Estimation of the low-wavenumber component of turbulent boundary layer pressure field using vibration data

In structures subjected to a high-speed flow, the convective region of the wall pressure field (WPF) beneath a turbulent boundary layer (TBL) plays a crucial role in their vibration behaviour. However, when it comes to underwater structures experiencing low-speed flow, they effectively filter out the convective domain of WPF and the bending wavenumber of structures align with the low-wavenumber domain of the WPF. As a result, the primary cause of vibration in this case is the low-wavenumber components of the WPF. Thus, accurate estimation of the WPF at low-wavenumber domain is crucial for predicting vibration responses of these structures. Existing models for WPF accurately predict the convective region but differ significantly in predicting the low-wavenumber levels. This numerical study aims to investigate the feasibility of estimating the low-wavenumber WPF by analysing measured vibration data from a flat plate excited by a TBL. The WPF's cross spectrum in the wavenumber domain can be linked to the cross spectrum of the plate's acceleration. By employing regularization techniques and solving an inverse problem, the low-wavenumber components of the WPF can be then estimated. Virtual experiments are performed to evaluate the accuracy of the studied process by comparing its prediction to the input WPF model.