3 results
Self-similar geometries within the inertial subrange of scales in boundary layer turbulence
- Michael Heisel, Charitha M. de Silva, Gabriel G. Katul, Marcelo Chamecki
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- Journal:
- Journal of Fluid Mechanics / Volume 942 / 10 July 2022
- Published online by Cambridge University Press:
- 23 May 2022, A33
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- Article
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The inertial subrange of turbulent scales is commonly reflected by a power law signature in ensemble statistics such as the energy spectrum and structure functions – both in theory and from observations. Despite promising findings on the topic of fractal geometries in turbulence, there is no accepted image for the physical flow features corresponding to this statistical signature in the inertial subrange. The present study uses boundary layer turbulence measurements to evaluate the self-similar geometric properties of velocity isosurfaces and investigate their influence on statistics for the velocity signal. The fractal dimension of streamwise velocity isosurfaces, indicating statistical self-similarity in the size of ‘wrinkles’ along each isosurface, is shown to be constant only within the inertial subrange of scales. For the transition between the inertial subrange and production range, it is inferred that the largest wrinkles become increasingly confined by the overall size of large-scale coherent velocity regions such as uniform momentum zones. The self-similarity of isosurfaces yields power-law trends in subsequent one-dimensional statistics. For instance, the theoretical 2/3 power-law exponent for the structure function can be recovered by considering the collective behaviour of numerous isosurface level sets. The results suggest that the physical presence of inertial subrange eddies is manifested in the self-similar wrinkles of isosurfaces.
On the role of return to isotropy in wall-bounded turbulent flows with buoyancy
- Elie Bou-Zeid, Xiang Gao, Cedrick Ansorge, Gabriel G. Katul
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- Journal:
- Journal of Fluid Mechanics / Volume 856 / 10 December 2018
- Published online by Cambridge University Press:
- 28 September 2018, pp. 61-78
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High Reynolds number wall-bounded turbulent flows subject to buoyancy forces are fraught with complex dynamics originating from the interplay between shear generation of turbulence ($S$) and its production or destruction by density gradients ($B$). For horizontal walls, $S$ augments the energy budget of the streamwise fluctuations, while $B$ influences the energy contained in the vertical fluctuations. Yet, return to isotropy remains a tendency of such flows where pressure–strain interaction redistributes turbulent energy among all three velocity components and thus limits, but cannot fully eliminate, the anisotropy of the velocity fluctuations. A reduced model of this energy redistribution in the inertial (logarithmic) sublayer, with no tuneable constants, is introduced and tested against large eddy and direct numerical simulations under both stable ($B<0$) and unstable ($B>0$) conditions. The model links key transitions in turbulence statistics with flux Richardson number (at $Ri_{f}=-B/S\approx$$-2$, $-1$ and $-0.5$) to shifts in the direction of energy redistribution. Furthermore, when coupled to a linear Rotta-type closure, an extended version of the model can predict individual variance components, as well as the degree of turbulence anisotropy. The extended model indicates a regime transition under stable conditions when $Ri_{f}$ approaches $Ri_{f,max}\approx +0.21$. Buoyant destruction $B$ increases with increasing stabilizing density gradients when $Ri_{f}<Ri_{f,max}$, while at $Ri_{f}\geqslant Ri_{f,max}$ limitations on the redistribution into the vertical component throttle the highest attainable rate of buoyant destruction, explaining the ‘self-preservation’ of turbulence at large positive gradient Richardson numbers. Despite adopting a ‘framework of maximum simplicity’, the model results in novel and insightful findings on how the interacting roles of energy redistribution and buoyancy modulate the variance budgets and the energy exchange among the components.
Foreword
- Ignacio Rodríguez-Iturbe, Princeton University, New Jersey, Amilcare Porporato, Duke University, North Carolina
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- Book:
- Ecohydrology of Water-Controlled Ecosystems
- Published online:
- 14 October 2009
- Print publication:
- 24 January 2005, pp xi-xiv
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Summary
Among the numerous and diverse subjects within the geosciences, hydrologic science is arguably the fastest evolving discipline. Born from chapters and appendices of standard hydraulics and agricultural science textbooks, hydrology went through its first metamorphism 40 years ago to become a prominent science dealing with the physical laws that govern water movement within watersheds. A second metamorphism occurred in the last 30 years with the realization that water is among the primary controlling factors of the Earth's climate, and thus, the coexistence of all three physical states and the cycling among them became a research priority. Over the past ten years, however, a third metamorphism has started to develop and is primarily motivated by the recognition that the water cycle strongly influences element cycling such as nitrogen and carbon. Within the terrestrial biosphere, water availability regulates the growth of plants and controls the rate of nitrogen uptake and carbon assimilation. Hence, the interaction between the hydrologic cycle and vegetation received simultaneous attention within the climate, hydrologic, and ecological communities. Ecohydrology is the emerging discipline that concentrates on the cycling of water and other elements within the context of the Earth's biological productivity, the subject of this book.
From its birth, ecohydrology bifurcated early on into a phase that is primarily observational and focused on a plant's response to its microclimate (primarily spear-headed by ecologists) and a phase that focused on detailed water flow models combined with plant models of varying complexity (primarily spear-headed by hydrologists). The trajectory of ecohydrology following this bifurcation was brief and predictable – increases in observational cataloging and increases in model complexity with little intersections amongst these two trajectories.