Recovery of radial-axial velocity in axisymmetric swirling flows of a viscous incompressible fluid in the Lagrangian consideration of vorticity evolution

Swirling laminar axisymmetric flows of viscous incompressible fluids in a potential field of body forces are considered. The study of flows is carried out in a cylindrical coordinate system. In the flows, the regions in which the axial derivative of the circumferential velocity cannot take on zero value in some open neighborhood (essentially swirling flows) and the regions in which this derivative is equal to zero (the region with layered swirl) are considered separately. It is shown that a well-known method (the method of viscous vortex domains) developed for non-swirling flows can be used for regions with layered swirling. For substantially swirling flows, a formula is obtained for calculating the radial-axial velocity of an imaginary fluid through the circumferential vorticity component, the circumferential circulation of a real fluid, and the partial derivatives of these functions. The particles of this imaginary fluid “transfer” vortex tubes of the radial-axial vorticity component while maintaining the intensity of these tubes, and also “transfer” the circumferential circulation and the product of the circular vorticity component by some function of the distance to the axis of symmetry. A non-integral method for reconstructing the velocity field from the vorticity field is proposed. It is reduced to solving a system of linear algebraic equations in two variables. The obtained result is proposed to be used to extend the method of viscous vortex domains to swirling axisymmetric flows.

A Gas-Particle Analogue to the Richtmyer-Meshkov Instability: Comparing Multiphase Simulations to Shock Tube Experiments

A research area emerging in the multiphase flow community is the study of Shock-Driven Multi-phase Instability (SDMI), a gas-particle analog of the traditional fluid-fluid Richtmyer-Meshkov instability (RMI). In this work, we study the interaction of planar air shocks with corrugated glass particle curtains through the use of numerical simulations with an Eulerian-Lagrangian approach. This approach has simulations track computational particle trajectories in a Lagrangian framework while evolving the surrounding fluid flow on a fixed Eulerian mesh. In addition to observing the evolution of the perturbed particle curtain in the simulations, we also observe the evolution of the curtain of gas which is initially trapped inside of the particle curtain as the simulation progresses. The objective of this study is to compare the evolving simulation curtains (both particle and gas) to a comparable set of shock tube experiments performed to analyze traditional fluid RMI evolution. The simulations are set to match the experimental shock Mach numbers and perturbation wavelengths (3.6 and 7.2 mm) while matching the Atwood number of the experiments to the multiphase Atwood number of the simulations. However, multiple particle diameters are tested in the simulations to get a view into the impact of the particle diameter on the evolution of the particle curtain. This simulation setup allows for a one-to-one comparison between RMI and SDMI under comparable conditions while also allowing for a separate study into the validity of the use of both the multiphase Atwood number and the fluid-only Atwood number to compare the single-phase and multiphase instabilities. In particular, we show that this validity is at least partly dependent on the diameters of the particles in the curtain (thus, dependent on the Stokes number of the flow). We also analyze the effect of the multiphase terms of the vorticity evolution equation on the vorticity deposition in SDMI. Also discussed is the effect of the particle diameter on the multiphase generation terms as well as in the baroclinic vorticity generation term in SDMI as the shock passes over the curtain.

Numerical study of viscous starting flow past wedges

This paper presents a numerical study of vortex formation in the impulsively started viscous flow past an infinite wedge, for wedge angles ranging from $60^{\circ }$ to $150^{\circ }$. 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.

Numerical Simulation of Air Vortex Interaction With Porous Screen

In this paper, numerical analysis of a two-dimensional vortex ring impinging through porous screen surface is investigated. The vortex ring is generated by a piston-cylinder assembly. The objective is to study the flow behavior of vortex ring when passing through porous screen and especially to obtain the values which are difficult to achieve in experiment method, such as kinetic energy and vorticity. A variety of parameters are set to be control groups, including porosity of porous screen (ϕ = 0.3, 0.6 and 0.8), Reynolds number of vortex ring (Re = 700 – 3000), piston diameter (D = 20mm, 34mm and 50mm) and gap between piston and porous screen (L = 50mm, 100mm and 150mm). The following results are acquired: (1) Porosity plays an important role on the vortex ring structure and flow behavior, (2) Reynolds number have notable influence on the vorticity evolution of vortex ring in the situation of low porosity, (3) Larger piston dimension results in slower progress of vortex ring transmission and sharper reduction of vortex ring kinetic energy, and (4) The gap length has significant effect on kinetic energy of vortex ring only in the situation of low porosity.

Topological effects on vorticity evolution in confined stratified fluids

For a stratified incompressible Euler fluid under gravity confined by rigid boundaries, sources of vorticity are classified with the aim of isolating those which are sensitive to the topological configurations of density isopycnals, for both layered and continuous density variations. The simplest case of a two-layer fluid is studied first. This shows explicitly that topological sources of vorticity are present whenever the interface intersects horizontal boundaries. Accordingly, the topological separation of the fluid domain due to the interface–boundary intersections can contribute additional terms to the vorticity balance equation. This phenomenon is reminiscent of Klein’s ‘Kaffeelöffel’ thought-experiment for a homogeneous fluid (Klein, Z. Math. Phys., vol. 59, 1910, pp. 259–262), and it is essentially independent of the vorticity generation induced by the baroclinic term in the bulk of the fluid. In fact, the two-layer case is generalized to show that for the continuously stratified case topological vorticity sources are generically present whenever density varies along horizontal boundaries. The topological sources are expressed explicitly in terms of local contour integrals of the pressure along the intersection curves of isopycnals with domain boundaries, and their effects on vorticity evolution are encoded by an appropriate vector, termed here the ‘topological vorticity’.

Vorticity Evolution Leading to Tornadogenesis and Tornadogenesis Failure in Simulated Supercells

A three-dimensional idealized cloud model was used to study the storm-scale differences between simulated supercells that produce tornado-like vortices and those that do not. Each simulation was initialized with a different Rapid Update Cycle, version 2 (RUC-2), sounding that was associated with tornadic and nontornadic supercells in nature. The focus is an analysis of vorticity along backward-integrated trajectories leading up to tornadogenesis (19 simulations) and tornadogenesis failure (14 simulations). In so doing, the differences between the nontornadic and tornadic cases can be explored in relation to their associated environmental sounding. Backward-integrated trajectories seeded in the near-surface circulation indicate that the largest differences in vertical vorticity production between the tornadic and nontornadic simulations occur in parcels that descend to the surface from aloft (i.e., descending). Thus, the results from this study support the hypothesis that descending air in the rear of the storm is crucial to tornadogenesis. In the tornadic simulations, the descending parcels experience more negative vertical vorticity production during descent and larger tilting of horizontal vorticity into positive vertical vorticity after reaching the surface, owing to stronger horizontal gradients of vertical velocity. The larger vertical velocities experienced by the trajectories just prior to tornadogenesis in the tornadic simulations are associated with environmental soundings of larger CAPE, smaller convective inhibition (CIN), and larger 0–1-km storm-relative environmental helicity. Furthermore, in contrast with what might be expected from previous works, trajectories entering the incipient tornadic circulations are more negatively buoyant than those entering the nontornadic circulations.

Tracking winter extra-tropical cyclones based on their relative vorticity evolution and sensitivity to prior data filtering (cycloTRACK v1.0)

In this study we present a new cyclone identification and tracking algorithm. Identification is based on a recognition pattern of enclosed contours of 850 hPa filtered relative vorticity values, while tracking is based on the minimization of a cost function. In particular, for each tracked cyclone our algorithm builds all possible tracks and finally chooses the one which presents the least differences of relative vorticity between consecutive track points. In parallel, for each track point the algorithm provides a cyclone area within which different physical diagnostics are calculated (such as pressure and wind speed). The area size is a function of the cyclone relative vorticity. To validate our approach we apply the algorithm on the Northern Hemisphere for the winters of 1989–2009. Three integrations of the algorithm were performed, each by using different filtering strengths. Using the three integrations, we assess the algorithm sensitivity to prior filtering the relative vorticity field. We show that filtering the input relative vorticity fields has an impact only on the weak cyclones, while in their majority the strong cyclones are independently detected and tracked.