Results are presented from an experimental study into the fine-scale structure of generic, Sc≈1, dynamically passive, conserved scalar fields in turbulent shear flows. The investigation was based on highly resolved, two-dimensional imaging of laser Rayleigh scattering, with measurements obtained in the self-similar far field of an axisymmetric coflowing turbulent jet of propane issuing into air at local outer-scale Reynolds numbers Reδ≡uδ/v of 11000 and 14000. The resolution and signal quality of these measurements allowed direct differentiation of the scalar field data ζ(x, t) to determine the instantaneous scalar energy dissipation rate field (Re Sc)−1∇ζ·∇ζ(x, t). Results show that, as for large-Sc scalars (Buch & Dahm 1996), the scalar dissipation rate field consists entirely of strained, laminar, sheet-like diffusion layers, despite the fact that at Sc≈1 the scale on which these layers are folded by vorticity gradients is comparable to the layer thickness. Good agreement is found between the measured internal structure of these layers and the self-similar local solution of the scalar transport equation for a spatially uniform but time-varying strain field. The self-similar distribution of dissipation layer thicknesses shows that the ratio of maximum to minimum thicknesses is only 3 at these conditions. The local dissipation layer thickness is related to the local outer scale as λD/δ ≡ΛRe−3/4δSc−1/2, with the average thickness found to be 〈Λ〉=11.2, with both the largest and smallest layer thicknesses following Kolmogorov Re−3/4δ) scaling.

We present results from an experimental and numerical investigation into the structure of vortex patterns and the dynamics of their interactions for the incompressible flow in the near field of a round coaxial jet issuing into a quiescent ambient fluid. A two-colour planar laser-induced-fluorescence technique is used to document the flow field via still photographs and ciné sequences over a limited range of parameters. We examine the effects of varying the velocity ratio as well as the absolute velocities of the two coaxial streams for equal densities and for a single area ratio. Results show that a variety of widely differing near-field vortex patterns can arise, with very different interaction dynamics, which can depend both on the velocity ratio and on the absolute velocities of the two streams. The observed vortex structures and their dynamics are interpreted in terms of the instability of the initially cylindrical and concentric vorticity layers separating each of the fluid streams, and their subsequent rollup to form wake-like or shear-layer-like vortices. Our results show that in addition to the velocity jump across each of these vorticity layers, an accounting of the layer thicknesses and the wake defect within each layer can be essential to understanding the resulting near-field structure that occurs. Ensuing dynamical interactions between the vortices formed from each layer can produce a strong coupling between the development of the two layers. These resulting vortex structures and interaction dynamics are also seen to produce widely differing mixing patterns in the jet near field.

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A direct Biot-Savart integration is used to decompose the strain rate into its local and nonlocal constituents, allowing the vorticity alignment with the local and nonlocal strain rate eigenvectors to be investigated. These strain rate tensor constituents are evaluated in a turbulent flow using data from highly-resolved direct numerical simulations. While the vorticity aligns preferentially with the intermediate eigenvector of the combined strain rate, as has been observed previously, the present results for the first time clearly show that the vorticity aligns with the most extensional eigenvector of the nonlocal strain rate. This in turn reveals a significant linear contribution to the vortex stretching dynamics in turbulent flows. 47.27.De The alignment of vorticity with the strain rate eigenvectors in turbulent flows has been a subject of considerable interest over the past two decades. Since the initial finding [1] that the vorticity shows a preferred alignment with the intermediate eigenvector of the strain rate tensor, there have been numerous studies seeking to understand the reasons for this result, and various theoretical approaches have been proposed to explain the failure of the vorticity to align with the most extensional strain rate eigenvector.In this Letter, we help resolve this issue by showing that vorticity in turbulence does tend toward alignment with the most extensional eigenvector of the nonlocal (background) strain, namely the strain field induced in the immediate region around any vortical structure by the surrounding vorticity outside this region. The anomalous alignment occurs with the eigenvectors of the combined strain rate, namely the sum of this nonlocal background strain and the local strain induced in the region by the vorticity within it.Alignment of the vorticity vector ω ≡ ∇ × u with the strain rate tensor S ij in three-dimensional incompressible turbulent flows is ultimately responsible for the transfer of kinetic energy between scales, and for the nonlinearity in the dynamics of the underlying vorticity field. The inverse curl operator is the Biot-Savart integral that gives the velocity field u from the vorticity field ω asThe resulting gradients of u define the strain rate tensor S ij = 1 2 (∂u i /∂x j + ∂u j /∂x i ) which, in turn, is coupled to the dynamics of the vorticity asOn the right side of (2), the magnitude of the stretching term |S ij ω j | ≡ ω[s 2 i (e i · e ω ) 2 ] 1/2 depends on the strain rate eigenvalues s i and the vorticity magnitude ω ≡ (ω i ω i ) 1/2 , and on the alignment cosines (e i · e ω ) between the vorticity unit vector e ω and the strain rate eigenvectors e i .The strain rate eigenvalues s i can be ordered as s 1 ≥ s 2 ≥ s 3 , so that incompressibility (s 1 + s 2 + s 3 ≡ 0) requires s 1 ≥ 0 and s 3 ≤ 0. The positivity of s 1 and the negativity of s 3 correspond, respectively, to extensional and compressional straining along the e 1 and e 3 directions. While the intermediate eigenvalue s 2 is on average weakly positive in turbulent flows, the in...

We present results from an experimental investigation into the fine-scale structure associated with the mixing of a dynamically passive conserved scalar quantity on the inner scales of turbulent shear flows. The present study was based on highly resolved two- and three-dimensional spatio-temporal imaging measurements. For the conditions studied, the Schmidt number (Sc ≡ v/D) was approximately 2000 and the local outerscale Reynolds number (Reσ≡ uσ/v) ranged from 2000 to 10000. The resolution and signal quality allow direct differentiation of the measured scalar field ζ(x, t) to give the instantaneous scalar energy dissipation rate field (Re Sc)−1 ∇ζċ∇ζ(x, t). The results show that the fine-scale structure of the scalar dissipation field, when viewed on the inner-flow scales for Sc ≡ 1, consists entirely of thin strained laminar sheet-like diffusion layers. The internal structure of these scalar dissipation sheets agrees with the one-dimensional self-similar solution for the local strain–diffusion competition in the presence of a spatially uniform but time-varying strain rate field. This similarity solution also shows that line-like structures in the scalar dissipation field decay exponentially in time, while in the vorticity field both line-like and sheet-like structures can be sustained. This sheet-like structure produces a high level of intermittency in the scalar dissipation field – at these conditions approximately 4% of the flow volume accounts for nearly 25% of the total mixing achieved. The scalar gradient vector field ∇ζ(x, t) for large Sc is found to be nearly isotropic, with a weak tendency for the dissipation sheets to align with the principal axes of the mean flow strain rate tensor. Joint probability densities of the conserved scalar and scalar dissipation rate have a shape consistent with this canonical layer-like fine-scale structure. Statistics of the conserved scalar and scalar dissipation rate fields are found to demonstrate similarity on inner-scale variables even at the relatively low Reynolds numbers investigated.

We present results from an experimental and numerical investigation into the dynamics of the interaction between a planar vortex pair or axisymmetric vortex ring with lengthscale a and circulation Γ encountering a planar interface of thickness δ across which the fluid density increases from ρ1 to ρ2. Similarity considerations indicate that baroclinic generation of vorticity and its subsequent interaction with the original vortex is governed by two dimensionless parameters, namely (a/δ) A and R, where A ≡ (ρρ2 − ρ1)/(ρ2 + ρ1) and R ≡ (a3g/Γ2). For thin interfaces (δ [Lt ] a), the interaction is governed only by the parameters A and R. Furthermore, in the Boussinesq limit (A → 0), the dynamics are governed solely by the product AR and the interaction is entirely invertible with respect to the initial locations and direction of propagation of the vortices. We document details of the interaction dynamics in the Boussinesq limit over a range of the parameter AR. Results show that, for relatively small values of AR, rather than the vortex simply rebounding at the interface, its outermost layers are instead successively ‘peeled’ away by baroclinically generated vorticity and form a topologically complex backflow in which the ring fluid, the light fluid and the heavy fluid are intertwined. For larger values of AR the vortex barely penetrates the interface, and our results suggest that in the limit AR → ∞ the interaction with a density interface becomes similar to the interaction at a solid wall. We also present results for thick interfaces in the Boussinesq limit, as well as larger density jumps for which the density parameter A enters as a second similarity quantity. Comparison of the experimental and numerical results demonstrate that many of the features of such interactions can be understood within the context of inviscid fluids, and that inviscid vortex methods can be used to accurately simulate the dynamics of such interactions.

Local and nonlocal contributions to the total strain rate tensor Sij at any point x in a flow are formulated from an expansion of the vorticity field in a local spherical neighborhood of radius R centered on x. The resulting exact expression allows the nonlocal (background) strain rate tensor S B ij (x) to be obtained from Sij (x). In turbulent flows, where the vorticity naturally concentrates into relatively compact structures, this allows the local alignment of vorticity with the most extensional principal axis of the background strain rate tensor to be evaluated. In the vicinity of any vortical structure, the required radius R and corresponding order n to which the expansion must be carried are determined by the viscous lengthscale λν. We demonstrate the convergence to the background strain rate field with increasing R and n for an equilibrium Burgers vortex, and show that this resolves the anomalous alignment of vorticity with the intermediate eigenvector of the total strain rate tensor. We then evaluate the background strain field S B ij (x) in DNS of homogeneous isotropic turbulence where, even for the limited R and n corresponding to the truncated series expansion, the results show an increase in the expected equilibrium alignment of vorticity with the most extensional principal axis of the background strain rate tensor.