Salmonids bury their eggs in hyporheic streambed gravel, forming an egg nest, called a redd, characterized by a pit and a hump topography resembling a dune. Embryos’ survival depends on downwelling oxygen-rich stream water fluxes, whose magnitudes are expected to depend on the interactions among redd shape, stream hydraulics, and the hydraulic conductivity of the streambed sediment. Here, we hypothesize that downwelling fluxes increase with stream discharge and redd aspect ratio, and such fluxes can be predicted using a set of dimensionless numbers, which include the stream flow Reynolds and Froude numbers, the redd aspect ratio, and the redd relative submergence. We address our goal by simulating the surface and subsurface flows with numerical hydraulic models linked through the near-bed pressure distribution quantified with a two-phase (air-water) two-dimensional surface water computational fluid dynamics model, validated with flume experiments. We apply the modeling approach to three redd sizes, which span the observed range in the field (from ~1 to ~4 m long), and by increasing discharge from shallow (0.1 m) and slow (0.15 m/s) to deep (8m) and fast (3.3 m/s). Results support our hypothesis of downwelling fluxes increasing with discharge and redd aspect ratio due to the increased near-bed head gradient over the redd. The derived equation may help evaluate the effect of regulated flow (e.g., hydroelectric and flood control dams) on redd-induced hyporheic flows.