The motion of tracer particles is kinematically simulated around three elementary flow patterns; a Burgers vortex, a shear-layer structure with coincident vortices and a node-saddle topology. These patterns are representative for their broader class of coherent structures in turbulence. Therefore, examining the dispersion in these elementary structures can improve the general understanding of turbulent dispersion at short time scales. The shear-layer structure and the node-saddle topology exhibit similar pair dispersion statistics compared to the actual turbulent flow for times up to (Formula presented.), where, (Formula presented.) is the Kolmogorov time scale. However, oscillations are observed for the pair dispersion in the Burgers vortex. Furthermore, all three structures exhibit Batchelor’s scaling. Richardson’s scaling was observed for initial particle pair separations (Formula presented.) for the shear-layer topology and the node-saddle topology and was related to the formation of the particle sheets. Moreover, the material line orientation statistics for the shear-layer and node-saddle topology are similar to the actual turbulent flow statistics, up to at least (Formula presented.). However, only the shear-layer structure can explain the non-perpendicular preferential alignment between the material lines and the direction of the most compressive strain, as observed in actual turbulence. This behaviour is due to shear-layer vorticity, which rotates the particle sheet generated by straining motions and causes the particles to spread in the direction of compressive strain also. The material line statistics in the Burgers vortex clearly differ, due to the presence of two compressive principal straining directions as opposed to two stretching directions in the shear-layer structure and the node-saddle topology. The tetrad dispersion statistics for the shear-layer structure qualitatively capture the behaviour of the shape parameters as observed in actual turbulence. In particular, it shows the initial development towards planar shapes followed by a return to more volumetric tetrads at approximately (Formula presented.), which is associated with the particles approaching the vortices inside the shear layer. However, a large deviation is observed in such behaviour in the node-saddle topology and the Burgers vortex. It is concluded that the results for the Burgers vortex deviated the most from actual turbulence and the node-saddle topology dispersion exhibits some similarities, but does not capture the geometrical features associated with material lines and tetrad dispersion. Finally, the dispersion around the shear-layer structure shows many quantitative (until 2–(Formula presented.)) and qualitative (until (Formula presented.)) similarities to the actual turbulence.

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Turbulence is implicitly present or explicitly desired in many natural and industrial processes, such as, flow over solid surfaces, cloud formation, pollination, combustion, and chemical mixing. Hence, a better understanding of turbulence can aid in fuel saving by reducing drag in the case of flow over solid surfaces, namely, cars, airplanes, and ships. Furthermore, cloud formation models for refining weather modeling as well as the modeling of chemical mixing and combustion can be enhanced. However, there are different approaches to understand turbulence and in this thesis, turbulence is studied in terms of coherent structures...@en

The scaling of turbulent motions is investigated by considering the flow in the eigenframe of the local strain-rate tensor. The flow patterns in this frame of reference are evaluated using existing direct numerical simulations of homogeneous isotropic turbulence over a Reynolds number range from up to 1131, and also with reference to data for inhomogeneous, anisotropic wall turbulence. The average flow in the eigenframe reveals a shear layer structure containing tube-like vortices and a dissipation sheet, whose dimensions scale with the Kolmogorov length scale, . The vorticity stretching motions scale with the Taylor length scale, , while the flow outside the shear layer scales with the integral length scale, . Furthermore, the spatial organization of the vortices and the dissipation sheet defines a characteristic small-scale structure. The overall size of this characteristic small-scale structure is in all directions based on the coherence length of the vorticity. This is considerably larger than the typical size of individual vortices, and reflects the importance of spatial organization at the small scales. Comparing the overall size of the characteristic small-scale structure with the largest flow scales and the vorticity stretching motions on the scale of shows that transitions in flow structure occur where and 250. Below these respective transitional Reynolds numbers, the small-scale motions and the vorticity stretching motions are progressively less well developed. Scale interactions are examined by decomposing the average shear layer into a local flow, which is induced by the shear layer vorticity, and a non-local flow, which represents the environment of the characteristic small-scale structure. The non-local strain is in width and height, which is consistent with observations in high Reynolds number flow of a wide instantaneous shear layer with many -scale vortical structures inside (Ishihara et al., Flow Turbul. Combust., vol. 91, 2013, pp. 895–929). In the average shear layer, vorticity aligns with the intermediate principal strain at small scales, while it aligns with the most stretching principal strain at larger scales, consistent with instantaneous turbulence. The length scale at which the alignment changes depends on the Reynolds number. When conditioning the flow in the eigenframe on extreme dissipation, the velocity is strongly affected over large distances. Moreover, the associated peak velocity remains Reynolds number dependent when normalized by the Kolmogorov velocity scale. It signifies that extreme dissipation is not simply a small-scale property, but is associated with large scales at the same time.@en

For channel flow, we explore how commonly found weak eddies can still auto-generate and produce new eddies. Before, only strong eddies (above a threshold strength) were considered to auto-generate. Such strong eddies are rarely observed in actual turbulent flows however. Here, the evolution of two weak conditional eddies with different initial strengths, initial sizes, and initial stream-wise spacing between them is studied. The numerical procedure followed is similar to Zhou et al. [“Mechanisms for generating coherent packets of hairpin vortices in channel flow,” J. Fluid Mech. 387, 353 (1999)]. The two eddies are found to merge into a single stronger eddy when the initial upstream eddy is taller than the downstream eddy, which further auto-generates when the initial stream-wise separation is small (<120 wall units). However, it is observed that non-merging cases with small initial stream-wise separation also auto-generated. In the initial condition, the two conditional eddies are placed near to each other so their velocity fields (low-speed streaks and ejection events) get superimposed and amplified as a function of stream-wise spacing. To examine this effect, a divergence free low-speed streak is superimposed on an eddy. It is found that these low-speed streak simulations do not auto-generate. On the other hand, a rapid lift-up of an eddy by ejection events plays a role in the onset of auto-generation, which also leads to a modified interpretation of auto-generation mechanism. It differed from the existing auto-generation mechanism at the later stages of auto-generation where blockage of mean flow and shear layer deformation is considered instead of vortex dynamics.@en

For channel flow, we explore how commonly found weak eddies can still auto-generate and produce new eddies. Before, only strong eddies (above a threshold strength) were considered to auto-generate. Such strong eddies are rarely observed in actual turbulent flows however. Here, the evolution of two weak conditional eddies aligned in stream-wise direction is studied. The numerical procedure followed is similar to Zhou et al. (1999). The two eddies are found to merge into a single stronger eddy when the initial upstream eddy is taller than the downstream eddy, which further auto-generates when the initial stream-wise separation is small (<120 wall units). It is also observed that non-merging cases with small initial stream-wise separation auto-generated. The rapid lift-up of an eddy by ejection events is found to play a role in the onset of auto-generation. This lead to a modified interpretation at the later stages of auto-generation mechanism where blockage of mean flow and shear layer deformation are considered instead of vortex dynamics.@en

For channel flow, we explore how the interaction of weak eddies produces additional eddies by means of auto-generation. This is done by DNS of two eddies with different initial strengths, initial sizes and initial stream-wise spacing between them. The numerical procedure followed is similar to Zhou et al[1]. The two eddies merge into a single stronger eddy when a larger upstream and a smaller downstream eddy are placed within a certain initial stream-wise separation distance. Subsequently, the resulting stronger eddy is observed to auto-generate new eddies. The non-merging cases with small initial stream wise separation also auto-generate. The auto-generation is characterized by a rapid lift-up of an initial eddy, which blocks the incoming flow and leads to shear- layer roll-up and formation of a new eddy. The same sequence of events is observed in a fully developed turbulent boundary layer[2].@en

Pair dispersion is studied to model scalar transport in many natural and industrial applications. The link between the particle pair dispersion and coherent flow structures is explored in this work. This was done by kinematically simulating tracer particles in an ideal flow structure [4] extracted from an isotropic turbulent flow. It was found that the variation of the mean and the mean square separation lengths with time were qualitative similar to the results in actual turbulent flows. It was also observed that the quantitative results matched till 4-5 Kolmogrov time units. Ideal structure with two vortices and a shear layer was able to emulate the qualitative results. Is the combination of shear layer and one/two vortices is sufficient or necessary to emulate pair dispersion statistics needs to be studied in the future.@en

For channel flow, we explore how a hairpin eddy may reach a threshold strength required to produce additional hairpins by means of auto-generation. This is done by studying the interaction of two eddies with different initial strengths (but both below the threshold strength), initial sizes and initial streamwise spacing between them. The numerical procedure followed is similar to Zhou et al. (1999). The two eddies were found to merge into a single stronger
eddy in case of a larger upstream and a smaller downstream eddy placed within a certain initial streamwise separation distance. Subsequently, the resulting stronger eddy was observed to auto-generate new eddies. Merging of eddies thus is a viable explanation for the creation of the threshold strength eddies.@en

For channel flow, we explore how a hairpin eddy may reach a threshold strength required to produce additional hairpins by means of auto-generation. This is done by studying the evolution of two eddies with different initial strengths (but both below the threshold strength), initial sizes and initial stream-wise spacing between them. The numerical procedure followed is similar to Zhou et al [1]. The two eddies were found to merge into a single stronger eddy in case of a larger upstream and a smaller downstream eddy placed within a certain initial stream-wise separation distance. Subsequently, the resulting stronger eddy was observed to auto-generate new eddies. Merging of eddies thus is a viable explanation for the creation of the threshold strength eddies. \[4pt] [1] J. Zhou, R.J. Adrian, S. Balachandar, and T.M. Kendall, Journal of Fluid Mechanics, 387:353-396, 1999.@en