  It has been recently proposed that a sterile neutrino \nu_h of mass
m_h=40--80 MeV, mixing |U_{\mu h}|^2=10^{-3}--10^{-2}, lifetime \tau_h \lsim
10^{-9} s, and a dominant decay mode (\nu_h \to \nu_\mu \gamma) 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 -> \nu_h \mu, K_L -> \nu_h \pi \mu). We use the Z-moment method
to evaluate its atmospheric flux and the frequency of its decays inside
neutrino telescopes. We show that the \nu_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_\nu = 0.1--10 TeV and \theta < 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 (\nu_e N \to 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.

High Energy Physics - Phenomenology;High Energy Astrophysical Phenomena