Geometry and dynamics of coherent structures in the stably stratified atmospheric boundary layer

Abstract

Turbulence in stable boundary layers (SBL) is often accompanied by the presence of large patches of non-turbulent flow regions, even close to the wall, a phenomenon referred in literature as global intermittency. Understanding the physical processes and dynamics of this mode of rotating, stratified and intermittent turbulence is important for the improvement of existing and/or development of new parametrizations of the SBL, which in turn, may be useful for many applications, including but not limited to numerical weather prediction, modeling gas dispersion events and understanding the Arctic climate system. In this thesis, the SBL is investigated by establishing a detailed comparison with the well-studied neutrally stratified atmospheric boundary layer. The datasets examined here were inherited through the work of Ansorge (Dissertation, Springer 2016). They used a simplified physical configuration, namely, an Ekman flow over a smooth wall where global intermittency is known to occur beyond a certain stability despite the absence of surface heterogeneities and other external perturbations.

Comparisons between both regimes is accomplished with the help of coherent structures, particularly with their geometry. This is motivated from previous observations where a change in the geometry of these structures from hairpin vortices under neutral conditions to thermal plumes under unstable conditions (where there is a positive buoyancy flux) has been detected. However, very little is known about the geometry of these structures, especially their three-dimensional character, when buoyancy has a stabilizing effect. Since a well-accepted definition of a coherent structure has not yet surfaced, the classification of boundary layer structures introduced by Robinson (Dissertation, Stanford 1991), henceforth referred to as Robinson structures, is used to study the various structures identified in literature in an organized manner. Suitable scalar indicators are identified for all eight categories of Robinson structures and they are grouped as quantitative and qualitative, the former of which can be extracted and geometrically characterized.

First, a framework to characterize the geometry of quantitative Robinson structures is developed. There are two main steps: extraction and geometrical characterization. In the extraction step, individual structures are obtained by thresholding scalar indicators. An improvement to the neighbor scanning procedure of Moisy and Jimenez (J. Fluid Mech. 2004) with the marching cubes algorithm is developed to extract visualization accurate structures. Optimum thresholds are identified with the percolation analysis approach of del Alamo et al. (J. Fluid Mech. 2006). However, it is seen that this fails when the flow is strongly intermittent. Therefore, an extension of this method where percolation analysis is applied in an iterative manner is introduced. In the second step, noise-like structures are filtered out by discarding structures having a fractal dimension less than 1. The remaining structures are subjected to the non-local methodology of Bermejo-Moreno and Pullin (J. Fluid Mech. 2008) to classify a structure as blob-like, tube-like or sheet-like based on its location within a three-dimensional visualization space composed of two differential geometry parameters - shape index and curvedness, and a stretching parameter.

Next, the framework is applied to structures obtained from instantaneous neutral and stably stratified Ekman flow fields with increasing stability. Results are discussed by dividing the flow field into four layers in the wall-normal direction: viscous sublayer, buffer, inner and outer layers. Geometrical characterization reveals that the structures are moderately stretched tube-like or moderate to strongly stretched sheet-like regardless of the strength of stratification. Furthermore, in the strongly stratified case, it is shown that global intermittency has a direct impact in the viscous sublayer where a large portion of the domain is occupied by a single low-speed streak which is reminiscent of the non-turbulent region aloft. Conclusions derived from the geometrical characterization are also compared with those obtained from conditional one-point statistics. To this end, a new definition of intermittency factor based on coherent structures is proposed to segregate the flow into turbulent and non-turbulent parts.

Since global intermittency is known to exhibit spatio-temporal variability, it may have an impact on the dynamics of coherent structures which can induce changes in their geometry. The geometrical characterization framework is modified with the addition of a region-based tracking procedure where correspondence is determined by measuring the degree of spatial overlap. Starting with structures having a similar geometry, i.e., with similar shape index, curvedness and stretching parameters from the instantaneous Ekman fields analyzed previously, the Robinson structures are tracked in time and temporal changes in their geometry are recorded. Similar to previous observations, these results also suggest mostly tube-like and sheet-like geometry for all Ekman flow cases. While all these results indicate that the geometry is mostly unaffected for increasing stability, the presence of non-turbulent flow patches that extend throughout the vertical length of the flow alters the spatial organization of coherent structures. This is particularly visible for hairpin-like vortex structures, whose abundance increases with stability and at the strongest stratification the head regions of these structures appears to be oriented in similar directions in the turbulent patches.

Finally, the orientation and abundance of hairpin-like structures are investigated. The region-based tracking scheme is improved to overcome the limitation of using a constant threshold in time by dynamically adjusting the thresholds such that the feature can freely grow or shrink in time. This is used to track hairpin-like structures from both neutral and stably stratified cases. Results show that the hairpin-like structures experience longer lifetime and higher number of interactions with increasing stability and a link between the number of split events and the autogeneration mechanism is proposed to be the underlying cause of the abundance of hairpins with increasing stability. To gain a better understanding of the dynamics, hairpin-like structures are also studied with a slender vortex filament approach, i.e., a vortex filament whose diameter d is much smaller than its characteristic radius of curvature R. The corrected thin-tube model of Klein and Knio (J. Fluid Mech. 1995) is used to calculate the motion of these filaments with the mean velocity profiles of the Ekman flow as the background flow. These results suggest that orientation of the filament in the spanwise direction is linked to its initial starting height under stable stratification whereas no such dependency can be observed with the neutrally stratified background flow.

Die Turbulenz in stabilen Grenzschichten (SG) geht häufig mit dem Vorhandensein großer Bereiche nichtturbulenter Strömungsregionen selbst in Wandnähe einher, ein Phänomen, das in der Literatur als globale Intermittenz bezeichnet wird. In dieser Arbeit wird die SG untersucht, indem ein detaillierter Vergleich mit der gut untersuchten neutral geschichteten atmosphärischen Grenzschicht angestellt wird. Die hier untersuchten Datensätze stammen aus der Arbeit von Ansorge (Dissertation, Springer 2016). Sie verwendeten eine vereinfachte physikalische Konfiguration, nämlich eine Ekman-Strömung über einer glatten Wand, bei der bekanntlich jenseits einer bestimmten Stabilität eine globale Intermittenz auftritt.

Vergleiche zwischen beiden Regimen werden mit Hilfe kohärenter Strukturen, insbesondere ihrer Geometrie, durchgeführt. Wurde die von Robinson (Dissertation, Stanford 1991) eingeführte Klassifizierung von Grenzschichtstrukturen erwendet, die im Folgenden als Robinson-Strukturen bezeichnet werden, um die verschiedenen in der Literatur identifizierten Strukturen in geordneter Weise zu untersuchen. Es wird ein Rahmen für die Charakterisierung der Geometrie von Robinson-Strukturen entwickelt. Einzelne Strukturen werden aus Skalarfeldern extrahiert, und die nichtlokale Methodik von Bermejo-Moreno and Pullin (J. Fluid Mech. 2008) wird verwendet, um eine Struktur als tropfen-, röhren oder blattartig zu klassifizieren.

Anschließend wird der Rahmen auf Strukturen angewandt, die sich aus momentanen neutralen und stabil geschichteten Ekman-Strömungsfeldern mit zunehmender Stabilität ergeben. Die geometrische Charakterisierung zeigt, dass die Strukturen unabhängig von der Stärke der Schichtung mäßig gestreckt röhrenförmig oder mäßig bis stark gestreckt blattförmig sind. Die aus der geometrischen Charakterisierung abgeleiteten Schlussfolgerungen werden auch mit denen verglichen, die sich aus der bedingten Ein-Punkt-Statistik ergeben. Zu diesem Zweck wird eine neue Definition des Intermittenzfaktors auf der Grundlage kohärenter Strukturen vorgeschlagen.

Da die globale Intermittenz bekanntermaßen eine räumlich-zeitliche Variabilität aufweist, kann sie sich auf die Dynamik kohärenter Strukturen auswirken, was zu Veränderungen ihrer Geometrie führen kann. Der Rahmen wird durch die Hinzufügung eines regionenbasierten Verfolgungsverfahrens modifiziert, und die Robinson-Strukturen werden zeitlich verfolgt, wobei zeitliche Veränderungen ihrer Geometrie aufgezeichnet werden. Diese Ergebnisse deuten ebenfalls darauf hin, dass die Geometrie in allen Fällen der Ekman-Strömung überwiegend röhren- und flächenförmig ist. Das Vorhandensein von nicht-turbulenten Strömungsfeldern, die sich über die gesamte vertikale Länge der Strömung erstrecken, verändert die räumliche Organisation der kohärenten Strukturen und ist besonders bei haarnadelartigen Wirbelstrukturen sichtbar, deren Häufigkeit mit der Stabilität zunimmt, und bei der stärksten Schichtung scheint der Kopfbereich dieser Strukturen in den turbulenten Teile in ähnliche Richtungen ausgerichtet zu sein. Schließlich werden die Ausrichtung und Häufigkeit haarnadelartiger Strukturen untersucht. Ersteres wird mit einem neuartigen Verfolgungsschema untersucht, das die Beschränkung der Verwendung eines zeitlich konstanten Schwellenwerts überwindet, indem die Schwellenwerte dynamisch angepasst werden, so dass das Merkmal im Laufe der Zeit frei wachsen oder schrumpfen kann, und letzteres mit einem schlanken Wirbelfadenansatz.