Generation of Localised Vertical Streams in Unstable Stratified Atmosphere

A new model of axially symmetric concentrated vortex generation was developed herein. In this work, the solution of a nonlinear equation for internal gravity waves in an unstable stratified atmosphere was obtained and analysed in the framework of ideal hydrodynamics. The related expressions for the velocities in the inner and outer regions of the vortex were described by Bessel functions and modified zeroth-order Bessel functions. The proposed new nonlinear analytical model allows the study of the structure and dynamics of vortices in the radial region. The formation of jets (i.e., structures elongated in the vertical direction with finite components of the poloidal (radial and vertical) velocities that grow exponentially in time in an unstable stratified atmosphere) was also analysed. The characteristic growth time was determined by the inverse growth rate of instability. It is shown that a seed vertical vorticity component may be responsible for the formation of vortices with a finite azimuthal velocity.

Experimental study of the flows in a non-axisymmetric ellipsoid under precession

Precession driven flows are of great interest for both, industrial and geophysical applications. While cylindrical, spherical and spheroidal geometries have been investigated in great detail, the numerically and theoretically more challenging case of a non-axisymmetric cavity has received less attention. We report experimental results on the flows in a precessing triaxial ellipsoid, with a focus on the base flow of uniform vorticity, which we show to be in good agreement with existing theoretical models. As predicted, the uniform vorticity component exhibits two branches of solutions leading to a hysteresis cycle as a function of the Poincaré number. The first branch is observed at low forcing and characterized by large amplitude of the total fluid rotation and a moderate tilt angle of the fluid rotation axis. In contrast, the second branch displays only a moderate fluid rotation and a large tilt angle of the fluid rotation axis, which tends to align with the precession axis. In addition, we observe the occurrence of parametric instabilities early in the first branch, which saturate in the second branch, where we observe the same order of the kinetic energy in the base flow and instabilities.

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 regularity criterion for liquid crystal flows in terms of the component of velocity and the horizontal derivative components of orientation field

<abstract><p>In this paper, we establish a regularity criterion for the 3D nematic liquid crystal flows. More precisely, we prove that the local smooth solution $ (u, d) $ is regular provided that velocity component $ u_{3} $, vorticity component $ \omega_{3} $ and the horizontal derivative components of the orientation field $ \nabla_{h}d $ satisfy</p> <p><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{eqnarray*} \int_{0}^{T}|| u_{3}||_{L^{p}}^{\frac{2p}{p-3}}+||\omega_{3}||_{L^{q}}^{\frac{2q}{2q-3}}+||\nabla_{h} d||_{L^{a}}^{\frac{2a}{a-3}} \mbox{d} t&lt;\infty,\nonumber \\ with\ \ 3&lt; p\leq\infty,\ \frac{3}{2}&lt; q\leq\infty,\ 3&lt; a\leq\infty. \end{eqnarray*} $\end{document} </tex-math></disp-formula></p> </abstract>

Particle image velocimetry measurement of turbulent wake past circular cylinder at Reynolds numbers from 2.5·103 to 1.5·104

A canonical case of air flow past a circular cylinder is studied by using Particle Image Velocimetry technique. This contribution focus to the ensemble statistics (first and second moment) of the stream-wise and transverse velocity component as well as to the in-plane vorticity component. Although the range of explored Reynolds numbers is narrow, we observe a significant shortening of recirculation bubble within this range.

Resonant absorption: Transformation of compressive motions into vortical motions

This paper investigates the changes in spatial properties when magnetohydrodynamic (MHD) waves undergo resonant damping in the Alfvén continuum. The analysis is carried out for a 1D cylindrical pressure-less plasma with a straight magnetic field. The effect of the damping on the spatial wave variables is determined by using complex frequencies that arise as a result of the resonant damping. Compression and vorticity are used to characterise the spatial evolution of the MHD wave. The most striking result is the huge spatial variation in the vorticity component parallel to the magnetic field. Parallel vorticity vanishes in the uniform part of the equilibrium. However, when the MHD wave moves into the non-uniform part, parallel vorticity explodes to values that are orders of magnitude higher than those attained by the transverse components in planes normal to the straight magnetic field. In the non-uniform part of the equilibrium plasma, the MHD wave is controlled by parallel vorticity and resembles an Alfvén wave, with the unfamiliar property that it has pressure variations even in the linear regime.

Interactions between vortical, acoustic and thermal components during hypersonic transition

Discrete unstable modes of hypersonic laminar boundary layers, obtained from an eigenvalue analysis, provide insight into key transition scenarios. The character of such modes near the leading edge is often identified with the corresponding asymptotic free-stream behaviour of acoustic, vortical or entropic (thermal) content, which we designate fluid-thermodynamic (FT) components. In downstream regions, however, this direct one-to-one correspondence between discrete modes and FT components does not hold, since FT components interact in well-defined ways with the basic state and with each other (even under linear scenarios). In the present work, we perform an FT decomposition of discrete modes using momentum potential theory, to yield a physics-based analysis that complements linear stability theory in the linear regime, and seamlessly extends to the nonlinear domain where direct numerical simulations are appropriate. Linear and nonlinear saturated disturbance effects, different forcing types and wall thermal conditions are considered, with emphasis on phenomena occurring near stability-mode synchronization locations. The results show that, in the linear regime, each discrete mode contains all FT components, whose relative amplitudes vary with streamwise distance. Vortical components are always the largest, followed by thermal and acoustic components. These latter two show distinct fore and aft signatures near mode synchronization. The vortical component displays a series of rope-shaped recirculation-cell patterns across the generalized inflection point. However, both acoustic and thermal components display ‘trapped’ structures. The former contains an alternating monopole array between the wall and the critical layer, while the latter is confined to an undulating region between the wall and a wavy locus straddling the generalized inflection point. Nonlinear saturation in the region of Mack-mode growth further strengthens the rope-shaped structures in the vortical component and higher harmonics appear, whose form and location depend on the specific component. Wall cooling modifies the eigenfunctions such that the acoustic component accounts for more of its composition, consistent with its destabilization. Analysis of energy interactions among the FT components indicates that, even though the vorticity component is the largest, the thermal component induces the most significant source term for the growth of acoustic perturbations, possibly due to the trapped nature of both.

Vorticity and particle polarization in heavy ion collisions (experimental perspective)

The recent measurements of the global polarization and vector meson spin alignment along the system orbital momentum in heavy ion collisions are briefly reviewed. A possible connection between the global polarization and the chiral anomalous effects is discussed along with possible experimental checks. Future directions, in particular those aimed on the detailed mapping of the vorticity fields, are outlined. The Blast Wave model is used for an estimate of the anisotropic flow effect on the vorticity component along the beam direction. We also point to a possibility of a circular pattern in the vorticity field in asymmetric, e.g. Cu+Au, central collisions.

Roles of Streamwise and Transverse Partial-Vorticity Components in Steady Inviscid Isentropic Supercell-Like Flows

Investigations of tornadogenesis in supercells attempt to find the origin of the tornado’s large vorticity by determining vorticity generation and amplification along trajectories that enter the tornado from a horizontally uniform unstable environment. Insights into tornadogenesis are provided by finding analytical formulas for vorticity variations along streamlines in idealized, steady, inviscid, isentropic inflows of dry air imported from the environment. The streamlines and vortex lines lie in the stationary isentropic surfaces so the vorticity is 2D. The transverse vorticity component (positive leftward of the streamlines) arises from imported transverse vorticity and from baroclinic vorticity accumulated in streamwise temperature gradients. The streamwise component stems from imported streamwise vorticity, from baroclinic vorticity accrued in transverse temperature gradients, and from positive transverse vorticity that is turned streamwise in cyclonically curved flow by a “river-bend process.” It is amplified in subsiding air as it approaches the ground. Streamwise stretching propagates a parcel’s streamwise vorticity forward in time. In steady flow, vorticity decomposes into baroclinic vorticity and two barotropic parts ωBTIS and ωBTIC arising from imported storm-relative streamwise vorticity (directional shear) and storm-relative crosswise vorticity (speed shear), respectively. The Beltrami vorticity ωBTIS is purely streamwise. It explains why abundant environmental storm-relative streamwise vorticity close to ground favors tornadic supercells. It flows directly into the updraft base unmodified apart from streamwise stretching, establishing mesocyclonic rotation and strong vortex suction at low altitudes. Increase (decrease) in storm-relative environmental wind speed with height near the ground accelerates (delays) tornadogenesis as positive (negative) ωBTIC is turned into streamwise (antistreamwise) vorticity within cyclonically curved flow around the mesocyclone.