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A model based on a convolutional neural network (CNN) is designed toreconstruct the three-dimensional turbulent flows beneath a free surface usingsurface measurements, including the surface elevation and surface velocity.Trained on datasets obtained from the direct numerical simulation (DNS) ofturbulent open-channel flows with a deformable free surface, the proposed modelcan accurately reconstruct the near-surface flow field and capture thecharacteristic large-scale flow structures away from the surface. Thereconstruction performance of the model, measured by metrics such as thenormalised mean squared reconstruction errors and scale-specific errors, isconsiderably better than that of the traditional linear stochastic estimation(LSE) method. We further analyse the saliency maps of the CNN model and thekernels of the LSE model and obtain insights into how the two models utilisesurface features to reconstruct subsurface flows. The importance of differentsurface variables is analysed based on the saliency map of the CNN, whichreveals knowledge about the surface-subsurface relations. The CNN is also shownto have a good generalization capability with respect to the Froude number if amodel trained for a flow with a high Froude number is applied to predict flowswith lower Froude numbers. The results presented in this work indicate that theCNN is effective regarding the detection of subsurface flow structures and byinterpreting the surface-subsurface relations underlying the reconstructionmodel, the CNN can be a promising tool for assisting with the physicalunderstanding of free-surface turbulence.

journal of fluid mechanics

Reconstruction of three-dimensional turbulent flow structures using  surface measurements for free-surface flows based on a convolutional neural  network