This thesis explores the implementation of an attached eddy model for high Reynolds number wall-bounded turbulent flows. The statistical structure of the eddies is obtained through the use of the linearised Navier-Stokes equations with an eddy viscosity diffusion term and stochastic forcing. A universal form for the stochastic forcing is pursued to apply the model across all wavenumbers and Reynolds numbers. A physics-aware data-driven approach is used to this end, determining the statistical structure of the forcing. This is done through a set of optimisation problems, ensuring the velocity spectra of the linear model closely match those from direct numerical simulation at a friction Reynolds number of Reτ ≈ 5200. This is first investigated with a white in time stochastic forcing. The forcing structure displays both self-similar and non-self-similar characteristics. By leveraging linearity and superposition of solutions, the contributions of individual forcing components are identified. It is demonstrated that the eddy viscosity term is crucial for modelling wall-attached features in the wall-parallel components. Based on a self-similar forcing structure, the attached eddy model is implemented in a data-driven quasi-linear approximation, using proper orthogonal decomposition modes to reconstruct the velocity covariance matrix. This quasi-linear approximation ensures the Reynolds shear stress profile is numerically consistent with with the mean momentum equation. This allows extrapolation of two-dimensional spectra and further statistics to higher Reynolds numbers. The results of the model support the attached eddy hypothesis with viscous corrections due to finite Reynolds numbers. Finally, the model's energetics are compared with DNS, constructing a spectral budget that links the Lyapunov-like equation to transport equations from DNS. The role of the eddy viscosity diffusion term is assessed, revealing its ability to mimic energy removal by turbulent transport, with discussions on model improvements and future considerations.