Determination of the statistics of the velocity gradient tensor as a function of scale : solution of the tetrad model

2009 ◽  
pp. 697-700
Author(s):  
A. Naso ◽  
A. Pumir
Keyword(s):  
Velocity Gradient ◽  
Gradient Tensor ◽  
Velocity Gradient Tensor

Invariants of velocity gradient tensor in supersonic turbulent pipe, nozzle, and diffuser flows

2018 ◽  
Vol 30 (1) ◽  
pp. 015104 ◽  
Author(s):  
Komal Kumari ◽  
Susila Mahapatra ◽  
Somnath Ghosh ◽  
Joseph Mathew
Keyword(s):  
Velocity Gradient ◽  
Gradient Tensor ◽  
Velocity Gradient Tensor

scholarly journals The nature and origins of decametre-scale porosity in Ordovician carbonate rocks, Halahatang oilfield, Tarim Basin, China

2020 ◽  
Vol 177 (5) ◽  
pp. 1074-1091
Author(s):  
Estibalitz Ukar ◽  
Vinyet Baqués ◽  
Stephen E. Laubach ◽  
Randall Marrett
Keyword(s):  
Tarim Basin ◽  
Velocity Gradient ◽  
Fractured Reservoirs ◽  
Gradient Tensor ◽  
Fault Rocks ◽  
Content Type ◽  
Velocity Gradient Tensor ◽  
Link Type ◽  
Isotopic Analyses ◽  
Supplementary Material

At >7 km depths in the Tarim Basin, hydrocarbon reservoirs in Ordovician rocks of the Yijianfang Formation contain large cavities (c. 10 m or more), vugs, fractures and porous fault rocks. Although some Yijianfang Formation outcrops contain shallow (formed near surface) palaeokarst features, cores from the Halahatang oilfield lack penetrative palaeokarst evidence. Outcrop palaeokarst cavities and opening-mode fractures are mostly mineral filled but some show evidence of secondary dissolution and fault rocks are locally highly (c. 30%) porous. Cores contain textural evidence of repeated formation of dissolution cavities and subsequent filling by cement. Calcite isotopic analyses indicate depths between c. 220 and 2000 m. Correlation of core and image logs shows abundant cement-filled vugs associated with decametre-scale fractured zones with open cavities that host hydrocarbons. A Sm–Nd isochron age of 400 ± 37 Ma for fracture-filling fluorite indicates that cavities in core formed and were partially cemented prior to the Carboniferous, predating Permian oil emplacement. Repeated creation and filling of vugs, timing constraints and the association of vugs with large cavities suggest dissolution related to fractures and faults. In the current high-strain-rate regime, corroborated by velocity gradient tensor analysis of global positioning system (GPS) data, rapid horizontal extension could promote connection of porous and/or solution-enlarged fault rock, fractures and cavities.Supplementary material: Stable isotopic analyses and the velocity gradient tensor and principal direction and magnitude calculation are available at https://doi.org/10.6084/m9.figshare.c.4946046Thematic collection: This article is part of the The Geology of Fractured Reservoirs collection available at: https://www.lyellcollection.org/cc/the-geology-of-fractured-reservoirs

scholarly journals Evolution of the velocity gradient tensor invariant dynamics in a turbulent boundary layer

2017 ◽  
Vol 815 ◽  
pp. 223-242 ◽  
Author(s):  
P. Bechlars ◽  
R. D. Sandberg
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Velocity Gradient ◽  
Evolution Equations ◽  
Turbulence Models ◽  
Turbulent Structures ◽  
Gradient Tensor ◽  
Velocity Gradient Tensor ◽  
The Mean ◽  
The Individual

In order to improve the physical understanding of the development of turbulent structures, the compressible evolution equations for the first three invariants $P$, $Q$ and $R$ of the velocity gradient tensor have been derived. The mean evolution of characteristic turbulent structure types in the $QR$-space were studied and compared at different wall-normal locations of a compressible turbulent boundary layer. The evolution of these structure types is fundamental to the physics that needs to be captured by turbulence models. Significant variations of the mean evolution are found across the boundary layer. The key features of the changes of the mean trajectories in the invariant phase space are highlighted and the consequences of the changes are discussed. Further, the individual elements of the overall evolution are studied separately to identify the causes that lead to the evolution varying with the distance to the wall. Significant impact of the wall-normal location on the coupling between the pressure-Hessian tensor and the velocity gradient tensor was found. The highlighted features are crucial for the development of more universal future turbulence models.

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