Resonant modes with frequencies 0.02-10 mHz are detected from the bow shock (BS) to the outer magnetosphere, with the nature of the resonances at frequencies 0.02-0.25 mHz being still unexplained. We propose a BS model in the form of a circular plate free along the outer edge that predicts resonant modes at frequencies 0.02-0.3 mHz or lower. We demonstrate the detection of these model resonant modes based on data from five satellites, with the resonance near 0.1 mHz predicted by the model being observed in the magnetosheath continuously for 17 hours downstream of both parallel and perpendicular shocks. Resonant BS modes produce three-wave nonlinear cascades that realize a broadband coherent coupling with resonances both near and inside the magnetopause. In our opinion, it is the coherent nature of the processes in an extended region with different linear resonant eigenmodes that determines the fairly new, nonlinear-cascade, approach to an efficient conversion of the energy of an inflow when interacting with an obstacle. This seems important for the entire nonlinear physics. We also provide arguments suggesting the possibility of resonant mode self-generation in the closed BS/magnetopause loop with a feedback in the form of narrow Poynting vector pulses at the cost of solar wind energy.
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