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Three-dimensional linear instability in pressure-driven two-layer channel flow of a Newtonian and a Herschel–Bulkley fluid
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10.1063/1.3502023
/content/aip/journal/pof2/22/11/10.1063/1.3502023
http://aip.metastore.ingenta.com/content/aip/journal/pof2/22/11/10.1063/1.3502023

Figures

Image of FIG. 1.
FIG. 1.

Schematic of a two-layer flow in a channel of height , where represents the thickness of the lower, non-Newtonian fluid.

Image of FIG. 2.
FIG. 2.

Basic state profiles of the steady, streamwise velocity component for , (a), and (b), respectively. The rest of the parameter values are , , and .

Image of FIG. 3.
FIG. 3.

The effect of increasing the order of Chebyshev polynomials in each layer, , on the variation of normalized growth rate, , with , where is the growth rate associated with the corresponding two-dimensional disturbance . The rest of the parameter values are , , , , , , , , and .

Image of FIG. 4.
FIG. 4.

The dispersion curves ( vs ) for different values of ; (a) and (b) . The rest of the parameter values are , , , , , , and . This corresponds to a case where both the layers are Newtonian fluids. The labels in (b) are used to designate the maxima in the dispersion curves; the energy budgets associated with these points are provided in Table II.

Image of FIG. 5.
FIG. 5.

The dispersion curves ( vs ) for different values of ; (a) and (b) . The rest of the parameter values are the same as in Fig. 4 but with .

Image of FIG. 6.
FIG. 6.

The dispersion curves ( vs ) for different values of ; (a) and (b) . Here, and the rest of the parameter values are the same as in Fig. 4. The labels and are used to designate maxima in the dispersion curves in (a) and (b), respectively; the energy budgets associated with these points are provided in Tables III and IV, respectively.

Image of FIG. 7.
FIG. 7.

The dispersion curves ( vs ) for different values of Bn; (a) and (b) . Here, and the rest of the parameter values are the same as in Fig. 4. The labels and are used to designate maxima in the dispersion curves in (a) and (b), respectively; the energy budgets associated with these points are provided in Tables V and VI, respectively.

Image of FIG. 8.
FIG. 8.

The dispersion curves ( vs ) for different values of ; (a) and (b) . Here, and the rest of the parameter values are the same as in Fig. 7.

Image of FIG. 9.
FIG. 9.

The effect of varying on the neutral stability curves of the shear mode, (a) and (b), the cross-stream structure of the real and imaginary parts of associated with the most dangerous interfacial and shear modes in panel (e) are shown in panels (c) and (d); the dispersion curves ( vs ) are shown in panels (e) and (f). Panels (a), (c), and (e), and (b), (d), and (f) are associated with and , respectively. The rest of the parameter values are , , , , , , and .

Image of FIG. 10.
FIG. 10.

The effect of varying on the neutral stability curves of the shear mode (a), (c), (e), (b), (d), and (f). The rest of the parameter values in the panels are , , , , , , , and .

Tables

Generic image for table
Table I.

Maximum normalized growth rate, in Fig. 3 for different values of .

Generic image for table
Table II.

Energy budgets for the points labeled , , , , and in Fig. 4(b).

Generic image for table
Table III.

Energy budgets for the points labeled , , , and in Fig. 6(a).

Generic image for table
Table IV.

Energy budgets for the points labeled , , , and in Fig. 6(b).

Generic image for table
Table V.

Energy budgets for the points labeled , , , and in Fig. 7(a).

Generic image for table
Table VI.

Energy budgets for the points labeled , , , and in Fig. 7(b).

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/content/aip/journal/pof2/22/11/10.1063/1.3502023
2010-11-01
2014-04-25
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Three-dimensional linear instability in pressure-driven two-layer channel flow of a Newtonian and a Herschel–Bulkley fluid
http://aip.metastore.ingenta.com/content/aip/journal/pof2/22/11/10.1063/1.3502023
10.1063/1.3502023
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