The global linear stability, where we assume no homogeneity in either of the spatial directions, of a two-dimensional laminar base flow through a spatially periodic converging–diverging channel is studied at low Reynolds numbers. A large wall-waviness amplitude is used to achieve instability at critical Reynolds numbers below ten. This is in contrast to earlier studies, which were at lower wall-waviness amplitude and had critical Reynolds numbers an order of magnitude higher. Moreover, our leading mode is a symmetry-breaking standing mode, unlike the traveling modes which are standard at higher Reynolds numbers. Eigenvalues in the spectrum lie on distinct branches, showing varied structure spanning the geometry. Our global stability study suggests that such modes can be tailored to give enhanced mixing in microchannels at low Reynolds numbers.
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March 2016
Research-Article
Global Linear Instability of Flow Through a Converging–Diverging Channel
Mamta R. Jotkar,
Mamta R. Jotkar
Tata Institute of Fundamental Research,
Centre for Interdisciplinary Sciences,
Hyderabad 500075, India
e-mail: mamtaj@tifrh.res.in
Centre for Interdisciplinary Sciences,
Hyderabad 500075, India
e-mail: mamtaj@tifrh.res.in
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Kirti Chandra Sahu,
Kirti Chandra Sahu
Department of Chemical Engineering,
Indian Institute of Technology Hyderabad,
Yeddumailaram, Telangana 502205, India
e-mail: ksahu@iith.ac.in
Indian Institute of Technology Hyderabad,
Yeddumailaram, Telangana 502205, India
e-mail: ksahu@iith.ac.in
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Rama Govindarajan
Rama Govindarajan
Tata Institute of Fundamental Research,
Centre for Interdisciplinary Sciences,
Hyderabad 500075, India
e-mail: rama@tifrh.res.in
Centre for Interdisciplinary Sciences,
Hyderabad 500075, India
e-mail: rama@tifrh.res.in
Search for other works by this author on:
Mamta R. Jotkar
Tata Institute of Fundamental Research,
Centre for Interdisciplinary Sciences,
Hyderabad 500075, India
e-mail: mamtaj@tifrh.res.in
Centre for Interdisciplinary Sciences,
Hyderabad 500075, India
e-mail: mamtaj@tifrh.res.in
Gayathri Swaminathan
Kirti Chandra Sahu
Department of Chemical Engineering,
Indian Institute of Technology Hyderabad,
Yeddumailaram, Telangana 502205, India
e-mail: ksahu@iith.ac.in
Indian Institute of Technology Hyderabad,
Yeddumailaram, Telangana 502205, India
e-mail: ksahu@iith.ac.in
Rama Govindarajan
Tata Institute of Fundamental Research,
Centre for Interdisciplinary Sciences,
Hyderabad 500075, India
e-mail: rama@tifrh.res.in
Centre for Interdisciplinary Sciences,
Hyderabad 500075, India
e-mail: rama@tifrh.res.in
1Corresponding author.
Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received December 31, 2014; final manuscript received July 11, 2015; published online October 1, 2015. Assoc. Editor: Sharath S. Girimaji.
J. Fluids Eng. Mar 2016, 138(3): 031301 (8 pages)
Published Online: October 1, 2015
Article history
Received:
December 31, 2014
Revised:
July 11, 2015
Citation
Jotkar, M. R., Swaminathan, G., Sahu, K. C., and Govindarajan, R. (October 1, 2015). "Global Linear Instability of Flow Through a Converging–Diverging Channel." ASME. J. Fluids Eng. March 2016; 138(3): 031301. https://doi.org/10.1115/1.4031429
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