SUMMARY: This work examines the dynamics of elliptical vortices in two-dimensional ideal fluid using an adaptively refined and remeshed vortex method. Four examples are considered comprising two compact vortices denoted by MMZ (smooth) and POLY (nonsmooth), and two noncompact vortices denoted by Gaussian and smooth Kirchhoff. The vortices all have the same maximum vorticity and 2:1 initial aspect ratio, but unlike the top-hat Kirchhoff vortex, they have continuous profiles with different degrees of regularity. In each case the phase portrait of the vortex in a corotating frame has two hyperbolic points, and the separatrix divides space into four regions, a center containing the vortex core, two crescent-shaped lobes next to the core, and the exterior. As the vortices start to rotate, two spiral filaments emerge and form a halo of low-amplitude vorticity around the core; this is attributed to vorticity advection along the unstable manifolds of the hyperbolic points. In the case of the Gaussian vortex the core rapidly axisymmetrizes, but later it starts to oscillate and two small lobes enclosing weak vortical fluid form within the halo; this is attributed to a resonance stemming from the core oscillation. In the case of the MMZ, POLY, and smooth Kirchhoff vortices, the core remains elliptical for longer time, and the filaments entrain weak vortical fluid into two large lobes which together with the core form a nonaxisymmetric tripole; afterwards, however, the lobes repeatedly detrain some of their fluid into the halo; the repeated detrainment is attributed to a heteroclinic tangle near the hyperbolic points. While prior work suggested that elliptical vortices could evolve to become either an axisymmetric monopole or a nonaxisymmetric tripole, the current results suggest they may oscillate between these states.

KEY WORDS: Euler equations, inviscid, elliptical vortex, filamentation, halo, phase plot

SUMMARY: The Lamb dipole is a steady translating structure in 2D ideal fluid flow with opposite-sign vorticity of compact support in a circular disk. Previous studies have shown that when viscosity is present, the resulting viscous Lamb dipole develops a head-tail structure in which the head expands in size, while a tail of low amplitude vorticity is left behind as the head moves forward; in addition, the maximum vorticity and total circulation on each side of the dipole decay in time. Here we examine these decay properties by comparing numerical solu- tions of the Navier–Stokes equation (NSE) and diffusion equation (DE) in the Reynolds number range 125 ! Re ! 1000 using the inviscid Lamb dipole as initial condition; this enables us to compare the combined effects of convection and diffusion in the NSE with the sole effect of diffusion in the DE. The results show that for a given Re, the vortex core size, shape, and maximum vorticity are nearly the same for the NSE and DE, indicating that convection has little effect on these properties. Nonetheless, compared to the DE, convection in the NSE inhibits circulation decay at low Re, while it enhances circulation decay at high Re, and the lateral separation of the vortex cores is a critical factor in this transition.

KEY WORDS:  Lamb dipole, Navier–Stokes equation, diffusion equation, vorticity decay, circulation decay

SUMMARY: Dust plumes originating from the Earth’s major arid and semi-arid areas can significantly affect the climate system and human health. Many existing methods have been developed to identify dust from non-dust pixels from a remote sensing point of view. However, these methods use empirical rules and therefore have difficulty detecting dust above or below the detectable thresholds. Supervised machine learning methods have also been applied to detect dust from satellite imagery, but these methods are limited especially when applying to areas outside the training data due to the inadequate amount of ground truth data. In this work, we proposed an automatic dust segmentation framework using semi-supervised machine learning, based on a collocated dataset using Visible Infrared Imaging Radiometer Suite (VIIRS) and Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO). The proposed method utilizes unsupervised machine learning for segmentation of VIIRS imagery, and leverages the guidance from the dust labels using the dust profile product of CALIPSO to determine the dust clusters as the final product. The dust clusters are determined based on the similarity of spectral signature from dust pixels along the CALIPSO tracks. Experiment results show that the accuracy of the proposed framework outperforms the traditional physical infrared method along CALIPSO tracks. In addition, the proposed method performs consistently over three different study areas, the North Atlantic Ocean, East Asia, and Northern Africa.

KEY WORDS:  dust detection, semi-supervised machine learning, multi-sensor remote sensing, image segmentation

SUMMARY: This paper presents a numerical study of vortex formation in the impulsively started viscous flow past an infinite wedge, for wedge angles ranging from 60∘ to 150∘. The Navier–Stokes equations are solved in the vorticity-streamfunction formulation using a time-splitting scheme. The vorticity convection is computed using a semi-Lagrangian method. The vorticity diffusion is computed using an implicit finite difference scheme, after mapping the physical domain conformally onto a rectangle. The results show details of the vorticity evolution and associated streamline and streakline patterns. In particular, a hierarchical formation of recirculating regions corresponding to alternating signs of vorticity is revealed. The appearance times of these vorticity regions of alternate signs, as well as their dependence on the wedge angles, are investigated. The scaling behaviour of the vortex centre trajectory and vorticity is reported, and solutions are compared with those available from laboratory experiments and the inviscid similarity theory.

KEY WORDS: boundary layer separation; coastal engineering; vortex dynamics

SUMMARY: Mucociliary clearance is the first line of defense in our airway. The purpose of this study is to identify and study key factors in the cilia motion that influence the transport ability of the mucociliary system. Using a rod- propel-fluid model, we examine the effects of cilia density, beating frequency, metachronal wavelength, and the extending height of the beating cilia. We first verify that asymmetry in the cilia motion is key to developing transport in the mucus flow. Next, two types of asymmetries between the effective and recovery strokes of the cilia motion are considered, the cilium beating velocity difference and the cilium height difference. We show that the cilium height difference is more efficient in driving the transport, and the more bend the cilium during the recovery stroke is, the more effective the transport would be. It is found that the transport capacity of the mucociliary system increases with cilia density and cilia beating frequency, but saturates above by a threshold value in both density and frequency. The metachronal wave that results from the phase lag among cilia does not contribute much to the mucus transport, which is consistent with the experimental observation of Sleigh (1989). We also test the effect of mucus viscosity, whose value is found to be inversely proportional to the transport ability. While multiple parts have to interplay and coordinate to allow for most effective mucociliary clearance, our findings from a simple model move us closer to understanding the effects of the cilia motion on the efficiency of this clearance system.  

KEY WORDS: Mucus, cilium, transport, propulsion, Navier-Stokes  

SUMMARY: Viscous flow past a finite flat plate accelerating in the direction normal to itself is studied numerically. The plate moves with nondimensional speed tp, where p = 0,1/2,1,2. The work focuses on resolving the flow at early to moderately large times, and determining the dependence on the acceleration parameter p. Three stages in the vortex evolution are identified and quantified. The first stage, referred to as the Rayleigh stage (Luchini & Tognaccini 2002), consists of a vortical boundary layer of roughly uniform thickness surrounding the plate and its tip, without any separating streamlines. This stage is present only for p > 0, for a time interval that scales like p^3, as p goes to 0. The second stage is one of self-similar growth. The vortex trajectory and circulation satisfy inviscid scaling laws, the boundary layer thickness satisfies viscous laws. The self-similar trajectory starts immediately after the Rayleigh stage ends, and lasts until the plate has moved a distance d = 0.5 to 1 times its length. Finally, in the third stage, the image vorticity due to the finite plate length becomes relevant and the flow departs from self-similar growth. The onset of an instability in the outer spiral vortex  turns is also observed, however, at least for the zero-thickness plate considered here, it is shown to be easily triggered numerically by  under-resolution. The present numerical results are compared with experimental results of Pullin & Perry (1980), and numerical results of  Koumoutsakos & Shiels (1996).

KEY WORDS: Starting vortex; power law; viscous flow; separation; Reynolds; streaklines; vortex center

Figure: Left column: Streaklines for flow past a wedge of angle β = 5 degrees, at t=1s, 1.6s, 2.8s, 4s and 5s, for p = 0.45 and  Re = 6621, obtained by Pullin and Perry (1980) from laboratory experiments (reproduced with permission from the Journal of Fluid Mechanics). Middle and Right columns: Numerical simulations of streaklines and streamlines, respectively, for flow past a flat plate at the same times, for p = 0.45 and Re = 6000.

SUMMARY: Viscous flow past a finite flat plate which is impulsively started in the direction normal to itself is studied numerically using a high order mixed finite-difference and semi- Lagrangian scheme. The goal is to resolve details of the vorticity generation, and to determine the dependence of the flow on time and Reynolds number. Vorticity contours, streaklines and streamlines are presented for a range of times t ∈ [0.0002, 5] and Reynolds numbers Re ∈ [250, 2000], nondimensionalized with respect to the driving velocity and the plate length. At early times, the starting vortex is small relative to the plate length and is expected to grow as if an external length scale were absent. We identify three different types of scaling behaviours consistent with this premise: At early times, (1) solutions with different values of Re are identical up to rescaling. (2) The solution for fixed Re satisfies a viscous similarity law in time, locally in space, as illustrated by the core vorticity maximum, the upstream boundary layer thickness, and the maximum speed, in three different regions of the flow. (3) The vortex core trajectory and the shed circulation satisfy inviscid scaling laws for several decades in time, and are consequently essentially Re-independent at these times. In addition, the computed induced drag and tangential forces are found to follow approximate scaling laws that define their dependence on time and Re.

KEY WORDS: viscous scaling for variable Re; viscous scaling in time for fixed Re;  inviscid scaling in time; Navier Stokes; vortex dynamics

Figure: Vorticity contours near the plate tip. (Left column): solution at a fixed time t = 0.005, for increasing values of Re. (Right column): solution for fixed Re = 500, at an increasing sequence of times.   

SUMMARY:  Damage in the form of cracks is predicted to assess  the susceptibility of a tunnel to failure due to a blast. The material-point method is used in conjunction with a decohesive failure model as the basis for the numerical simulations. The assumption of a cylindrical charge as the source for the blast allows the restriction of plane strain and two-dimensional analyses. In the simulation, a further restriction of a single pressure pulse is used as the source of stress waves that are reflected and refracted after reaching the free surface of the tunnel wall. Three critical zones of significant cracking in the vicinity of a tunnel are identified as potential contributors to tunnel failure.

KEY WORDS: blast wave simulation; material-point method; tunnel failure; decohesive model for rock failure