A New Analytical Framework for Blasius Boundary Layer Approximation via Quadratic–Exponential Similarity Closure

A generalized closure formulation for the Blasius boundary layer is developed through a consistent coupling between a quadratic algebraic structure and an exponential similarity representation of the velocity gradient. By enforcing compatibility with the classical Blasius equation, a nonlinear constraint linking the auxiliary function $H(f)$ to the similarity variables is derived.

The resulting formulation yields a logarithmic representation of the similarity integral and introduces a quadratic discriminant structure that governs the admissible behavior of the solution. A closed-form asymptotic representation for $H(f)$ is constructed based on the underlying algebraic--exponential coupling.

Numerical verification against the classical Blasius solution demonstrates excellent agreement, with a root-mean-square error of $1.3 \times 10^{-6}$ across the full domain. The proposed formulation provides a high-accuracy analytical approximation perspective on boundary-layer similarity solutions and their closure structure.