  This paper investigates the potential to detect tau neutrinos in the energy
range of 1-1000 PeV searching for very inclined showers with imaging Cherenkov
telescopes. A neutrino induced tau lepton escaping from the Earth may decay and
initiate an air shower which can be detected by a fluorescence or Cherenkov
telescope. We present here a study of the detection potential of Earth-skimming
neutrinos taking into account neutrino interactions in the Earth crust, local
matter distributions at various detector sites, the development of tau-induced
showers in air and the detection of Cherenkov photons with IACTs. We analyzed
simulated shower images on the camera focal plane and implemented generic
reconstruction chains based on Hillas parameters. We find that present IACTs
can distinguish air showers induced by tau neutrinos from the background of
hadronic showers in the PeV-EeV energy range. We present the neutrino trigger
efficiency obtained for a few configurations being considered for the
next-generation Cherenkov telescopes, i.e. the Cherenkov Telescope Array.
Finally, for a few representative neutrino spectra expected from astrophysical
sources, we compare the expected event rates at running IACTs to what is
expected for the dedicated IceCube neutrino telescope.
