The Okubo-Weiss criterion in hydrodynamic flows:Geometric aspects and further extension

The Okubo [5]-Weiss [6] criterion has been extensively used as a diagnostic tool to divide a two-dimensional (2D) hydrodynamical flow field into hyperbolic and elliptic regions and to serve as a useful qualitative guide to the complex quantitative criteria. The Okubo-Weiss criterion is frequently validated on empirical grounds by the results ensuing its application. So, we will explore topological implications into the Okubo-Weiss criterion and show the Okubo-Weiss parameter is, to within a positive multiplicative factor, the negative of the Gaussian curvature of the underlying vorticity manifold. The Okubo-Weiss criterion is reformulated in polar coordinates, and is validated via several examples including the Lamb- Oseen vortex, and the Burgers vortex. These developments are then extended to 2D quasi- geostrophic (QG) flows. The Okubo-Weiss parameter is shown to remain robust under the -plane approximation to the Coriolis parameter. The Okubo-Weiss criterion is shown to be able to separate the 2D flow-field into coherent elliptic structures and hyperbolic flow configurations very well via numerical simulations of quasi-stationary vortices in QG flows. An Okubo-Weiss type criterion is formulated for 3D axisymmetric flows, and is validated via application to the round Landau-Squire Laminar jet flow.

A Combined Vortex Lattice Lifting Line Method for Unsteady Propeller Calculations

This paper presents a Combined Method for the calculation of propeller forces in inhomogeneous inflow. It consists of an extended Goldstein approach based on Lifting Line Theory and a Vortex Lattice Method. After a brief overview of both methods is given, the coupling strategy is described and the additional modifications are explained. A correction factor accounting for the vortex which develops under a separated and later reattached flow on the suction side of the propeller blade is implemented as the first modification. Further, the Lamb-Oseen vortex model is used for the vortices in the free vortex system of the propeller. Finally, some results achieved with the described method are presented and compared to measured values.

Transient energy growth of a swirling jet with vortex breakdown

We investigate the existence of short-time, local transient growth in the helical modes of a rapidly swirling, high-speed jet that has transitioned into an axisymmetric bubble breakdown state. The time-averaged flow consisting of the bubble and its wake downstream constitute the base state, which we show to exhibit strong transient amplification owing to the non-modal behaviour of the continuous eigenspectrum. A pseudospectrum analysis mathematically identifies the so-called potential modes within this continuous spectrum and the resultant non-orthogonality between these modes and the existing discrete stable modes is shown to be the main contributor to such growth. As the swirling flow develops post the collapsed bubble, the potential spectrum moves further toward the unstable half-plane, which along with the concurrent weakening of exponential growth from the discrete unstable modes, increases the dynamic importance of transient growth inside the wake region. The transient amplifications calculated at several locations inside the bubble and wake confirm this, where strong growths inside the wake far outstrip the corresponding modal growths (if available) at shorter times, but especially at the higher helical orders and smaller streamwise wavenumbers. The corresponding optimal perturbations at initial times consist of streamwise streaks of azimuthal velocity, which if concentrated inside the core vortical region, unfold via the classical Orr mechanism to yield structures resembling core (or viscous) Kelvin waves of the corresponding Lamb–Oseen vortex. However, in contrast to that in Lamb–Oseen vortex flow, where critical-layer waves are associated with higher transient gains, here, such core Kelvin modes with the more compact spiral structure at the vortex core are seen to yield the maximum transient amplifications.

Investigation of Lamb–Oseen Vortex Evolution and Decay in Ground Proximity With Obstacle

The physical mechanism for the evolution and decay of Lamb–Oseen vortex pair in ground proximity with an obstacle has been investigated in detail by adopting the large eddy simulation (LES). In the present research, we mainly focus on the vortex evolution and decay mechanism in ground proximity with obstacle, so we chose one fixed height of the obstacle case (h0 = 0.5b0) to investigate, and the obstacle is placed transversally to the axis of the primary wake to be analyzed. The trajectories of the primary wake-vortex cores and the circulation profiles, as well as the distribution of the tangential velocity on different axial positions, have been specifically captured and analyzed. The “strake,” “claw,” and “ivory” vortices have been newly found and defined at the initial evolution stage, and they subsequently begin to harshly wind and rotate with the primary vortex. A flow structure with double helix conical shapes of the primary vortex has been found in the obstacle case. The pressure waves along the vortex axis have also been analyzed in detail. The wake-vortex on each side would be pulled in opposite axial directions and eventually pinched off at the upper surface of obstacle. Moreover, it has also been newly found that the trajectories of the wake-vortex in longitudinal directions at different axial distances away from the obstacle will experience two kinds of motion: only descending and rebounding after descending. Results obtained in this study provide a better understanding of mechanisms for the interaction of wake-vortex and the obstacle.