent Poiseuille flow. Similar solutions of the Stokes equations for the rigid wall (the no-slip boundary condition) depend on the period and their profile depends on time.

Investigation on Energy Distribution in Steady and Unsteady Flow Instabilities through a Bend Square Pipe

Fluid flow analysis through a bend pipe is extensively conducted in practical and cell separation operations. It is observed that flow behaviors in the bend pipe are influenced by some parameters such as curvature, aspect ratio, etc. As a result, various phenomena, steady solution branches, unsteady solutions, energy transfer are changed. In this paper, the acts of flows are performed together for fixed curvature, δ = 0.2, and Prandtl number, Pr = 7.0 (water). Here, for a wide variety of Dean numbers (100 ≤ Dn ≤ 1000) and three fixed Grashof numbers, Gr = 100, 500, and 1000; time-independent solutions with linear stabilities are investigated first where only the first steady branch exhibits linear stability out of two steady solution branches obtained. Then, different flow transitions between the required range of Dean numbers (Dn) and several Grashof numbers (Gr) are investigated using time-dependent solutions. Power spectrum density (PSD) is further revealed in order to gain a deeper understanding of periodic and multi-periodic flows. Flow velocity contours including axial flow (AF) and secondary flow (SF) and their temperature profiles (TP) are also exposed. The SFs reveal that two- to four-vortex flows are produced due to the turning of steady branch and the flow instabilities. Furthermore, the energy transfer between the cooled and heated sidewalls of the pipe is calculated. Finally, a link between centrifugal and body force with the energy transfer has been shown in this research which reveals that the fluid has merged that certainly rises the overall energy transfer.

A Period-Aware Routing Method for IEEE 802.1Qbv TSN Networks

The IEEE 802.1Qbv standard provides deterministic delay and low jitter guarantee for time-critical communication using a precomputed cyclic transmission schedule. Computing such transmission schedule requires routing the flows first, which significantly affects the quality of the schedule. So far off-the-shelf algorithms like load-balanced routing, which minimize the maximum scheduled traffic load (MSTL), have been used to accommodate more time-triggered traffic. However, they do not consider that the bandwidth utilization of periodic flows is decentralized and their criteria for bottleneck of scheduling are imprecise. In this paper, we firstly explore the combinability among different periods of flows, which can measure their ability to share bandwidth without conflict. Then, we propose a novel period-aware routing algorithm to reduce the scheduling bottleneck, thus more flows can be accommodated. The experiment results show that the success rate of scheduling is significantly improved compared to shortest path routing and load balanced routing.

Instability of surface quasigeostrophic spatially periodic flows

<p>The surface quasigeostrophic (SQG) model is developed to describe the dynamics of flows with zero potential vorticity in the presence of one or two horizontal boundaries (Earth surface and tropopause). Within the framework of this model, the problems of linear and nonlinear stability of zonal spatially periodic flows are considered. To study the linear stability of flows with one boundary, two approaches are used. In the first approach, the solution is sought by decomposing into a trigonometric series, and the growth rate of the perturbations is found from the characteristic equation containing an infinite continued fraction. In the second approach, few-mode Galerkin approximations of the solution are constructed. It is shown that both approaches lead to the same dependence of the growth increment on the wavenumber of perturbations. The existence of instability with a preferred horizontal scale on the order of the wavelength of the main flow follows from this dependence. A similar result is obtained within the framework of the SQG model with two horizontal boundaries. The Galerkin method with three basis trigonometric functions is also used to study the nonlinear dynamics of perturbations, described by a system of three nonlinear differential equations similar to that describing the motion of a symmetric top in classical mechanics. An analysis of the solutions of this system shows that the exponential growth of disturbances at the linear stage is replaced by a stage of stable nonlinear oscillations (vacillations). The results of numerical integration of full nonlinear SQG equations confirm this analysis.</p><p>The work was supported by the Russian Foundation for Basic Research (Project 18-05-00414) and the Russian Science Foundation (Project 19-17-00248).</p>

Spectroscopic detection of coronal plasma flows in loops undergoing thermal non-equilibrium cycles

Context. Long-period intensity pulsations were recently detected in the EUV emission of coronal loops and attributed to cycles of plasma evaporation and condensation driven by thermal non-equilibrium (TNE). Numerical simulations that reproduce this phenomenon also predict the formation of periodic flows of plasma at coronal temperatures along some of the pulsating loops. Aims. We aim to detect these predicted flows of coronal-temperature plasma in pulsating loops. Methods. We used time series of spatially resolved spectra from the EUV imaging spectrometer (EIS) onboard Hinode and tracked the evolution of the Doppler velocity in loops in which intensity pulsations have previously been detected in images of SDO/AIA. Results. We measured signatures of flows that are compatible with the simulations but only for a fraction of the observed events. We demonstrate that this low detection rate can be explained by line of sight ambiguities combined with instrumental limitations, such as low signal-to-noise ratio or insufficient cadence.