  The rapid expansion of wind power worldwide underscores the critical
significance of engineering-focused analytical wake models in both the design
and operation of wind farms. These theoretically-derived ana lytical wake
models have limited predictive capabilities, particularly in the near-wake
region close to the turbine rotor, due to assumptions that do not hold.
Knowledge discovery methods can bridge these gaps by extracting insights,
adjusting for theoretical assumptions, and developing accurate models for
physical processes. In this study, we introduce a genetic symbolic regression
(SR) algorithm to discover an interpretable mathematical expression for the
mean velocity deficit throughout the wake, a previously unavailable insight. By
incorporating a double Gaussian distribution into the SR algorithm as domain
knowledge and designing a hierarchical equation structure, the search space is
reduced, thus efficiently finding a concise, physically informed, and robust
wake model. The proposed mathematical expression (equation) can predict the
wake velocity deficit at any location in the full-wake region with high
precision and stability. The model's effectiveness and practicality are
validated through experimental data and high-fidelity numerical simulations.
