Statistical characterization of oceanic flows has been a long standing issue; such information is invaluable for formulating hypotheses and testing them. Another motivation stems from the fact that it allows us to understand the energy pathways within the ocean, which is highly turbulent. Here, we apply the wavelet approach to wavenumber spectral analysis, which has recently been proved to be beneficial in quantifying its spatially heterogeneous and anisotropic nature. We utilize an eddy-rich ensemble simulation of the North Atlantic and examine the spectral transfers of eddy kinetic energy (EKE) and effect of potential energy, here defined via dynamic enthalpy, on the EKE spectral budget. We find that vertical advection of EKE modulates the up- and down-scale direction and strength of EKE spectral flux throughout the North Atlantic domain. The vertical eddy buoyancy flux tends to be small below the mixed layer, suggesting that the flow is largely adiabatic. In maintaining this adiabatic nature, the eddy advection of dynamic enthalpy and practical salinity tend to partially compensate for the eddy advection of potential temperature, a phenomenon similar to the thermodynamic spice variable.