Keiko K. Nomura

The structure and dynamics of vorticity and rate of strain in incompressible homogeneous turbulence

The structure and dynamics of vorticity ω and rate of strain S are studied using direct numerical simulations (DNS) of incompressible homogeneous isotropic turbulence. In particular, characteristics of the pressure Hessian Π , which describe non-local interaction of ω and S , are presented. Conditional Lagrangian statistics which distinguish high-amplitude events in both space and time are used to investigate the physical processes associated with their evolution. The dynamics are examined on the principal strain basis which distinguishes vortex stretching and induced rotation of the principal axes of S . The latter mechanism is associated with misaligned ω with respect to S , a condition which predominates in isotropic turbulence and is dynamically significant, particularly in rotation-dominated regions of the flow. Locally-induced rotation of the principal axes acts to orient ω towards the direction of either the intermediate or most compressive principal strain. The tendency towards compressive straining of ω is manifested at the termini of the high-amplitude tube-like structures in the flow. Non-locally-induced rotation, associated with Π , tends to counteract the locally-induced rotation. This is due to the strong alignment between ω and the eigenvector of Π corresponding to its smallest eigenvalue and is indicative of the controlling influence of the proximate structure on the dynamics. High-amplitude rotation-dominated regions deviate from Burgers vortices due to the misalignment of ω . Although high-amplitude strain-dominated regions are promoted primarily by local dynamics, the associated spatial structure is less organized and more discontinuous than that of rotation-dominated regions.

Mixing characteristics of an inhomogeneous scalar in isotropic and homogeneous sheared turbulence

Turbulent mixing of an inhomogeneous passive scalar field is studied in the context of a nonpremixed reacting flow. Direct numerical simulations of an initial steplike scalar field subjected to homogeneous sheared turbulence have been performed and the results compared with those of the case of decaying isotropic turbulence. For both flow conditions, the gradient of the conserved scalar tends to align itself with the axis of the most compressive strain rate and orthogonal to the local vorticity. The magnitude of the scalar gradient is directly influenced by the local strain rate while its orientation is controlled by the local vorticity. Because of the directional features of sheared turbulence, the orientation of the scalar gradient is more ordered than in isotropic turbulence. In addition, the magnitude of vorticity indirectly affects that of the scalar gradient through strain‐rate amplification by vortex stretching. In both flows, regions of high scalar‐gradient magnitude or scalar dissipation (and the...

Interaction of vorticity, rate-of-strain, and scalar gradient in stratified homogeneous sheared turbulence

The structure and dynamics of stably stratified homogeneous sheared turbulence is investigated in terms of the triadic interaction of vorticity ω, rate-of-strain S, and scalar (density fluctuation) gradient G≡∇ρ′. Results of direct numerical simulations are presented. Due to the presence of the mean velocity and scalar gradients, distinct directional preferences develop which affect the dynamics of the flow. The triadic interaction is described in terms of the direct coupling of primary mechanism pairs and influential secondary effects. Interaction of ω and S is characterized by the coupling of vortex stretching and locally-induced rotation of the S axes. Due to the intrinsic directionality of baroclinic torque, the generated ω acts to impede S axes rotation. Interaction of ω and G involves an inherent negative feedback between baroclinic torque and reorientation of G by ω. This causes baroclinic torque to act as a sink which promotes decay of ω2. Interaction of S and G is characterized by a positive feed...

The physics of vortex merger : Further insight

Results of numerical simulations provide further insight on the physical mechanisms associated with symmetric vortex merger. The relative contributions of filament and exchange band fluid to the reduction in the vortex separation are determined and the latter is found to be dominant. A key underlying process is the interaction of strain rate and vorticity gradient near the center of rotation, through which a tilt in the vorticity contours is established. This leads to the entrainment of core fluid into the exchange band, which is transformed into a single vortex.

The structure of inhomogeneous turbulence in variable density nonpremixed flames

Some observations concerning the structure of turbulence associated with an exothermic nonpremixed reacting flow are presented. Direct numerical simulations (DNS) with a resolution of 1283 grid points and an initial Reynolds number Rλ=33 provide data for the analysis. In these simulations the density varies with temperature and the resulting flow field is inhomogeneous. Conditional probabilities of the vorticity and rate-of-strain, three-dimensional visualization, and topological characteristics are presented and compared with those of a constant density flow. Initially, thermal expansion causes significant changes in the small-scale statistics. As the development continues, the statistics reflect the competing mechanisms of vortex stretching, dilatation, and baroclinic torque. Preferential alignment of the vorticity with the eigenvector associated with either the intermediate or most extensional principal strain is observed depending on the value of the local mixture fraction. Intermittent vortex structures tend to exist as sheets or ribbons rather than tubes due to the diminishing levels of vorticity and a change in the distribution and preferential orientation of the principal strains. Topological characteristics not present in constant density flows are observed. However, as the flow develops and the divergence decreases, the topology becomes similar to those of incompressible turbulence.

Short-wavelength instability and decay of a vortex pair in a stratified fluid

The evolution of a counter-rotating vortex pair in a stably stratified fluid is investigated using direct numerical simulations. The study focuses on the short-wavelength elliptic instability occurring in this flow and the subsequent decay of the vortices. Depending on the level of stratification, as characterized by the Froude number which indicates the time scale of buoyancy to that of the instability, and the stage of evolution, stratification effects may significantly alter the behaviour of the flow. In the case of weak to moderate stratification, the elliptic instability develops qualitatively in the same manner as in unstratified fluid. The primary effect of stratification is to reduce the vortex separation distance which enhances the mutually induced strain. Consequently, the instability has an earlier onset and higher growth rate with increasing stratification. The behaviour is essentially described by linear stability theory for unstratified flow if the varying separation distance is taken into account. On the other hand, the final breakdown and decay of the flow may be greatly modified by stratification since buoyancy effects eventually emerge after sufficient time has elapsed. The decay is enhanced owing to additional mechanisms not present in unstratified flow. Secondary vertical vortex structures form between the primary vortices promoting fluid exchange in the transverse direction. Detrainment of fluid from the primary vortices by the generated baroclinic torque also contributes to the more rapid breakdown of the flow. In the case of strong stratification, in which the time scale of buoyancy is comparable to that of the instability, the flow is significantly altered. As a result of strong baroclinic torque, the primary vortices are brought together and detrainment occurs earlier. The associated reduction in radii of the vortices results in a higher axial wave mode and a more complex radial structure of the instability. Detrainment and mixing accelerate their decay. Late time evolution is dominated by the successive generation of alternate signed baroclinic torque which results in an oscillation of the total flow circulation at the buoyancy frequency.

The interaction of vorticity and rate-of-strain in homogeneous sheared turbulence

The coupled interaction of vorticity ω and rate-of-strain S in homogeneous sheared turbulence is investigated using direct numerical simulation. Conditional sampling and comparison with linear simulations reveal various aspects of the structure and dynamics. Due to the influence of the imposed ω and S, distinct directional features develop. Initial stretching of fluctuating ω by mean extensional strain and the presence of mean vorticity establish a predominant misalignment of ω with respect to the principal axes of S. The associated locally induced rotation of the S axes results in preferred orientations in ω and S. In high amplitude rotation-dominated regions of the flow, distinct characteristics are exhibited by the pressure Hessian Π due to the presence of small-scale spatial structure. Nonlocally induced S axes rotation through Π tends to counteract locally induced rotation in these regions. These features are absent in the linear flow which suggests a lack of spatial coherence in the corresponding in...

The physics of vortex merger and the effects of ambient stable stratification

The merging of a pair of symmetric, horizontally oriented vortices in unstratified and stably stratified viscous fluid is investigated. Two-dimensional numerical simulations are performed for a range of flow conditions. The merging process is resolved into four phases of development and key underlying physics are identified. In particular, the deformation of the vortices, explained in terms of the interaction of vorticity gradient, ∇ω, and rate of strain, S , leads to a tilt in ω contours in the vicinity of the center of rotation (a hyperbolic point). In the diffusive/deformation phase, diffusion of the vortices establishes the interaction between ∇ω and mutually induced S . During the convective/deformation phase, induced flow by filaments and, in stratified flow, baroclinically generated vorticity (BV), advects the vortices thereby modifying S , which, in general, may enhance or hinder the development of the tilt. The tilting and diffusion of ω near the center hyperbolic point causes ω from the core region to enter the exchange band where it is entrained. In the convective/entrainment phase, the vortex cores are thereby eroded and ultimately entrained into the exchange band, whose induced flow becomes dominant and transforms the flow into a single vortex. The critical aspect ratio, associated with the start of the convective/entrainment phase, is found to be the same for both the unstratified and stratified flows. In the final diffusive/axisymmetrization phase, the flow evolves towards axisymmetry by diffusion. In general, the effects of stratification depend on the ratio of the diffusive time scale (growth of cores) to the turnover time (establishment of BV), i.e. the Reynolds number. A crossover Reynolds number is found, above which convective merging is accelerated with respect to unstratified flow and below which it is delayed.

The structure and dynamics of overturns in stably stratified homogeneous turbulence

Direct numerical simulations of stably stratified homogeneous turbulence, with and without mean shear, are used to investigate the three-dimensional structure, evolution and energetic significance of density overturns. Although the flow conditions are idealized, examination of the full-field simulation data provides insight into flow energetics and mixing which may assist in the interpretation of physical measurements, typically limited to one-dimensional vertical profiles. Overturns, defined here through the density field as contiguous regions of non-zero Thorpe displacement, are initially generated by the stirring action of coherent vortex structures present in the flow and further develop through merging with adjacent overturns. During this growth phase, overturns exhibit irregular spatial structure in unsheared flow and elongated structure with distinct orientation in shear flow. Although most of the available potential energy (APE) and buoyancy flux are associated with stable (non-overturning) regions in the flow, young overturns actively contribute to the flow energetics. In particular, overturn peripheries are sites of high levels of APE, buoyancy flux and diapycnal mixing. A collapse phase may follow the growth phase in the absence of adequately strong mean shear. During this phase, buoyancy gradually assumes control of the overturns and their vertical scale steadily decreases. The energetic significance of the overturns diminishes, although high APE and diapycnal mixing continue to occur near their boundaries. In the final phase of their evolution, overturns contribute negligibly to the energetics. The remaining overturns are characterized by a viscous–buoyant balance which maintains their vertical scale. The overturns eventually vanish due to homogenization of their internal density distribution by diffusion. Activity diagrams, sampled at different points of flow evolution, show significant variation in overturn Reynolds and Froude numbers which may have implications for vertical sampling of a turbulent event.

Modernization of Legacy Application Software

Legacy application software is typically written in a dialect of Fortran, and must be reprogrammed to run on today’s microprocessor-based multicomputer architectures. We describe our experiences in modernizing a legacy direct numerical simulation (DNS) code with the KeLP software infrastructure. The resultant code runs on the IBM SP2 with higher numerical resolutions than possible with the legacy code running on a vector mainframe.