Convective instability in a time-dependent buoyancy driven boundary layer

Brooker, A. M. H.; Patterson, John C.; Graham, Tasman; Schöpf, Wolfgang

doi:10.1016/s0017-9310(99)00127-1

Cited by 26 publications

(25 citation statements)

References 17 publications

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“…In contrast, Brooker et al. (2000) reported that the temperature signal is amplified more rapidly than the velocity signal for water ( ). This suggests that the ratio of to could be Prandtl number dependent.…”

Section: Direct Numerical Simulation (Dns)mentioning

confidence: 94%

“…A similar numerical approach was adopted by Brooker et al. (2000), who investigated the transient stability properties of a NCBL at and in a square cavity both experimentally and numerically. Despite the quasi-static assumption in the eigenvalue calculations, the numerical results are still in good agreement with their experimental measurements.…”

Section: Introductionmentioning

confidence: 99%

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Stability of a temporally evolving natural convection boundary layer on an isothermal wall

Williamson

Armfield

et al. 2019

J. Fluid Mech.

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The stability properties of a natural convection boundary layer adjacent to an isothermally heated vertical wall, with Prandtl number 0.71, are numerically investigated in the configuration of a temporally evolving parallel flow. The instantaneous linear stability of the flow is first investigated by solving the eigenvalue problem with a quasi-steady assumption, whereby the unsteady base flow is frozen in time. Temporal responses of the discrete perturbation modes are numerically obtained by solving the two-dimensional linearized disturbance equations using a ‘frozen’ base flow as an initial-value problem at various $Gr_{\unicode[STIX]{x1D6FF}}$, where $Gr_{\unicode[STIX]{x1D6FF}}$ is the Grashof number based on the velocity integral boundary layer thickness $\unicode[STIX]{x1D6FF}$. The resultant amplification rates of the discrete modes are compared with the quasi-steady eigenvalue analysis, and both two-dimensional and three-dimensional direct numerical simulations (DNS) of the temporally evolving flow. The amplification rate predicted by the linear theory compares well with the result of direct numerical simulation up to a transition point. The extent of the linear regime where the perturbations linearly interact with the base flow is thus identified. The value of the transition $Gr_{\unicode[STIX]{x1D6FF}}$, according to the three-dimensional DNS results, is dependent on the initial perturbation amplitude. Beyond the transition point, the DNS results diverge from the linear stability predictions as nonlinear mechanisms become important.

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Section: Direct Numerical Simulation (Dns)mentioning

confidence: 94%

Section: Introductionmentioning

confidence: 99%

Stability of a temporally evolving natural convection boundary layer on an isothermal wall

Williamson

Armfield

et al. 2019

J. Fluid Mech.

View full text Add to dashboard Cite

show abstract

“…In recent years, direct stability analysis has gained popularity for studying the stability and resonance properties of natural convection boundary layers (e.g. [9][10][11][12]). This approach is able to extend investigations into the nonlinear regime of the boundary layers.…”

Section: Introductionmentioning

confidence: 99%

Transition of natural convection boundary layers—a revisit by Bicoherence analysis

Zhao

Lei

Patterson

2014

International Communications in Heat and Mass Transfer

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“…Direct numerical simulations of the natural convection cavity flow have been reported in [10][11][12][13][14][15][16][17][18][19][20][21][22][23] and of the unbounded plate with stratified ambient in [24][25][26]. The cavity studies were mainly concerned with the occurrence of global …”

Section: Introductionmentioning

confidence: 99%

“…Thus while the linear stability analysis of the boundary layer can provide some insights into the cavity flow, further analysis of the cavity flow will not provide the detailed information on the semi-infinite plate boundary layer that is sought here. Brooker et al [21,22] investigated the stability of the natural convection boundary layer using direct numerical simulation and the non-parallel linear parabolized stability theory, as well as the standard parallel method, to in particular examine the importance of the non-parallel effects. They found excellent agreement for the critical Rayleigh number predictions between the parallel and non-parallel approaches for the higher unstable frequencies, but not for the lower unstable frequencies.…”

Section: Introductionmentioning

confidence: 99%

Boundary layer instability of the natural convection flow on a uniformly heated vertical plate

Aberra

Armfield

Behnia

et al. 2012

International Journal of Heat and Mass Transfer

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Convective instability in a time-dependent buoyancy driven boundary layer

Cited by 26 publications

References 17 publications

Stability of a temporally evolving natural convection boundary layer on an isothermal wall

Stability of a temporally evolving natural convection boundary layer on an isothermal wall

Transition of natural convection boundary layers—a revisit by Bicoherence analysis

Boundary layer instability of the natural convection flow on a uniformly heated vertical plate

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