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This paper focuses on the laminar boundary layer startup process (momentum and thermal) in incompressible flows. The unsteady boundary layer equations can be solved via similarity analysis by normalizing the stream-wise (x), wall-normal (y) and time (t) coordinates by a variable η and τ, respectively. The resulting ODEs are solved by a finite difference explicit algorithm. This can be done for two cases: flat plate flow where the change in pressure are zero (Blasius solution) and wedge or Falkner-Skan flow where the changes in pressure can be favorable (FPG) or adverse (APG). In addition, transient passive scalar transport is examined by setting several Prandtl numbers in the governing equation at two different wall thermal conditions: isothermal and isoflux. Numerical solutions for the transient evolution of the momentum and thermal boundary layer profiles are compared with analytical approximations for both small times (unsteady flow) and large (steady-state flow) times.
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This content will become publicly available on May 10, 2026
Turbulent boundary layers under spatially and temporally varying pressure gradients
The spatiotemporal dynamics of a turbulent boundary layer subjected to an unsteady pressure gradient are studied. A dynamic sequence of favourable to adverse pressure gradients (FAPGs) is imposed by deforming a section of the wind tunnel ceiling, transitioning the pressure gradient from zero to a strong FAPG within 0.07 s. At the end of the transient, the acceleration parameter is K=6x10^-6 in the favourable pressure gradient (FPG) region and K=-4.8x10^-6 in the adverse pressure gradient (APG) region. The resulting unsteady response of the boundary layer is compared with equivalent steady pressure gradient cases in terms of turbulent statistics and coherent structures. While the steady FAPG effects, as shown by Parthasarathy & Saxton-Fox (2023), caused upstream stabilisation in the FPG, a milder APG response downstream, and the formation of an internal layer, the unsteady case presented in this paper shows a reduced stabilisation in the FPG region, a stronger APG response and a weaker internal layer. This altered response is hypothesised to stem from the different spatiotemporal pressure gradient histories experienced by turbulent structures when the pressure gradient changes at a time scale comparable to their convection.
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- Award ID(s):
- 2339665
- PAR ID:
- 10648388
- Publisher / Repository:
- Journal of Fluid Mechanics
- Date Published:
- Journal Name:
- Journal of Fluid Mechanics
- Volume:
- 1010
- ISSN:
- 0022-1120
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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