The triple-deck stage of marginal separation.

Area of Science:

• Fluid dynamics
• Aerodynamics
• Computational fluid dynamics

Background:

• Transitional separation bubbles are critical in fluid flow phenomena.
• Understanding laminar-turbulent transition is essential for aerodynamic efficiency.

Purpose of the Study:

• To investigate transitional separation bubbles using matched asymptotic expansions.
• To focus on the triple-deck stage (III) of the transition process.
• To develop a composite asymptotic model for regularization.

Main Methods:

• Application of matched asymptotic expansions for large Reynolds numbers.
• Numerical investigation using a Chebyshev collocation method.
• Development of a composite asymptotic model for ill-posed Cauchy problems.

Main Results:

• Characterization of four key stages in incipient laminar-turbulent transition.
• Resolution of finite-time singularities in the triple-deck model.
• Reproduction of spike formation preceding vortex shedding.
• Development of a regularization method for ill-posed problems.

Conclusions:

• The triple-deck stage is crucial for understanding separation bubble dynamics.
• The developed numerical and asymptotic methods effectively model transitional phenomena.
• The study provides insights into spike formation and unsteady separation.