Coherent structures on a boundary layer in Rayleigh-Benard turbulence

Michael Shelley, M. Vinson

Research output: Contribution to journalArticle

Abstract

Observations of Rayleigh-Benard convection have shown the existence of various coherent structures in the boundary layer region of the convection cell in the regime of hard turbulence (Zocchi et al 1990). These structures include long-lived waves, plumes and propagating regions of rotational fluid, termed 'swirls'. Besides providing visualizations of these flow structures, the experimenters have conjectured that the observed waves are normal modes associated with the buoyant shear layer at the wall, and have provided a measured dispersion relation. The authors study a simple model of such an unstably stratified boundary layer. The model consists of a two-dimensional layer of constant vorticity against a wall; this models the effect of viscosity and the large-scale rolling motion in creating shear at the wall. The effect of buoyancy is included as a sharp density jump across the boundary of the shear layer. They study both the linear analysis of the model, and its nonlinear behaviour through numerical simulation. The model reproduces much of the behaviour observed in the experiment. They observe the formation of both plumes and swirls, similar in form and dynamics to those in the experiment. They find that plumes and swirls arise from the same instability mechanism, only differing in the amount of shear acting upon them. The linear and nonlinear behaviour of the model's neutrally stable normal modes are inconsistent with that of the observed waves on the boundary layer; neutrally stable waves of the model obey a different dispersion relation, and are nonlinearly unstable to superharmonic Rayleigh-Taylor instabilities. They suggest that the observed waves reflect some other collective action of the system.

Original languageEnglish (US)
Article number003
Pages (from-to)323-351
Number of pages29
JournalNonlinearity
Volume5
Issue number2
DOIs
StatePublished - 1992

Fingerprint

Coherent Structures
Rayleigh
Boundary Layer
Turbulence
boundary layers
Boundary layers
turbulence
plumes
Normal Modes
Dispersion Relation
shear layers
Model
superharmonics
Rayleigh-Bénard Convection
Stable Models
shear
convection cells
Buoyancy
Rayleigh-Benard convection
Taylor instability

ASJC Scopus subject areas

  • Mathematical Physics
  • Statistical and Nonlinear Physics
  • Applied Mathematics
  • Mathematics(all)

Cite this

Coherent structures on a boundary layer in Rayleigh-Benard turbulence. / Shelley, Michael; Vinson, M.

In: Nonlinearity, Vol. 5, No. 2, 003, 1992, p. 323-351.

Research output: Contribution to journalArticle

Shelley, Michael ; Vinson, M. / Coherent structures on a boundary layer in Rayleigh-Benard turbulence. In: Nonlinearity. 1992 ; Vol. 5, No. 2. pp. 323-351.
@article{52afd9aa4eed41c8bf419c3939ba0c61,
title = "Coherent structures on a boundary layer in Rayleigh-Benard turbulence",
abstract = "Observations of Rayleigh-Benard convection have shown the existence of various coherent structures in the boundary layer region of the convection cell in the regime of hard turbulence (Zocchi et al 1990). These structures include long-lived waves, plumes and propagating regions of rotational fluid, termed 'swirls'. Besides providing visualizations of these flow structures, the experimenters have conjectured that the observed waves are normal modes associated with the buoyant shear layer at the wall, and have provided a measured dispersion relation. The authors study a simple model of such an unstably stratified boundary layer. The model consists of a two-dimensional layer of constant vorticity against a wall; this models the effect of viscosity and the large-scale rolling motion in creating shear at the wall. The effect of buoyancy is included as a sharp density jump across the boundary of the shear layer. They study both the linear analysis of the model, and its nonlinear behaviour through numerical simulation. The model reproduces much of the behaviour observed in the experiment. They observe the formation of both plumes and swirls, similar in form and dynamics to those in the experiment. They find that plumes and swirls arise from the same instability mechanism, only differing in the amount of shear acting upon them. The linear and nonlinear behaviour of the model's neutrally stable normal modes are inconsistent with that of the observed waves on the boundary layer; neutrally stable waves of the model obey a different dispersion relation, and are nonlinearly unstable to superharmonic Rayleigh-Taylor instabilities. They suggest that the observed waves reflect some other collective action of the system.",
author = "Michael Shelley and M. Vinson",
year = "1992",
doi = "10.1088/0951-7715/5/2/003",
language = "English (US)",
volume = "5",
pages = "323--351",
journal = "Nonlinearity",
issn = "0951-7715",
publisher = "IOP Publishing Ltd.",
number = "2",

}

TY - JOUR

T1 - Coherent structures on a boundary layer in Rayleigh-Benard turbulence

AU - Shelley, Michael

AU - Vinson, M.

PY - 1992

Y1 - 1992

N2 - Observations of Rayleigh-Benard convection have shown the existence of various coherent structures in the boundary layer region of the convection cell in the regime of hard turbulence (Zocchi et al 1990). These structures include long-lived waves, plumes and propagating regions of rotational fluid, termed 'swirls'. Besides providing visualizations of these flow structures, the experimenters have conjectured that the observed waves are normal modes associated with the buoyant shear layer at the wall, and have provided a measured dispersion relation. The authors study a simple model of such an unstably stratified boundary layer. The model consists of a two-dimensional layer of constant vorticity against a wall; this models the effect of viscosity and the large-scale rolling motion in creating shear at the wall. The effect of buoyancy is included as a sharp density jump across the boundary of the shear layer. They study both the linear analysis of the model, and its nonlinear behaviour through numerical simulation. The model reproduces much of the behaviour observed in the experiment. They observe the formation of both plumes and swirls, similar in form and dynamics to those in the experiment. They find that plumes and swirls arise from the same instability mechanism, only differing in the amount of shear acting upon them. The linear and nonlinear behaviour of the model's neutrally stable normal modes are inconsistent with that of the observed waves on the boundary layer; neutrally stable waves of the model obey a different dispersion relation, and are nonlinearly unstable to superharmonic Rayleigh-Taylor instabilities. They suggest that the observed waves reflect some other collective action of the system.

AB - Observations of Rayleigh-Benard convection have shown the existence of various coherent structures in the boundary layer region of the convection cell in the regime of hard turbulence (Zocchi et al 1990). These structures include long-lived waves, plumes and propagating regions of rotational fluid, termed 'swirls'. Besides providing visualizations of these flow structures, the experimenters have conjectured that the observed waves are normal modes associated with the buoyant shear layer at the wall, and have provided a measured dispersion relation. The authors study a simple model of such an unstably stratified boundary layer. The model consists of a two-dimensional layer of constant vorticity against a wall; this models the effect of viscosity and the large-scale rolling motion in creating shear at the wall. The effect of buoyancy is included as a sharp density jump across the boundary of the shear layer. They study both the linear analysis of the model, and its nonlinear behaviour through numerical simulation. The model reproduces much of the behaviour observed in the experiment. They observe the formation of both plumes and swirls, similar in form and dynamics to those in the experiment. They find that plumes and swirls arise from the same instability mechanism, only differing in the amount of shear acting upon them. The linear and nonlinear behaviour of the model's neutrally stable normal modes are inconsistent with that of the observed waves on the boundary layer; neutrally stable waves of the model obey a different dispersion relation, and are nonlinearly unstable to superharmonic Rayleigh-Taylor instabilities. They suggest that the observed waves reflect some other collective action of the system.

UR - http://www.scopus.com/inward/record.url?scp=4544230102&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=4544230102&partnerID=8YFLogxK

U2 - 10.1088/0951-7715/5/2/003

DO - 10.1088/0951-7715/5/2/003

M3 - Article

AN - SCOPUS:4544230102

VL - 5

SP - 323

EP - 351

JO - Nonlinearity

JF - Nonlinearity

SN - 0951-7715

IS - 2

M1 - 003

ER -