Study on the effect of wave age on the wake recovery of offshore wind turbine clusters based on <i>k</i> − <i>ε</i> – <i> f _p </i> turbulence model

Studying the wakes of large offshore wind-turbine clusters is critical because upstream wakes directly affect the power output of downstream and adjacent turbines. In the complex marine environment, the interaction between wind and the fluctuating sea surface further complicates the wake recovery process. To address these challenges, using RANS simulations with ak−ε–fpturbulence model and Charnock wave-age roughness formulation, we investigate the influence of four turbine configurations (aligned 5 D/7 D, staggered 5 D/7 D) under two sea states (β∗=3.37, maximal roughness;β∗=10, developing waves) on wake recovery and farm efficiency. Results show that, in the near wake, aligned layouts produce six periodic “speed troughs” while staggered layouts shift and narrow these troughs. Aligned arrays exhibit 2.5-5% higher RMS of velocity fluctuations than staggered arrays; increasing spacing to 7 D raises RMS by 4-7% and reduces variance by 40-80%. Beyond 2.5 farm lengths downstream, wakes nearly fully recover. Staggered arrangements boost overall farm power by 24-28%. Wake-profile features are consistent acrossβ∗cases, withβ∗=3.37 yielding 1-2% higher power and faster recovery thanβ∗=10. This work constructs a multi-scale coupling framework of wind-wave-turbine-wake interactions, providing quantitative guidance for offshore wind farm micro-siting.