An Orthogonally Modulated Framework for Generating Exact Solutions to the Navier-Stokes Equations
Year: 2025
Type: preprint
Abstract: We propose a novel framework-orthogonal modulation-for constructing exact solutions to the Navier-Stokes (NS) equations. By applying dual exponential modulation via spatial functions a(x)−b(x) and temporal functions f 2 (t)−f 1 (t) to a base divergence-free field U(x), we generate a rich family of controllable exact solutions. The key innovation is the orthogonality constraint (∇(a−b))⋅ U=0, which guarantees incompressibility of the modulated velocity field. This framework unifies compressible and incompressible regimes: when the constraint holds, the solution is exactly incompressible; otherwise, it naturally describes compressible flow. In contrast to our prior works (Ling, 2025), which were limited to compressible turbulence modeling, the present method enables seamless switching between physical scenarios and supports programmable behaviors-including blow-up, shock formation, and steady states-providing a high-dimensional, parameterized solution space for CFD validation and wind-tunnel benchmarking.
Author: Hongtao Ling
Institution: Anhui Institute of International Business
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4416218596