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Dynamics near the subcritical transition of the 3D Couette flow II : above threshold case / Jacob Bedrossian, Pierre Germain, Nader Masmoudi.
Math/Physics/Astronomy Library QA3 .A57 no.1377
Available
- Format:
- Book
- Author/Creator:
- Bedrossian, Jacob, 1984- author.
- Germain, Pierre, 1979- author.
- Masmoudi, Nader, 1974- author.
- Series:
- Memoirs of the American Mathematical Society ; no. 1377.
- Memoirs of the American Mathematical Society, 0065-9266 ; number 1377
- Language:
- English
- Subjects (All):
- Viscous flow--Mathematical models.
- Viscous flow.
- Stability.
- Shear flow.
- Inviscid flow.
- Mixing.
- Damping (Mechanics).
- Three-dimensional modeling.
- Physical Description:
- v, 135 pages : illustrations ; 26 cm
- Place of Publication:
- Providence : American Mathematical Society, 2022.
- Summary:
- "This is the second in a pair of works which study small disturbances to the plane, periodic 3D Couette flow in the incompressible Navier-Stokes equations at high Reynolds number Re. In this work, we show that there is constant , independent of Re, such that sufficiently regular disturbances of size for any exist at least until and in general evolve to be due to the lift-up effect. Further, after times , the streamwise dependence of the solution is rapidly diminished by a mixing-enhanced dissipation effect and the solution is attracted back to the class of "2.5 dimensional" streamwise-independent solutions (sometimes referred to as "streaks"). The largest of these streaks are expected to eventually undergo a secondary instability at . Hence, our work strongly suggests, for all (sufficiently regular) initial data, the genericity of the "lift-up effect streak growth streak breakdown" scenario for turbulent transition of the 3D Couette flow near the threshold of stability forwarded in the applied mathematics and physics literature"-- Provided by publisher.
- Contents:
- Outline of the proof
- Regularization and continuation
- Multiplier and paraproduct tools
- High norm estimate on Q²
- High norm estimate on Q³
- High norm estimate on Q¹₀
- High norm estimate on Q¹/=
- Coordinate system controls
- Enhanced dissipation estimates
- Sobolev estimates.
- Notes:
- Includes bibliographical references.
- Other Format:
- Online version:
- ISBN:
- 9781470472252
- 1470472252
- OCLC:
- 1343647570
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