Unsteady vortex shedding dynamics behind a circular cylinder in very shallow free-surface flows

The turbulent wake generated by a horizontal circular cylinder in free-surface flows of increasing shallowness with submergence-to-diameter ratios between 0.5 and 2.1 are investigated using large-eddy simulation. At Froude number (Fr) = 0.26, the free-surface deformation is small with little influence on the wake, whereas at Fr = 0.53 there is a drop in the free-surface downstream of the cylinder that impacts the coherence of the vortex shedding. Irrespective to the relative submergence, the close location of the cylinder to the bottom wall generates an asymmetric von-Kármán vortex street. Proper Orthogonal Decomposition (POD) is used to analyse the spatio-temporal coherence of the turbulent structures shed in the cylinder wake. The spatial patterns of the first two POD modes, those containing the most energy, depict the von-Kármán vortices. As Fr increases, the energy content of the first pair of POD modes decreases from 56% at Fr = 0.26 to 26.8% at Fr = 0.53, as large-scale vortices lose coherence more rapidly with shallower conditions. This energy redistribution leads to the smaller flow structures to contain a relatively higher energy when Fr is larger. The frequency of the dominating vortex shedding determined from the spectra of the POD temporal coefficients unveils that the first two coefficients feature a dominant peak at the von-Kármán vortex shedding frequency. At Fr< 0.45, the reconstructed flow field using the first 20 POD modes agrees well with the instantaneous velocities from LES, whereas free-surface effects on the wake dynamics at increasing Fr requires more POD modes to reconstruct the flow field with reduced error.