Spectral Density#
Spectral density analysis is a detailed examination of the frequency distribution of turbulent fluctuations in the incoming wind. By decomposing the turbulent signal into its constituent frequencies, spectral density provides valuable information about the energy distribution across different scales.
Spectral characteristics of the inflow helps in validating CFD simulations to replicate the diverse range of turbulent eddies present in the atmospheric boundary layer, contributing to a more realistic depiction of turbulence structures and their impact on the flow.
The relationship between spectral density and LES mesh size can be expressed through a power-law scaling, recognizing that the mesh size influences the resolved range of turbulent eddies. The correlation can be formulated as:
The scaling exponent depends on the specific characteristics of the turbulent flow being simulated and the numerical methods employed. It reflects the rate at which spectral density diminishes with decreasing mesh size. Smaller mesh sizes allow for the resolution of higher-frequency turbulent structures, impacting the spectral content of the simulation.
The correlation suggests that as the LES mesh size decreases, enabling finer resolution of turbulent eddies, the spectral density increases, capturing a broader range of frequencies. Conversely, coarser meshes may result in a loss of information about high-frequency turbulent structures, resulting in cut-off frequency range, which scales will not be captured.