  Machine learning techniques have been applied to enhance turbulence modeling
in recent years. However, the "black box" nature of most machine learning
techniques poses significant interpretability challenges in improving
turbulence models. This paper introduces a novel unit-constrained turbulence
modeling framework using symbolic regression to overcome these challenges. The
framework amends the constitutive equation of linear eddy viscosity models
(LEVMs) by establishing explicit equations between the Reynolds stress
deviation and mean flow quantities, thereby improving the LEVM model's
predictive capability for large separated turbulence. Unit consistency
constraints are applied to the symbolic expressions to ensure physical
realizability. The framework's effectiveness is demonstrated through its
application to the separated flow over 2D periodic hills. Numerical simulations
are conducted to validate the accuracy and generalization capabilities of the
learned turbulence model. Compared to the standard k-{\epsilon} model, the
learned model exhibits significantly enhanced predictive accuracy for
anisotropic Reynolds stresses and flow velocities. It also more accurately
identifies flow separations and exhibits promising generalization capabilities
across different flow geometries.
