J. E. Martin

Numerical investigation of three-dimensionally evolving jets subject to axisymmetric and azimuthal perturbations

We study the inviscid mechanisms governing the three-dimensional evolution of an axisymmetric jet by means of vortex filament simulations. The spatially periodic calculations provide a detailed picture of the processes leading to the concentration, reorientation, and stretching of the vorticity. In the purely axisymmetric case, a wavy perturbation in the streamwise direction leads to the formation of vortex rings connected by braid regions, which become depleted of vorticity. The curvature of the jet shear layer leads to a loss of symmetry as compared to a plane shear layer, and the position of the free stagnation point forming in the braid region is shifted towards the jet axis. As a result, the upstream neighbourhood of a vortex ring is depleted of vorticity at a faster rate than the downstream side. When the jet is also subjected to a sinusoidal perturbation in the azimuthal direction, it develops regions of counter-rotating streamwise vorticity, whose sign is determined by a competition between global and local induction effects. In a way very similar to plane shear layers, the streamwise braid vorticity collapses into counter-rotating round vortex tubes under the influence of the extensional strain. In addition, the cores of the vortex rings develop a wavy dislocation. As expected, the vortex ring evolution depends on the ratio R /θ of the jet radius and the jet shear-layer thickness. When forced with a certain azimuthal wavenumber, a jet corresponding to R /θ = 22.6 develops vortex rings that slowly rotate around their unperturbed centreline, thus preventing a vortex ring instability from growing. For R /θ = 11.3, on the other hand, we observe an exponentially growing ring waviness, indicating a vortex ring instability. Comparison with stability theory yields poor agreement for the wavenumber, but better agreement for the growth rate. The growth of the momentum thickness is much more dramatic in the second case. Furthermore, it is found that the rate at which streamwise vorticity develops is strongly affected by the ratio of the streamwise and azimuthal perturbation amplitudes.

The non-Boussinesq lock-exchange problem. Part 2. High-resolution simulations

The present investigation explores the unsteady dynamics of large density contrast non-Boussinesq lock-exchange flows by means of high-resolution two-dimensional simulations of the incompressible variable-density Navier–Stokes equations, employing a combination of spectral and compact finite-difference methods. For small density contrasts, the simulations closely reproduce earlier Boussinesq results for corresponding flows. Across the entire range of density contrasts, good agreement is obtained between the computed front propagation velocities and corresponding experimental observations reported in Part 1 of this investigation and by other authors. The simulations yield the required quantitative information with respect to the light and dense front heights, their propagation velocities, and the spatial structure of the dissipation fields in order to determine conclusively which of the scenarios developed in Part 1 is observed in reality. Simulations are conducted for fluids with the same kinematic viscosity, as well as for fluids with the same dynamic viscosity. For both slip and no-slip boundary conditions, and for all Re values, we find that for larger density contrasts, the dense front dissipates an increasing amount of energy. In contrast, the energy dissipated by the light front remains near its Boussinesq level for all values of the density ratio. In addition, for all density ratios, the height of the light front is very close to half the channel height, and it propagates with a non-dimensional velocity close to a half. This provides strong evidence that the dynamics of the light front is indeed approximated by the energy-conserving solution described in an earlier theoretical analysis. In contrast, the height of the dense front is substantially less than half the channel height. In addition, its velocity is close to the value derived in Part 1 for a dissipative gravity current. Together with the above results for the dissipation field, this confirms that the dense front behaves as a dissipative gravity current.

The accumulation and dispersion of heavy particles in forced two‐dimensional mixing layers. I. The fundamental and subharmonic cases

This paper presents detailed computational results for the dispersion of heavy particles in transitional mixing layers forced at both the fundamental and subharmonic frequencies. The results confirm earlier observations of particle streaks forming in the braid region between successive vortices. A scaling argument based on the idealization of the spatially periodic mixing layer as a row of point vortices shows that the formation of these concentrated particle streaks proceeds with optimum efficiency for St≂1. It thereby provides a quantitative basis for experimental and numerical observations of preferential particle dispersion at Stokes numbers of order unity. Both the model and full simulation furthermore exhibit oscillatory particle motion, as well as the formation of two bands of high particle concentrations, for larger Stokes numbers. The particle dispersion as a function of time and the Stokes number is quantified by means of two different integral scales. These show that the number of dispersed par...

On the stability of the swirling jet shear layer

The linear stability analysis of a simple model of a swirling jet illuminates the competition and interaction of centrifugal and Kelvin–Helmholtz instabilities. By employing potential theory, analytical expressions are derived for the growth rate and propagation velocity of both axisymmetric and helical waves. The results show that centrifugally stable flows become destabilized by sufficiently short Kelvin–Helmholtz waves. The asymptotic limits demonstrate that for long axisymmetric waves the centrifugal instability dominates, while long helical waves approach the situation of a Kelvin–Helmholtz instability in the azimuthal direction, modulated by a stable or unstable centrifugal stratification. Both short axisymmetric and short helical waves converge to the limit of a plane Kelvin–Helmholtz instability feeding on the azimuthal vorticity.

Numerical investigation of three-dimensionally evolving jets under helical perturbations

We study the three-dimensional evolution of a nominally axisymmetric jet subject to helical perturbations. Our approach is a computational one, employing an inviscid vortex filament technique to gain insight into the vorticity dynamics of jets dominated by helical vortices. For the case of a helical perturbation only, the streamwise vorticity forming in the braid is of the same sign everywhere, with the vortex helix representing streamwise vorticity of opposite sign. Owing to the helical symmetry, concentrated structures do not form in the braid. By introducing an additional periodic perturbation in the azimuthal direction, the helical symmetry is broken and we observe the emergence of concentrated streamwise braid vortices all of the same sign, in contrast to the counter-rotating braid vortices of ring-dominated jets. A Kelvin—Helmholtz-like instability of the braid vorticity layer plays a significant role in their generation. We furthermore find that the initial evolution of the braid vorticity is strongly dependent upon the ratio between the helical and azimuthal perturbation amplitudes. Smaller azimuthal perturbation amplitudes slow down the concentration process of the braid vorticity. However, we find that the long-time strength of the streamwise braid vortices should not depend on the amplitudes of the streamwise and azimuthal perturbation waves, but rather on their wavenumbers. The evolution of the helical vortex varies with the ratio between jet radius R and shear-layer momentum thickness θ. While for a jet with R /θ = 22.6 and azimuthal wavenumber five, the emerging helix continuously rotates and thereby avoids instability, we observe in a jet with R /θ = 11.3 the reduction of this rotation and the near exponential growth of waves on the helical vortex, characteristic of vortex helix instability.

Nonlinear axisymmetric and three-dimensional vorticity dynamics in a swirling jet model

The mechanisms of vorticity concentration, reorientation, and stretching are investigated in a simplified swirling jet model, consisting of a line vortex along the jet axis surrounded by a jet shear layer with both azimuthal and streamwise vorticity. Inviscid three‐dimensional vortex dynamics simulations demonstrate the nonlinear interaction and competition between a centrifugal instability and Kelvin–Helmholtz instabilities feeding on both components of the base flow vorticity. Under axisymmetric flow conditions, it is found that the swirl leads to the emergence of counter‐rotating vortex rings, whose circulation, in the absence of viscosity, can grow without bounds. Scaling laws are provided for the growth of these rings, which trigger a pinch‐off mechanism resulting in a strong decrease of the local jet diameter. In the presence of an azimuthal disturbance, the nonlinear evolution of the flow depends strongly on the initial ratio of the azimuthal and axisymmetric perturbation amplitudes. The long term ...

Experimental and Numerical Analysis of the Three-Dimensional Evolution of an Axisymmetric Jet

We study the three-dimensional evolution of a transitional axisymmetric jet subjected to periodic perturbations both in the streamwise and in the circumferential direction. The combined analysis of flow visualization experiments and inviscid vortex dynamics simulations provides a detailed picture of the processes leading to the concentration, reorientation, and stretching of the vorticity. A single perturbation in the streamwise direction leads to the formation of vortex rings, while a free stagnation point forms in the downstream half of the braid region between successive vortices. If we also introduce a subharmonic perturbation in the streamwise direction, neighboring vortices proceed towards a pairing process. In addition, it is shown that when the jet is also subjected to a sinusoidal perturbation in the azimuthal direction, counterrotating pairs of streamwise vortex tubes are formed in the braid regions, and the cores of the vortex rings develop a wavy dislocation. We discuss the importance of global and local induction for the evolution and interaction of these three-dimensional instability modes.

Three-Dimensional Evolution of Axisymmetric Jets: a Comparison Between Computations and Experiments

We analyze the three-dimensional evolution of a transitional axisymmetric jet for the two cases of an axisymmetric perturbation in the streamwise direction combined with an azimuthal corrugation and a helical perturbation, respectively. The combined analysis of flow visualization experiments and inviscid vortex dynamics simulations elucidates the processes leading to the concentration, reorientation, and stretching of the vorticity. In the first case, counterrotating pairs of streamwise vortex tubes form in the braid regions, and the cores of the vortex rings develop a wavy dislocation. The mechanism for the collapse of the streamwise braid vorticity is the same as in a plane mixing layer. For the helical perturbation, only one sign of streamwise vorticity forms in the braid, while the vortex helix represents streamwise vorticity of the opposite sign. The early stages of the flow visualization experiments show good agreement with the numerical observations, thus confirming that even at moderate values of the Reynolds number the evolution is dominated by inviscid mechanisms.

The Nonlinear Dynamics of a Jet Shear Layer with Swirl

The present computational study concerns the three-dimensional evolution of a nominally axisymmetric jet with swirl subject to axisymmetric and azimuthal perturbations. We employ an inviscid vortex filament technique to gain insight into the vorticity dynamics of the flow. As a first step, we consider the effect of streamwise vorticity in the jet shear layer only. For the case of an axisymmetric perturbation, we observe the formation of weakly swirling vortex rings connected by braids in which the effect of the swirl is relatively more important. The streamwise vorticity forming in the braid is of the same sign everywhere, however, due to the axisymmmetry, concentrated structures do not formn in the braid. By introducing an additional periodic perturbation in the azimuthal direction, the axisymmetry is broken and the emergence of concentrated streamwise braid vortices all of the same sign is observed. A Kelvin-Helmholtz-like instability of the curved braid vorticity layer plays a significant role in their generation.

High resolution simulation of particle-driven lock-exchange flow for non-Boussinesq conditions

The structure and dynamics of particle-driven lock exchange flows are examined by means of simulations of the variable density, incompressible NavierStokes equations. A large starting contrast is taken in the bulk density or instead in the interstitial fluid density. We record the streamwise liftoff location for the dense current as a function of the chosen density contrast for settling velocities beyond the range of validity of present day models.