Thermocapillary and buoyant flows with low frequency jitter. I. Jitter confined to the plane

P. Grassia, G. M. Homsy

Research output: Contribution to journalArticle

14 Citations (Scopus)

Abstract

A temperature gradient is applied along a fluid filled slot with a flat upper interface, establishing flow via thermocapillarity and/or buoyancy. There is a known parallel flow along the slot, in which the fluid velocity varies vertically, and there is a known convected temperature profile. This parallel flow is then subjected to gravitational modulation or “jitter” which is applied at low frequency and in various directions. For gravity modulations in the plane of the basic flow, analytic solutions for velocity and temperature profiles are obtained for jitter of arbitrary amplitude. These solutions involve modifications to the earlier parallel flow solutions. Jitter in the vertical direction generates vorticity due to coupling with the applied horizontal temperature gradient. This alternately cooperates or competes with the steady basic flow over a cycle of the modulation, but does not qualitatively change the flow or temperature profiles. Jitter applied along the slot produces vorticity only when coupled to vertical convected temperature gradients and so is important when the basic flow is sufficiently strong (large Marangoni and/or Rayleigh number). Various cases are considered for the basic flow, which may be driven by thermocapillarity alone, by vertical gravity alone or by a mixture of thermocapillarity and vertical gravity. When strong streamwise jitter is added to any of these cases, the flow profile alternates during the modulation cycle between boundary layer structures and vertically stacked cells. The type of structure selected depends on the sense of the horizontal thermal stratification with respect to the jitter, and in that part of the cycle where this stratification is unstable, there are particular amplitudes of jitter which can give strong cellular motions or runaways. These runaways represent a resonant interaction with stationary Rayleigh-Bénard cells.
LanguageEnglish
Pages1273-1290
Number of pages18
JournalPhysics of Fluids
Volume10
Issue number6
DOIs
Publication statusPublished - Jun 1998

Fingerprint

Jitter
low frequencies
vibration
parallel flow
Parallel flow
Modulation
slots
temperature profiles
Thermal gradients
modulation
temperature gradients
Gravitation
gravitation
stratification
Vorticity
vorticity
cycles
Benard cells
Thermal stratification
Fluids

Keywords

  • thermocapillary flows
  • vortex dynamics
  • interfacial flows
  • buoyancy
  • fluid structure interaction
  • fluids
  • gravitation
  • heat transfer
  • mathematical models
  • problem solving
  • temperature
  • thermal gradients
  • thermal stratification
  • velocity
  • vortex flow

Cite this

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title = "Thermocapillary and buoyant flows with low frequency jitter. I. Jitter confined to the plane",
abstract = "A temperature gradient is applied along a fluid filled slot with a flat upper interface, establishing flow via thermocapillarity and/or buoyancy. There is a known parallel flow along the slot, in which the fluid velocity varies vertically, and there is a known convected temperature profile. This parallel flow is then subjected to gravitational modulation or “jitter” which is applied at low frequency and in various directions. For gravity modulations in the plane of the basic flow, analytic solutions for velocity and temperature profiles are obtained for jitter of arbitrary amplitude. These solutions involve modifications to the earlier parallel flow solutions. Jitter in the vertical direction generates vorticity due to coupling with the applied horizontal temperature gradient. This alternately cooperates or competes with the steady basic flow over a cycle of the modulation, but does not qualitatively change the flow or temperature profiles. Jitter applied along the slot produces vorticity only when coupled to vertical convected temperature gradients and so is important when the basic flow is sufficiently strong (large Marangoni and/or Rayleigh number). Various cases are considered for the basic flow, which may be driven by thermocapillarity alone, by vertical gravity alone or by a mixture of thermocapillarity and vertical gravity. When strong streamwise jitter is added to any of these cases, the flow profile alternates during the modulation cycle between boundary layer structures and vertically stacked cells. The type of structure selected depends on the sense of the horizontal thermal stratification with respect to the jitter, and in that part of the cycle where this stratification is unstable, there are particular amplitudes of jitter which can give strong cellular motions or runaways. These runaways represent a resonant interaction with stationary Rayleigh-B{\'e}nard cells.",
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year = "1998",
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language = "English",
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Thermocapillary and buoyant flows with low frequency jitter. I. Jitter confined to the plane. / Grassia, P.; Homsy, G. M.

In: Physics of Fluids, Vol. 10, No. 6, 06.1998, p. 1273-1290.

Research output: Contribution to journalArticle

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T1 - Thermocapillary and buoyant flows with low frequency jitter. I. Jitter confined to the plane

AU - Grassia, P.

AU - Homsy, G. M.

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N2 - A temperature gradient is applied along a fluid filled slot with a flat upper interface, establishing flow via thermocapillarity and/or buoyancy. There is a known parallel flow along the slot, in which the fluid velocity varies vertically, and there is a known convected temperature profile. This parallel flow is then subjected to gravitational modulation or “jitter” which is applied at low frequency and in various directions. For gravity modulations in the plane of the basic flow, analytic solutions for velocity and temperature profiles are obtained for jitter of arbitrary amplitude. These solutions involve modifications to the earlier parallel flow solutions. Jitter in the vertical direction generates vorticity due to coupling with the applied horizontal temperature gradient. This alternately cooperates or competes with the steady basic flow over a cycle of the modulation, but does not qualitatively change the flow or temperature profiles. Jitter applied along the slot produces vorticity only when coupled to vertical convected temperature gradients and so is important when the basic flow is sufficiently strong (large Marangoni and/or Rayleigh number). Various cases are considered for the basic flow, which may be driven by thermocapillarity alone, by vertical gravity alone or by a mixture of thermocapillarity and vertical gravity. When strong streamwise jitter is added to any of these cases, the flow profile alternates during the modulation cycle between boundary layer structures and vertically stacked cells. The type of structure selected depends on the sense of the horizontal thermal stratification with respect to the jitter, and in that part of the cycle where this stratification is unstable, there are particular amplitudes of jitter which can give strong cellular motions or runaways. These runaways represent a resonant interaction with stationary Rayleigh-Bénard cells.

AB - A temperature gradient is applied along a fluid filled slot with a flat upper interface, establishing flow via thermocapillarity and/or buoyancy. There is a known parallel flow along the slot, in which the fluid velocity varies vertically, and there is a known convected temperature profile. This parallel flow is then subjected to gravitational modulation or “jitter” which is applied at low frequency and in various directions. For gravity modulations in the plane of the basic flow, analytic solutions for velocity and temperature profiles are obtained for jitter of arbitrary amplitude. These solutions involve modifications to the earlier parallel flow solutions. Jitter in the vertical direction generates vorticity due to coupling with the applied horizontal temperature gradient. This alternately cooperates or competes with the steady basic flow over a cycle of the modulation, but does not qualitatively change the flow or temperature profiles. Jitter applied along the slot produces vorticity only when coupled to vertical convected temperature gradients and so is important when the basic flow is sufficiently strong (large Marangoni and/or Rayleigh number). Various cases are considered for the basic flow, which may be driven by thermocapillarity alone, by vertical gravity alone or by a mixture of thermocapillarity and vertical gravity. When strong streamwise jitter is added to any of these cases, the flow profile alternates during the modulation cycle between boundary layer structures and vertically stacked cells. The type of structure selected depends on the sense of the horizontal thermal stratification with respect to the jitter, and in that part of the cycle where this stratification is unstable, there are particular amplitudes of jitter which can give strong cellular motions or runaways. These runaways represent a resonant interaction with stationary Rayleigh-Bénard cells.

KW - thermocapillary flows

KW - vortex dynamics

KW - interfacial flows

KW - buoyancy

KW - fluid structure interaction

KW - fluids

KW - gravitation

KW - heat transfer

KW - mathematical models

KW - problem solving

KW - temperature

KW - thermal gradients

KW - thermal stratification

KW - velocity

KW - vortex flow

UR - http://strathprints.strath.ac.uk/52223/

UR - http://scitation.aip.org/content/aip/journal/pof2

U2 - 10.1063/1.869655

DO - 10.1063/1.869655

M3 - Article

VL - 10

SP - 1273

EP - 1290

JO - Physics of Fluids

T2 - Physics of Fluids

JF - Physics of Fluids

SN - 1070-6631

IS - 6

ER -