### Abstract

Horizontal convection driven by a linear temperature profile along the bottom of a two-dimensional rectangular enclosure is perturbed by a small tuned synthetic (zero-net-mass-flux/ZNMF) jet. The jet permits instability in the horizontal convection boundary layer to be investigated in a controlled manner. At a Prandtl number *Pr* = 6.14 and Rayleigh number *Ra* = 2.5 × 10^{8}, slightly below the natural onset of instability, the boundary layer is found to be convectively unstable, exhibiting a disturbance pattern consistent with a Rayleigh–Bénard mechanism. Advection of the boundary layer disturbance gives rise to unsteadiness in the vertical end-wall plume. Nusselt number is enhanced across a range of frequencies for all perturbation amplitudes, with the response dominated by two frequencies differing by approximately a factor of two: each invokes the periodic shedding of vorticity into the vertical end-wall plume at the higher frequency. This suggests that there exists a natural sensitivity in this flow to disturbances convecting in the upstream boundary layer. That is, a convective instability in the horizontal convection boundary layer serves as a disturbance amplifier, with the end-wall plume controlling the frequency of the resulting instability mode. The increase in Nusselt number achieved by a jet with peak speed of the same order as the horizontal convective velocity in the unperturbed flow is consistent with a greater than two-fold increase in Rayleigh number.

Original language | English |
---|---|

Pages (from-to) | 251-260 |

Number of pages | 10 |

Journal | International Journal of Thermal Sciences |

Volume | 110 |

DOIs | |

Publication status | Published - 1 Dec 2016 |

### Keywords

- Boundary-layer instability
- Horizontal convection
- Nusselt number
- Synthetic jet

### Cite this

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*International Journal of Thermal Sciences*, vol. 110, pp. 251-260. https://doi.org/10.1016/j.ijthermalsci.2016.07.007

**Probing horizontal convection instability via perturbation of the forcing boundary layer using a synthetic jet.** / Leigh, Matthew A.; Tsai, Tzekih; Sheard, Gregory J.

Research output: Contribution to journal › Article › Research › peer-review

TY - JOUR

T1 - Probing horizontal convection instability via perturbation of the forcing boundary layer using a synthetic jet

AU - Leigh, Matthew A.

AU - Tsai, Tzekih

AU - Sheard, Gregory J.

PY - 2016/12/1

Y1 - 2016/12/1

N2 - Horizontal convection driven by a linear temperature profile along the bottom of a two-dimensional rectangular enclosure is perturbed by a small tuned synthetic (zero-net-mass-flux/ZNMF) jet. The jet permits instability in the horizontal convection boundary layer to be investigated in a controlled manner. At a Prandtl number Pr = 6.14 and Rayleigh number Ra = 2.5 × 108, slightly below the natural onset of instability, the boundary layer is found to be convectively unstable, exhibiting a disturbance pattern consistent with a Rayleigh–Bénard mechanism. Advection of the boundary layer disturbance gives rise to unsteadiness in the vertical end-wall plume. Nusselt number is enhanced across a range of frequencies for all perturbation amplitudes, with the response dominated by two frequencies differing by approximately a factor of two: each invokes the periodic shedding of vorticity into the vertical end-wall plume at the higher frequency. This suggests that there exists a natural sensitivity in this flow to disturbances convecting in the upstream boundary layer. That is, a convective instability in the horizontal convection boundary layer serves as a disturbance amplifier, with the end-wall plume controlling the frequency of the resulting instability mode. The increase in Nusselt number achieved by a jet with peak speed of the same order as the horizontal convective velocity in the unperturbed flow is consistent with a greater than two-fold increase in Rayleigh number.

AB - Horizontal convection driven by a linear temperature profile along the bottom of a two-dimensional rectangular enclosure is perturbed by a small tuned synthetic (zero-net-mass-flux/ZNMF) jet. The jet permits instability in the horizontal convection boundary layer to be investigated in a controlled manner. At a Prandtl number Pr = 6.14 and Rayleigh number Ra = 2.5 × 108, slightly below the natural onset of instability, the boundary layer is found to be convectively unstable, exhibiting a disturbance pattern consistent with a Rayleigh–Bénard mechanism. Advection of the boundary layer disturbance gives rise to unsteadiness in the vertical end-wall plume. Nusselt number is enhanced across a range of frequencies for all perturbation amplitudes, with the response dominated by two frequencies differing by approximately a factor of two: each invokes the periodic shedding of vorticity into the vertical end-wall plume at the higher frequency. This suggests that there exists a natural sensitivity in this flow to disturbances convecting in the upstream boundary layer. That is, a convective instability in the horizontal convection boundary layer serves as a disturbance amplifier, with the end-wall plume controlling the frequency of the resulting instability mode. The increase in Nusselt number achieved by a jet with peak speed of the same order as the horizontal convective velocity in the unperturbed flow is consistent with a greater than two-fold increase in Rayleigh number.

KW - Boundary-layer instability

KW - Horizontal convection

KW - Nusselt number

KW - Synthetic jet

UR - http://www.scopus.com/inward/record.url?scp=85006995972&partnerID=8YFLogxK

U2 - 10.1016/j.ijthermalsci.2016.07.007

DO - 10.1016/j.ijthermalsci.2016.07.007

M3 - Article

VL - 110

SP - 251

EP - 260

JO - International Journal of Thermal Sciences

JF - International Journal of Thermal Sciences

SN - 1290-0729

ER -