What question did this study set out to answer?

The aim is to provide a detailed closed-form solution for the nonlinear ordinary differential equation governing turbulent boundary flow.

February 5, 2026Transport Phenomena

Closed form solution of plane turbulent boundary flow – solution process, validity conditions and extension

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Analysis rederives the turbulent boundary flow solution, clarifying conditions and suggesting enhancements.

The aim is to provide a detailed closed-form solution for the nonlinear ordinary differential equation governing turbulent boundary flow.
Independent re-derivation of the original closed-form solution.
Step-by-step explanation of the solution process.
Clarification of the solution's validity conditions.
Proposition of a modified analytical extension incorporating van Driest damping.
A comprehensive closed-form solution process is established.
Validity conditions such as smooth wall and zero pressure gradient are thoroughly examined.
A semi-empirical extension is proposed, aligning well with direct numerical simulation results.
The enhancement improves applicability while acknowledging it is not an exact solution.

Bo Hua Sun (2026) studied this question.

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