It has been recently proposed that a sterile neutrino ν_h of mass m_h=40--80 MeV, mixing |U_μ h|^2=10^-3--10^-2, lifetime τ_h 10^-9 s, and a dominant decay mode (ν_h →ν_μγ) could be the origin of the experimental anomalies observed at LSND, KARMEN and MiniBooNE. Such a particle would be abundant inside air showers, as it can be produced in kaon decays (K -> ν_h μ, K_L -> ν_h πμ). We use the Z-moment method to evaluate its atmospheric flux and the frequency of its decays inside neutrino

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... s. We show that the ν_h would imply around 10^4 contained showers per year inside a 0.03 km^3 telescope like ANTARES or the DeepCore in IceCube. These events would have a characteristic energy and zenith-angle distribution (E_ν = 0.1--10 TeV and θ < 90^o), which results from a balance between the reach of the heavy neutrino (that disfavors low energies) and a sizeable production rate and decay probability. The standard background from contained neutrino events (ν_e N → e X and neutral-current interactions of high inelasticity) is 100 times smaller. Therefore, although it may be challenging from an experimental point of view, a search at ANTARES and IceCube could confirm this heavy-neutrino possibility.