Estimates of the ocean biological carbon pump are limited by uncertainties in the magnitude of the physical injection of particulate and dissolved organic carbon to the ocean interior. A major challenge is to evaluate the contribution of these physical pumps at small spatial and temporal scales (<100 km and <1 month). Here, we use a submesoscale permitting biophysical model covering a large domain representative of a subpolar and a subtropical gyre to quantify the impact of small‐scale physical carbon pumps.The model successfully simulates intense eddy‐driven subduction hot spots with a magnitude comparable to what has been observed in nature (1,000–6,000 mg C·m−2·day−1). These eddy‐driven subduction events are able to transfer carbon below the mixed‐layer, down to 500‐ to 1,000‐m depth. However, they contribute <5% to the annual flux at the scale of the basin, due to strong compensation between upward and downward fluxes. The model also simulates hot spots of export associated with small‐scale heterogeneity of the mixed layer, which intermittently export large amounts of suspended particulate and dissolved organic carbon. The mixed‐layer pump contributes ∼20% to the annual flux. High‐resolution measurements of export flux are needed to test models such as this one and to improve our mechanistic understanding of the biological pump and how it will respond to climate change. Key Points A high‐resolution model simulates realistic hot spots of organic carbon export by physical subduction Eddy‐driven subduction contributes little to annual export due to compensation between upward and downward fluxes Eddy‐driven spatiotemporal variations in the mixed‐layer efficiently export dissolved and particulate organic carbon