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Nonlinear Vortex Structures in Blasius Boundary Layer Flow

This research study focuses on investigating the existence and stability of nonlinear unstable recurrent solutions, known as three-dimensional non-linear vortex structures, in the Blasius boundary layer flow. The study aims to understand the importance of these solutions and their relevance in turbulent flows. The research includes contributions from various researchers and explores the parallel and non-parallel effects in the boundary layer. The findings provide insights into the behavior and dynamics of the flow and contribute towards the development of a rational theory of statistical hydrodynamics.

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Nonlinear Vortex Structures in Blasius Boundary Layer Flow

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  1. Three-dimensionalnon-linearvortexstructures in the Blasiusboundarylayer flowH. Wedin, G. Zampogna & A. BottaroDICCA, University of Genova, Italy … including a contribution by Hanifi FOI and Linné Flow Center Stockholm, Sweden

  2. Why are nonlinearunstablerecurrentsolutionsimportant?

  3. 1

  4. 2 Separatrix, edge … “Chaotic attractor” Laminar fixedpoint Typically, plots in the (power,dissipation) space are used. Projectingontosuch global quantitiesis “a bit likehopingtoland ‘Curiosity’ on anotherplanetbytracking the sum of the kineticenergiesofallplanets versus the sum oftheirangularmomentasquared” (Cvinatović 2013)

  5. “Old” TWS: Uhlmann, Wedin etc. Kerswell, Ekhardt, etc.

  6. Asymptoticsuctionboundarylayer, Kreiloset al. (2013)

  7. Includingnon-paralleleffects: Biau (2012); sinuousstreaks Duguetet al. (2012); varicose/hairpin Cherubini et al. (2011); twosolutions on the edge …

  8. Here: the “parallel” Blasius boundary layer is studied to identify TWS. Of interest since:and non-parallel effects are likely small at Re sufficiently large

  9. Facts:

  10. Dhawan, 1953

  11. Add a forcing termtox-momentumequationtoensure a parallel flow. Then:and solve forKptosatisfy the asymptoticcondition at y∞ (Milinazzo & Saffman 1985, Rotenberry 1993). Kp = 1 when the disturbanceisinfinitesimal.

  12. Re

  13. Start from the “self-sustainingprocess”

  14. Stabilityof the solutionsfound

  15. Tosimplifyanalysis, base flow is the meanover X

  16. Secondarymodes at Re = 400, b = 0.728 (z+=100)

  17. CONCLUSIONS 1. Blasius boundary layer rendered artificially parallel via a body force2. TWs found (mainly by application of SSP process), similar to the edge state solutions found by Biau (2012)3. Solutions found are unstable4. Still a long way from Hopf (1948) goal of a “rational theory of statistical hydrodynamics where […] properties of turbulent flows can be mathematically deduced from the fundamental equations of hydromechanics”

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