Lagrangian analysis of the laminar flat plate boundary layer

TL;DR

This paper uses a Lagrangian approach to analyze the laminar boundary layer at a flat plate's leading edge, revealing Gaussian velocity profiles and comparing them with classical solutions to enhance understanding of laminar flow physics.

Contribution

It introduces a Lagrangian analysis method to study the leading edge of laminar boundary layers, providing new insights and comparisons with traditional Blasius solutions.

Findings

Gaussian velocity profiles at the leading edge

Exact match with experimental observations

Enhanced understanding of laminar flow physics

Abstract

The flow properties at the leading edge of a flat plate represent a singularity to the Blasius laminar boundary layer equations; by applying the Lagrangian approach the leading edge velocity profiles of the laminar boundary layer over a flat plate are studied. Experimental observations as well as the theoretical analysis show an exact Gaussian distribution curve as the original starting profile of the laminar flow. Comparisons between the Blasius solution and the Gaussian curve solution are carried out providing a new insight into the physics of the laminar flow.