Starting vortex

About: Starting vortex is a research topic. Over the lifetime, 4785 publications have been published within this topic receiving 100419 citations.

On the connection between thin vortex layers and vortex sheets

Abstract: The equations for the two-dimensional motion of a layer of uniform vorticity in an incompressible, inviscid fluid are examined in the limit of small thickness. Under the right circumstances, the limit is a vortex sheet whose strength is the vorticity multiplied by the local thickness of the layer. However, vortex sheets can develop singularities in finite time, and their subsequent nature is an open question. Vortex layers, on the other hand, have motions for all time, though they may develop singularities on their boundaries. Fortunately, a material curve within the layer does exist for all time. Under certain assumptions, its limiting motion is again the vortex sheet, and thus its behaviour may indicate the nature and possible existence of the vortex sheet after the singularity time. Similar asymptotic results are obtained also for the limiting behaviour of the centre curve as defined by Moore (1978). By examining the behaviour of a sequence of layers, some physical understanding of the formation of the curvature singularity for a vortex sheet is gained. A strain flow, induced partly by the periodic extension of the sheet, causes vorticity to be advected to a certain point on the sheet rapidly enough to form the singularity. A vortex layer, however, simply bulges outwards as a consequence of incompressibility and subsequently forms a core with trailing arms that wrap around it. The evidence indicates that no singularities form on the boundary curves of the layer. Beyond the singularity time of the vortex sheet, the limiting behaviour of the vortex layers is non-uniform. Away from the vortex core, the layers converge to a smooth curve which has the appearance of a doubly branched spiral. While the circulation around the core vanishes, approximations to the vortex sheet strength become unbounded, indicating a complex, local structure whose precise nature remains undetermined.

Design and evaluation of a Dean vortex-based micromixer

Abstract: A mixer, based on the Dean vortex, is fabricated and tested in an on-chip format. When fluid is directed around a curve under pressure driven flow, the high velocity streams in the center of the channel experience a greater centripetal force and so are deflected outward. This creates a pair of counter-rotating vortices moving fluid toward the inner wall at the top and bottom of the channel and toward the outer wall in the center. For the geometries studied, the vortices were first seen at Reynolds numbers between 1 and 10 and became stronger as the flow velocity is increased. Vortex formation was monitored in channels with depth/width ratios of 0.5, 1.0, and 2.0. The lowest aspect ratio strongly suppressed vortex formation. Increasing the aspect ratio above 1 appeared to provide improved mixing. This design has the advantages of easy fabrication and low surface area.

Three-Dimensional Alignment and Corotation of Weak, TC-like Vortices via Linear Vortex Rossby Waves

Abstract: The vertical alignment of an initially tilted geostrophic vortex is shown here to be captured by linear vortex Rossby wave dynamics when the vortex cores at upper and lower levels overlap. The vortex beta Rossby number, defined as the ratio of nonlinear advection in the potential vorticity equation to linear radial advection, is less than unity in this case. A useful means of characterizing a tilted vortex flow in this parameter regime is through a wave‐mean flow decomposition. From this perspective the alignment mechanism is elucidated using a quasigeostrophic model in both its complete and linear equivalent barotropic forms. Attention is focused on basicstate vortices with continuous and monotonically decreasing potential vorticity profiles. For internal Rossby deformation radii larger than the horizontal scale of the tilted vortex an azimuthal wavenumber 1 quasi mode exists. The quasi mode is characterized by its steady cyclonic propagation, long lifetime, and resistance to differential rotation, behaving much like a discrete vortex Rossby wave. The quasi mode traps disturbance energy causing the vortex to precess, or corotate, and thus prevents alignment. For internal deformation radii smaller than the horizontal vortex scale, the quasi mode disappears into the continuous spectrum of vortex Rossby waves. Alignment then proceeds through the irreversible redistribution of potential vorticity by the sheared vortex Rossby waves. Further decreases in the internal deformation radius result in a decreased dependence of vortex evolution on initial tilt magnitude, consistent with a reduction of the vortex beta Rossby number. These results are believed to have relevance to the problem of tropical cyclone (TC) genesis. Cyclogenesis initiated through the merger and alignment of low-level convectively generated positive potential vorticity within a weak incipient vortex is captured by quasi-linear dynamics. A potential dynamical barrier to TC development in which the quasi mode frustrates vertical alignment can be identified using the linear alignment theory in this case.