Role of critical points of the skin friction field in formation of plumes in thermal convection

Publikation: Beiträge in ZeitschriftenZeitschriftenaufsätzeForschungbegutachtet

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Role of critical points of the skin friction field in formation of plumes in thermal convection. / Bandaru, Vinodh; Kolchinskaya, Anastasiya; Padberg-Gehle, Kathrin et al.
in: Physical Review E, Jahrgang 92, Nr. 4, 043006, 06.10.2015.

Publikation: Beiträge in ZeitschriftenZeitschriftenaufsätzeForschungbegutachtet

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Bandaru V, Kolchinskaya A, Padberg-Gehle K, Schumacher J. Role of critical points of the skin friction field in formation of plumes in thermal convection. Physical Review E. 2015 Okt 6;92(4):043006. doi: 10.1103/PhysRevE.92.043006

Bibtex

@article{9c19fb1df58746baa85a64c15333c4a2,
title = "Role of critical points of the skin friction field in formation of plumes in thermal convection",
abstract = "The dynamics in the thin boundary layers of temperature and velocity is the key to a deeper understanding of turbulent transport of heat and momentum in thermal convection. The velocity gradient at the hot and cold plates of a Rayleigh-B{\'e}nard convection cell forms the two-dimensional skin friction field and is related to the formation of thermal plumes in the respective boundary layers. Our analysis is based on a direct numerical simulation of Rayleigh-B{\'e}nard convection in a closed cylindrical cell of aspect ratio Γ=1 and focused on the critical points of the skin friction field. We identify triplets of critical points, which are composed of two unstable nodes and a saddle between them, as the characteristic building block of the skin friction field. Isolated triplets as well as networks of triplets are detected. The majority of the ridges of linelike thermal plumes coincide with the unstable manifolds of the saddles. From a dynamical Lagrangian perspective, thermal plumes are formed together with an attractive hyperbolic Lagrangian coherent structure of the skin friction field. We also discuss the differences from the skin friction field in turbulent channel flows from the perspective of the Poincar{\'e}-Hopf index theorem for two-dimensional vector fields.",
keywords = "Mathematics",
author = "Vinodh Bandaru and Anastasiya Kolchinskaya and Kathrin Padberg-Gehle and J{\"o}rg Schumacher",
note = "Publisher Copyright: {\textcopyright} 2015 American Physical Society.",
year = "2015",
month = oct,
day = "6",
doi = "10.1103/PhysRevE.92.043006",
language = "English",
volume = "92",
journal = "Physical Review E",
issn = "2470-0045",
publisher = "American Physical Society",
number = "4",

}

RIS

TY - JOUR

T1 - Role of critical points of the skin friction field in formation of plumes in thermal convection

AU - Bandaru, Vinodh

AU - Kolchinskaya, Anastasiya

AU - Padberg-Gehle, Kathrin

AU - Schumacher, Jörg

N1 - Publisher Copyright: © 2015 American Physical Society.

PY - 2015/10/6

Y1 - 2015/10/6

N2 - The dynamics in the thin boundary layers of temperature and velocity is the key to a deeper understanding of turbulent transport of heat and momentum in thermal convection. The velocity gradient at the hot and cold plates of a Rayleigh-Bénard convection cell forms the two-dimensional skin friction field and is related to the formation of thermal plumes in the respective boundary layers. Our analysis is based on a direct numerical simulation of Rayleigh-Bénard convection in a closed cylindrical cell of aspect ratio Γ=1 and focused on the critical points of the skin friction field. We identify triplets of critical points, which are composed of two unstable nodes and a saddle between them, as the characteristic building block of the skin friction field. Isolated triplets as well as networks of triplets are detected. The majority of the ridges of linelike thermal plumes coincide with the unstable manifolds of the saddles. From a dynamical Lagrangian perspective, thermal plumes are formed together with an attractive hyperbolic Lagrangian coherent structure of the skin friction field. We also discuss the differences from the skin friction field in turbulent channel flows from the perspective of the Poincaré-Hopf index theorem for two-dimensional vector fields.

AB - The dynamics in the thin boundary layers of temperature and velocity is the key to a deeper understanding of turbulent transport of heat and momentum in thermal convection. The velocity gradient at the hot and cold plates of a Rayleigh-Bénard convection cell forms the two-dimensional skin friction field and is related to the formation of thermal plumes in the respective boundary layers. Our analysis is based on a direct numerical simulation of Rayleigh-Bénard convection in a closed cylindrical cell of aspect ratio Γ=1 and focused on the critical points of the skin friction field. We identify triplets of critical points, which are composed of two unstable nodes and a saddle between them, as the characteristic building block of the skin friction field. Isolated triplets as well as networks of triplets are detected. The majority of the ridges of linelike thermal plumes coincide with the unstable manifolds of the saddles. From a dynamical Lagrangian perspective, thermal plumes are formed together with an attractive hyperbolic Lagrangian coherent structure of the skin friction field. We also discuss the differences from the skin friction field in turbulent channel flows from the perspective of the Poincaré-Hopf index theorem for two-dimensional vector fields.

KW - Mathematics

UR - http://www.scopus.com/inward/record.url?scp=84944753339&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/56fe5abe-979f-37b8-a5f8-313bf3b34f74/

U2 - 10.1103/PhysRevE.92.043006

DO - 10.1103/PhysRevE.92.043006

M3 - Journal articles

C2 - 26565331

VL - 92

JO - Physical Review E

JF - Physical Review E

SN - 2470-0045

IS - 4

M1 - 043006

ER -

DOI