Vortex

About: Vortex is a research topic. Over the lifetime, 72362 publications have been published within this topic receiving 1304130 citations. The topic is also known as: vortices.

Elementary Fluid Dynamics

Abstract: Introduction Elementary viscous flow Waves Classical aerofoil theory Vortex motion The Navier-Stokes equations Very viscous flow Boundary layers Instability Appendix hints and answers for exercises Bibliography Index.

Coherent structures and turbulence.

Abstract: This is a personal statement on the present state of understanding of coherent structures, in particular their spatial details and dynamical significance. The characteristic measures of coherent structures are discussed, emphasizing coherent vorticity as the crucial property. We present here a general scheme for educing structures in any transitional or fully turbulent flow. From smoothed vorticity maps in convenient flow planes, this scheme recognizes patterns of the same mode and parameter size, and then phase-aligns and ensemble-averages them to obtain coherent structure measures. The departure of individual realizations from the ensemble average denotes incoherent turbulence. This robust scheme has been used to educe structures from velocity data using a rake of hot wires as well as direct numerical simulations and can educe structures using newer measurement techniques such as digital image processing. Our recent studies of coherent structures in several free shear flows are briefly reviewed. Detailed data in circular and elliptic jets, mixing layers, and a plane wake reveal that incoherent turbulence is produced at the ‘saddles’ and then advected to the ‘centres’ of the structures. The mechanism of production of turbulence in shear layers is the stretching of longitudinal vortices or ‘ribs’ which connect the predominantly spanwise ‘rolls’; the ribs induce spanwise contortions of rolls and cause mixing and dissipation, mostly at points where they connect with rolls. We also briefly discuss the role of coherent structures in aerodynamic noise generation and argue that the structure breakdown process, rather than vortex pairing, is the dominant mechanism of noise generation. The ‘cut-and-connect’ interaction of coherent structures is proposed as a specific mechanism of aerodynamic noise generation, and a simple analytical model of it shows that it can provide acceptable predictions of jet noise. The coherent-structures approach to turbulence, apart from explaining flow physics, has also enabled turbulence management via control of structure evolution and interactions. We also discuss some new ideas under investigation: in particular, helicity as a characteristic property of coherent structures.

Stability theory for a pair of trailing vortices

Abstract: x(/3) Trailing vortices do not decay by simple diffusion. Usually they undergo a symmetric and nearly sinusoidal instability, until eventually they join at intervals to form a train of vortex rings. The present theory accounts for the instability during the early stages of its growth. The vortices are idealized as interacting lines; their core diameters are taken into account by a cutoff in the line integral representing self-induction. The equation relating induced velocity to vortex displacement gives rise to an eigenvalue problem for the growth rate of sinusoidal perturbations. Stability is found to depend on the products of vortex separation 6 and cutoff distance d times the perturbation wavenumber. Depending on those products, both symmetric and antisymmetric eigenmodes can be unstable, but only the symmetric mode involves strongly interacting long waves. An argument is presented that d/b = 0.063 for the vortices trailing from an elliptically loaded wing. In that case, the maximally unstable long wave has a length 8.66 and grows by a factor e in a time 9.4(^4#/CL)(6/F0), where AR is the aspect ratio, CL is the lift coefficient, and V0 is the speed of the aircraft. The vortex displacements are symmetric and are confined to fixed planes inclined at 48° to the horizontal.

The emergence of isolated coherent vortices in turbulent flow

Abstract: A study is made of some numerical calculations of two-dimensional and geostrophic turbulent flows. The primary result is that, under a broad range of circumstances, the flow structure has its vorticity concentrated in a small fraction of the spatial domain, and these concentrations typically have lifetimes long compared with the characteristic time for nonlinear interactions in turbulent flow (i.e. an eddy turnaround time). When such vorticity concentrations occur, they tend to assume an axisymmetric shape and persist under passive advection by the large-scale flow, except for relatively rare encounters with other centres of concentration. These structures can arise from random initial conditions without vorticity concentration, evolving in the midst of what has been traditionally characterized as the ‘cascade’ of isotropic, homogeneous, large-Reynolds-number turbulence: the systematic elongation of isolines of vorticity associated with the transfer of vorticity to smaller scales, eventually to dissipation scales, and the transfer of energy to larger scales. When the vorticity concentrations are a sufficiently dominant component of the total vorticity field, the cascade processes are suppressed. The demonstration of persistent vorticity concentrations on intermediate scales - smaller than the scale of the peak of the energy spectrum and larger than the dissipation scales - does not invalidate many of the traditional characterizations of two-dimensional and geostrophic turbulence, but I believe it shows them to be substantially incomplete with respect to a fundamental phenomenon in such flows.

On the development of turbulent wakes from vortex streets

Abstract: Wake development behind circular cylinders at Reynolds numbers from 40 to 10,000 was investigated in a low-speed wind tunnel. Standard hotwire techniques were used to study the velocity fluctuations. The Reynolds number range of periodic vortex shedding is divided into two distinct subranges. At R = 40 to 150, called the stable range, regular vortex streets are formed and no turbulent motion is developed. The range R = 150 to 300 is a transition range to a regime called the irregular range, in which turbulent velocity fluctuations accompany the periodic formation of vortices. The turbulence is initiated by laminar-turbulent transition in the free layers which spring from the separation points on the cylinder. This transition first occurs in the range R = 150 to 300. Spectrum and statistical measurements were made to study the velocity fluctuations. In the stable range the vortices decay by viscous diffusion. In the irregular range the diffusion is turbulent and the wake becomes fully turbulent in 40 to 50 diameters downstream. It was found that in the stable range the vortex street has a periodic spanwise structure. The dependence of shedding frequency on velocity was successfully used to measure flow velocity. Measurements in the wake of a ring showed that an annular vortex street is developed.