This talk consists of two topics. The first problem we consider is obtaining energy flux across scales from measured data, which can be achieved by analyzing the third-order structure functions. We generalize the classic inertial-range theories to capture the bidirectional energy flux and energy injection scale. Using the new theory, we analyze the summer and winter drifter data obtained from the Gulf of Mexico and find that (i) bidirectional energy flux exists and (ii) the dominant kinetic energy sources are the baroclinic instabilities associated with the ocean depth and the mixed-layer depth. The second one relates to the energy puzzle of mesoscale eddies, whose energy injection is much larger than the known energy dissipation. The estimation of mesoscale energy flux mainly bases on the quasigeostrophic theory, where energy cascade upscales and finally dissipates at the boundaries. However, inertia-gravity waves may modify this energy flux picture qualitatively. We study this problem using an asymptotically derived model that captures the interaction between near-inertial waves and mesoscale eddies. This model has a Hamiltonian structure and preserves conserved quantities such as the total energy, potential enstrophy and wave action, based on which we argue the existence of wave-induced downscale energy flux, which is overlooked in the mesoscale energy budget. We numerically study the turbulent states of this model and find that the wave-induced downscale flux of mesoscale energy can be substantial, which provides a candidate to resolve the energy puzzle of mesoscale eddies. An implication of jet formation on a beta-plane is also presented.