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Spatio-temporal linear stability of double-diffusive two-fluid channel flow
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10.1063/1.4718775
/content/aip/journal/pof2/24/5/10.1063/1.4718775
http://aip.metastore.ingenta.com/content/aip/journal/pof2/24/5/10.1063/1.4718775
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Figures

Image of FIG. 1.
FIG. 1.

Schematic of the three-layer base state flow. The fluids “1” and “2” occupy the channel core and the region adjacent to the channel walls, respectively. The two fluids are separated by a mixed layer of uniform thickness q, with fluid “1” located in the region −hyh.

Image of FIG. 2.
FIG. 2.

Comparison of DD with SC convective instability for h = 0.6 and q = 0.1: (a) dispersion curve (ω i, max versus α r ) for Re = 200, (b) neutral stability curve. Curves C DD, with Sc = 50, R s = 5, R f = −0.5, and δ = 10 are for a DD system. The SC cases, denoted by C SC, are obtained by setting one of the stratification rates, R f in this case, to zero. To make the two systems equivalent, for the SC case we set Sc = 9.091 and R s = 4.5. To obtain the maximum convective temporal growth rate, we have set the imaginary part of the disturbance wavenumber, α i = 0.

Image of FIG. 3.
FIG. 3.

Comparison of DD with SC stability for the case where the slower diffusing species is stabilizing, with Re = 200, h = 0.6, and q = 0.1. Curve C DD, with Sc = 50, R s = −0.5, R f = 4, and δ = 10 is for a DD system, while C SC with Sc = 9.091, R s = 3.5, and R f = 0 is for an SC fluid. Here, α i = 0.

Image of FIG. 4.
FIG. 4.

Isocontours of (a) ω r and (b) ω i in the complex wavenumber plane for a DD system at Re = 200. The rest of the parameters are Sc = 50, δ = 10, h = 0.6, q = 0.1, R s = 4, and R f = −0.5. The absolute frequency ω0, i.e., ω at the saddle point, is 1.156 + 0.041i, showing absolute instability.

Image of FIG. 5.
FIG. 5.

Isocontours of (a) ω r and (b) ω i in the complex wavenumber plane for a single component system equivalent to the double-diffusive system of Figure 4. The parameters are Re = 200, Sc = 9.091, h = 0.6, q = 0.1, R s = 3.5, and R f = 0. At the saddle point, ω0 is 1.265 − 0.266i, i.e., the flow is not absolutely unstable. In fact, the zero group velocity mode is damped out rapidly.

Image of FIG. 6.
FIG. 6.

Isocontours of (a) ω r and (b) ω i in the complex wavenumber plane. The parameters are Re = 200, Sc = 50, δ = 10, h = 0.6, q = 0.1, R s = 4, and R f = 0. At the saddle point, ω0 is 0.787 + 0.007i.

Image of FIG. 7.
FIG. 7.

Isocontours of (a) ω r and (b) ω i in the complex wavenumber plane. The parameters are the same as those used to generate the C DD curve of Figure 3. The absolute frequency ω0, i.e., ω at the saddle point, is 1.366 − 0.485i, showing that the flow is not absolutely unstable.

Image of FIG. 8.
FIG. 8.

Variation of the absolute growth rate with R s for different δ values for (a) q = 0.1 and (b) q = 0.05, respectively. The rest of the parameter values are R f = −1, Re = 200, Sc = 50, and h = 0.6. The absolute instability is stronger for a DD case than for an SC one.

Image of FIG. 9.
FIG. 9.

Stability diagrams showing the regions of convective and absolute instabilities in R s -Re space for (a) q = 0.1 and (b) q = 0.05, respectively. The rest of the parameter values are Sc = 50, δ = 10, h = 0.6, and q = 0.1. The horizontal lines in each case show the location where R s + R f = 0. Above this line, the average viscosity increases as we move from the centerline of the channel towards the wall.

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/content/aip/journal/pof2/24/5/10.1063/1.4718775
2012-05-15
2014-04-24
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Spatio-temporal linear stability of double-diffusive two-fluid channel flow
http://aip.metastore.ingenta.com/content/aip/journal/pof2/24/5/10.1063/1.4718775
10.1063/1.4718775
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