Multi-cycle large-eddy simulation (LES) is performed to investigate cycle-to-cycle variations (CCV) of in-cylinder flow in a single-cylinder spark ignition optically-accessible research engine under motored conditions. The bivariate 2D empirical mode decomposition (EMD) is improved regarding the mode combination and computational efficiency of handling LES data. For the first time, the EMD is extended for trivariate 3D data and is applied to 3D in-cylinder flow fields to investigate large-scale flow structures and turbulence. The bivariate 2D EMD is applied to velocity fields in the central tumble plane obtained from LES to separate turbulent fluctuations from large-scale organized motions, and regions of significant CCV are identified for different instants during intake and compression strokes. The energy transfer analysis shows that the contribution of CCV to the fluctuating kinetic energy is dominant compared to that of turbulence. The characterization of the tumble vortex in 3D is made by a vortex detection approach and the 3D EMD. The shape and rotation intensity of the tumble are evaluated, and results show that a tumble deformation occurs mainly during the second half of compression stroke, strongly contributing to CCV. The flow field is decomposed by the trivariate 3D EMD, which allows the quantification of kinetic energy contained in large and small-scale structures inside the cylinder. The local turbulent energy surrounding the spark plug is found to be partially related to the tumble motion intensity, especially in the central region. An attempt is made to link flow features extracted from 2D and 3D analyses, showing that the tumble ratio computed in the 2D tumble plane can be used to quantify the tumble deformation in 3D but is not representative of the in-cylinder kinetic energy of the large-scale tumble motion and small eddies.