Vorticity dynamics in turbulence growth

The mechanisms of vorticity amplification in the formation of turbulence are investigated by means of direct numerical simulations of the Navier–Stokes equations with different initial conditions and Reynolds numbers. The simulations show good universality of the enstrophy evolution, that occurs in two stages. The first stage is dominated by the effect of vortex stretching, and it finishes with a k ^?3 power-law energy spectrum. The second stage is dominated by the action of viscosity on the small scales, and it finishes with a Kolmogorov k ^?5/3 energy spectrum.     

Vorticity measurements in turbulent grid flows

Results of direct simultaneous measurements of vorticity and velocity are reported for a turbulent flow past a grid of air and (slightly salted) water by two qualitatively different methods. Both experiments were preformed in the same geometry and at the same Taylor microscale Reynolds number 75. The experiments with salted water flow were performed in water tunnel of the laboratory for vorticity-helicity studiesx Faculty of Engineering, Tel-Aviv University and the experiments with air flow were performed in the wind tunnel of the Turbulent Flow Laboratory, University of Maryland. One of the most striking results is that in both experiments the flow is found to lack reflexional symmetry.     

Contour Dynamics with Non-uniform Background Vorticity

In this paper it is demonstrated how a contour dynamics method can be used to simulate the behaviour of vortices in the presence of non-uniform background vorticity in general, and on the γ-plane in particular. For standard contour dynamics in case of zero, or uniform background vorticity, the initial continuous vorticity distributions of the vortices are replaced by appropriate piecewise-uniform distributions. Then, the evolution of the contours separating the several regions of uniform vorticity, are followed in time. In the case of non-uniform background vorticity, it is necessary to replace the sum of the (relative) vorticity of the vortices and the background vorticity by a piecewise-uniform distribution. This has several consequences for applying the method of contour dynamics, which are discussed in this paper. The resulting method is tested on some numerical examples. One of them is (qualitatively) compared with laboratory experiments carried out in a rotating tank.     

Vorticity produced by shock wave diffraction

Numerical simulations with a monotonicity preserving flow solver have been performed to study shock diffraction phenomena and shock wave generated vorticity. The computations were performed using the conservative Finite Element Method-Flux Corrected Transport (FEM-FCT) scheme, which has been shown to have an excellent predictive capability for various compressible flows with both strong and weak shocks. An adaptive unstructured methodology based on adapting to high density and entropy gradients was used in conjunction with a conservative shock-capturing scheme to adequately resolve strong and weak flowfield gradients. The chief interest was the formation of vorticity arising from shock wave propagation over a sharp corner and the high accuracy and resolution of the interacting compressible wave features. Numerical simulations were compared with previous experimental results and exhibited remarkably good agreement in terms of compressible wave propagation, as well as vorticity development and transport. The computations also allowed insight into the fundamental fluid dynamics, specifically shock diffraction, vortex convection and shock-vortex interactions.     

Exact Solitary Water Waves with Vorticity

The solitary water wave problem is to find steady free surface waves which approach a constant level of depth in the far field. The main result is the existence of a family of exact solitary waves of small amplitude for an arbitrary vorticity. Each solution has a supercritical parameter value and decays exponentially at infinity. The proof is based on a generalized implicit function theorem of the Nash–Moser type. The first approximation to the surface profile is given by the “KdV” equation. With a supercritical value of the surface tension coefficient, a family of small amplitude solitary waves of depression with subcritical parameter values is constructed for an arbitrary vorticity.     

Vorticity and curvature at a stream surface

If S is a stream surface in a flow, we show the relationship between the three components of the vorticity field on S and the curvatures of the streamlines (geodesic torsion, normal curvature and geodesic curvature).     

Vorticity meter calibration using a cross-wires survey

A vorticity meter of the vane-type has been used in this study for direct and quantitative measurements of vertical flows. The vane calibration procedure is carried out by using measurements deduced from a preliminary cross-wires survey of the flow-field generated in the wake of a half wing set at incidence in the wind tunnel. Emphasis is placed on the resulting calibration law which relates the vane rotational speed to the fluid angular velocity. Specially it is shown that this calibration law can be obtained as a linear expression by taking into account the minimum threshold rotational speed necessary for vane rotation. When comparing vorticity distributions obtained through the vortical wing wake by the indirect cross-wires technique, good agreements are found with the corresponding vorticity distributions as deduced from the so calibrated vorticity meter.List of symbols c Airfoil chord, m - K, K dimensionless constants in calibration relations [Eqs. (1, 2)] - N rotational speed of the vorticity meter, rps - N _f , N_f rotational speed of the fluid, rps - N f ₀, N_{f 0} threshold of fluid angular velocity necessary for vane rotation, rps [Eqs. (1, 2)] - r radial distance measured from the vortex center, mm - r ₀ radius of the vorticity meter, mm - R _c Reynolds number refered to wing chord - U, V, W velocity components along X, Y, Z axis respectively, m/s - V Freestream velocity, m/s - V _t Tangential velocity, V _t ² = V ² + W ², m/s - X, Y, Z axial, lateral, and vertical distances (Fig. 1) - geometric airfoil incidence, deg - relative error estimation [Eq. (3)] - streamwise vorticity component, rad/s [Eq. (4)] - efficiency factor, = N /N _f - , pitch and yaw angles, deg, (Fig. 1) - angular velocity, rad/s     

Moderately Strong Vorticity in a Bathtub-Type Flow

Theoretical and numerical analysis is performed for an inviscid axisymmetric vortical bathtub-type flow. The level of vorticity is kept high so that the image of the flow on the radial–axial plane (r–z plane)is not potential. The most significant findings are: (1) the region of validity of the strong vortex approximation is separated from the drain by a buffer region, (2) the power-law asymptote of the stream function, specified by Δψ∼r ^4/3Δz, appears near the axis when vorticity in the flow is sufficiently strong and (3) the local Rossby number in the region of the power-law is not very sensitive to the changes of the initial vorticity level in the flow and the global Rossby number. Received 3 April 2000 and accepted 29 September 2000     

Vorticity characteristics of the turbulent intermediate wake

Measurements of the lateral components _j (j=2 and 3) of the vorticity fluctuation vector have been made, using a vorticity probe consisting of two X-wires, in the intermediate wake of a circular cylinder. The effect of the spatial resolution of the probe on the measurement of _j has been studied. As the spatial resolution impairs, the variance and flatness factor of _j decrease whereas the skewness of _j increases. Reasonably accurate values of _j ² can be obtained by applying spectral corrections for the spatial resolution effect.Near the beginning of the intermediate wake, the variance of ₂ is larger than that of ₃ due to the significant contribution from ribs which connect consecutive spanwise roll vortices. This difference decreases with downstream distance. Also, the presence of the rolls is reflected by a local extremum in the skewness of ₃ on each side of the wake centerline. The magnitude of the extremum decreases with downstream distance.The support of the Australian Research Council is gratefully acknowledged.     

Vorticity jump across a shock in nonuniform flow

A new relation is derived for the vorticity just downstream of a shock wave when the upstream flow is nonuniform. Aside from the vorticity contribution from a curved shock, there is an amplified upstream vorticity contribution and terms associated with upstream Mach number and stagnation enthalpy gradients, along the shock, that may be present even if the upstream flow is irrotational.     

Vorticity field in a cascade model of turbulence

We propose a model which interprets the behavior of the spontaneous singularity and the intermittent structure in fully developed turbulence simultaneously. The model is justified in the framework of a cascade model of turbulence.     

Periodic Traveling Gravity Water Waves with Discontinuous Vorticity

We use elliptic theory to prove the existence of steady two-dimensional periodic waterwaves of large amplitude in a flowwith an arbitrary bounded but discontinuous vorticity. This is achieved by developing a local and global bifurcation construction of weak solutions of the elliptic partial differential equations that are relevant to this hydrodynamical context.     

Singularities in Three-Dimensional Compressible Euler Flows with Vorticity

It is known from earlier work that three-dimensional incompressible Euler flows with vorticity can develop a singularity in a finite time, at least if the initial conditions are of a certain class. Here we discuss corresponding possibilities for flows with compressibility. Naturally, it is known that the shock-wave phenomenon represents an important singular field in compressible fluid dynamics especially in the irrotational case. However, here we are concerned not with that phenomenon but rather with compressible flows where any singularity is associated with the presence of vorticity. In particular we expose the role played by the ratio of specific heats in an adiabatic flow field. Received 9 December 1996 and accepted 4 April 1997     

Nearly-Hamiltonian Structure for Water Waves with Constant Vorticity

We show that the governing equations for two-dimensional gravity water waves with constant non-zero vorticity have a nearly-Hamiltonian structure, which becomes Hamiltonian for steady waves.      

Spectral Vorticity and Lagrangian Velocity Measurements in Turbulent Jets

In this paper we report an experimental investigation of various statistical properties of the spatial Fourier modes of the vorticity field in turbulent jets for a large range of Reynolds numbers (530 ≤R _λ≤ 6100). The continuous time evolution of a spatial Fourier mode of the vorticity distribution, characterized by a well-defined wavevector, is obtained from acoustic scattering measurements. The spatial enstrophy spectrum, as a function of the spatial wave-vector, is determined by scanning the incoming sound frequencies. Time-frequency analysis of the turbulent vorticity fluctuations is also performed for different length scales of the flows. Vorticity time-correlations show that the characteristic time of a Fourier mode behaves as the sweeping time. Finally, we report preliminary Lagrangian velocity measurements obtained using acoustic scattering by soap bubbles inflated with helium. Gathering a large number of passages of isolated bubbles in the scattering volume, one is able to compute the Lagrangian velocity PDF and velocity spectrum. Despite the spatial filtering due to the finite size of the bubble, the latter exhibits a power law, with the -2 exponent predicted by the Kolmogorov theory, over one decade of frequencies.     

On the Flame-generated Vorticity Dynamics of Bluff-body-stabilized Premixed Flames

This investigation considers the dynamics of flame-generated vorticity for a premixed, submerged bluff-body stabilized flame. Experimentation characterizes the far-field region in particular with a level of detail not previously afforded to this type of flow. Simultaneous particle imaging velocimetry (PIV), Mie scattering and CH ^? chemiluminescence are used to obtain velocity fields and flame location. Mean static pressure measurements at the combustion chamber wall capture the pressure field. Analysis of the flame fronts in relation to the mean velocity and vorticity fields provides useful insight into the interaction of the flame and the flow. The unique nature of the velocity and vorticity fields and their effect on downstream flame structures are explained by the baroclinic torque generation of vorticity. The coupling that exists among pressure, heat release, and baroclinic generation is acknowledged and will influence strategies for control of the baroclinic mechanism.     

Blow-up Solutions Appearing in the Vorticity Dynamics with Linear Strain

We consider a model equation for 3D vorticity dynamics of incompressible viscous fluid proposed by K. Ohkitani and the second author of the present paper. We prove that a solution blows up in finite time if the -norm of the initial vorticity is greater than the viscosity.     

Unsteady Viscous Flows about Bodies: Vorticity Release and Forces

The force (drag and lift) exerted on a body moving in a viscous fluid is expressed via the free and bound vorticity moments, and the role of vortex shedding is discussed. The formulation encompasses classical, inviscid flows, and leads to efficient computational methods. Numerical results for a few prototype flows are presented.     

Comparative Study of Vorticity and Material Lines Evolution in Numerical Turbulence

A comparative study of the differences in the evolution processes of vorticity and material lines based on DNS of NSE is performed at low Reynolds number $Re_\lambda \approx 50$ for time periods up to 15 Kolmogorov microscales. In order to observe such differences we looked for regions in which the forcing and the viscous terms are approximately balancing each other (in the sense as defined in the main text) and used the Lagrangian tracking of fluid particles originating from these regions for time periods during which the above balance between the forcing and the viscous terms remain valid.