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2000 Instability of a free swirling jet driven by a halfline vortex
 Proc
"... By studying similarity solutions of the Navier–Stokes equations, which represent swirling jets of a viscous incompressible fluid, we develop a new stability approach, and elucidate the nature of perturbations that cause hysteresis and break axisymmetry. As an example, we consider a jet in an infini ..."
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By studying similarity solutions of the Navier–Stokes equations, which represent swirling jets of a viscous incompressible fluid, we develop a new stability approach, and elucidate the nature of perturbations that cause hysteresis and break axisymmetry. As an example, we consider a jet in an infinite fluid driven by a halfline vortex: a model of a tornado and of a leadingedge vortex above the delta wing of an aircraft. The approach reduces the problem of spatial stability of these strongly nonparallel flows to an ordinary differential system and thereby eases the analysis. We show how nonuniqueness of the solutions appears through cusp and fold catastrophes as the swirl Reynolds number, Res, increases, and find that the fold instability is due to disturbances at the outer boundary of the flow. Also, we study the breaking of axisymmetry due to steady threedimensional disturbances, and reveal that a helical instability occurs due to disturbances at the inner boundary of the flow. Both the fold and helical instabilities occur for moderate values of Res. Finally, we deduce an amplitude equation, similar to the Ginzburg–Landau equation, to describe the weakly nonlinear spatiotemporal growth of disturbances when Res is slightly above its critical value for linear stability. Thus, our results reveal new features of axisymmetric and helical vortex breakdown in jets.
Lamb vector properties of swirling jets
 15th Australasian Fluid Mechanics Conference
, 2004
"... Swirling jets show at Reynolds numbers in the transitional and low turbulence regime several competing flow forms due to shear and centrifugal instabilities. The swirling flow in jets at swirl numbers high enough to generate breakdown bubbles is simulated numerically using an accurate NavierStokes ..."
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Swirling jets show at Reynolds numbers in the transitional and low turbulence regime several competing flow forms due to shear and centrifugal instabilities. The swirling flow in jets at swirl numbers high enough to generate breakdown bubbles is simulated numerically using an accurate NavierStokes solver in cylindrical coordinates. The vector lines for vorticity and the Lamb vector are computed and analyzed in detail. The main result is that the set of critical points of the Lamb vector field contains stable and unstable manifolds characterizing high shear regions.
Effect of deceleration on jet instability
, 2001
"... A nonparallel analysis of timeoscillatory instability of conical jets reveals important features not found in prior studies. Flow deceleration significantly enhances the shearlayer instability for both swirlfree and swirling jets. In swirlfree jets, flow deceleration causes the axisymmetric ins ..."
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A nonparallel analysis of timeoscillatory instability of conical jets reveals important features not found in prior studies. Flow deceleration significantly enhances the shearlayer instability for both swirlfree and swirling jets. In swirlfree jets, flow deceleration causes the axisymmetric instability (absent in the parallel approximation). The critical Reynolds number Rea for this instability is an order of magnitude smaller than the critical Rea predicted before for the helical instability (where Rea = rva/ν, r is the distance from the jet source, va is the jet maximum velocity at a given r, and ν is the viscosity). Swirl, intensifying the divergence of streamlines, induces an additional, divergent instability (which occurs even in shearfree flows). For the swirl Reynolds number Res (circulation to viscosity ratio) exceeding 3, the critical Rea for the singlehelix counterrotating mode becomes smaller than those for axisymmetric and multihelix modes. Since the critical Res is less than 10 for the nearaxis jets, the boundarylayer approximation (used before) is invalid, as is Long’s Type II boundarylayer solution (whose stability has been extensively studied). Thus, the nonparallel character of jets strongly affects their stability. Our results, obtained in a farfield approximation allowing reduction of the linear stability problem to ordinary differential equations, are more valid for short wavelengths. 1.
Evolution of topology in axisymmetric and 3d viscous flows
"... Topological methods are used to establish global and to extract local structure properties of vector fields in axisymmetric and 3d flows as function of time. The notion of topological skeleton is applied to the interpretation of vector fields generated numerically by the NavierStokes equations. T ..."
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Topological methods are used to establish global and to extract local structure properties of vector fields in axisymmetric and 3d flows as function of time. The notion of topological skeleton is applied to the interpretation of vector fields generated numerically by the NavierStokes equations. The flows considered are swirling jets with supercritical swirl numbers that show low Reynolds number turbulence in the breakup region. 1
Generation of collimated jets by a point source of heat and gravity
"... New solutions of the Boussinesq equations describe the onset of convection as well as the development of collimated bipolar jets near a point source of both heat and gravity. Stability, bifurcation, and asymptotic analyses of these solutions reveal details of jet formation. Convection (with l cells ..."
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New solutions of the Boussinesq equations describe the onset of convection as well as the development of collimated bipolar jets near a point source of both heat and gravity. Stability, bifurcation, and asymptotic analyses of these solutions reveal details of jet formation. Convection (with l cells) evolves from the rest state at the Rayleigh number Ra = Ra cr = (l − 1)l(l + 1)(l + 2). Bipolar (l = 2) flow emerges at Ra = 24 via a transcritical bifurcation: Re = 7(24 − Ra)/(6 + 4P r), where Re is a convection amplitude (dimensionless velocity on the symmetry axis) and P r is the Prandtl number. This flow is unstable for small positive values of Re but becomes stable as Re exceeds some threshold value. The highRe stable flow emerges from the rest state and returns to the rest state via hysteretic transitions with changing Ra. Stable convection attains high speeds for small P r (typical of electrically conducting media, e.g. in cosmic jets). Convection saturates due to negative 'feedback': the flow mixes hot and cold fluids thus decreasing the buoyancy force that drives the flow. This 'feedback' weakens with decreasing P r, resulting in the development of highspeed convection with a collimated jet on the axis. If swirl is imposed on the equatorial plane, the jet velocity decreases. With increasing swirl, the jet becomes annular and then develops flow reversal on the axis. Transforming the stability problem of this strongly nonparallel flow to ordinary differential equations, we find that the jet is stable and derive an amplitude equation governing the hysteretic transitions between steady states. The results obtained are discussed in the context of geophysical and astrophysical flows. Introduction This paper deals with a very simple buoyancy problem: thermal convection near a point source of heat and gravity. Despite its apparent simplicity, the problem is rich in interesting effects such as hysteresis, flow reversal, and collapse; the most intriguing among them is the development of highly collimated bipolar jets. We attempt here to explain these effects with the help of exact solutions of the Boussinesq equations. The spherical symmetry of the equilibrium state of rest and the conical similarity of the emerging buoyancydriven flow allow us to obtain analytical solutions for (i) the linear stability problem of the rest state, (ii) the weakly nonlinear problem of flow bifurcation, and (iii) the strongly nonlinear problem of the formation of highspeed jets. There is a practical relevance of this simple convection problem to geophysical and astrophysical situations, particularly in the formation of collimated cosmic jets. This relevance is discussed at the end of the paper. Here, we present (i) a new stability approach for conically similar convection, (ii) a