  We study the gravitational clustering of big bang relic neutrinos onto
existing cold dark matter (CDM) and baryonic structures within the flat
$\Lambda$CDM model, using both numerical simulations and a semi-analytical
linear technique, with the aim of understanding the neutrinos' clustering
properties for direct detection purposes. In a comparative analysis, we find
that the linear technique systematically underestimates the amount of
clustering for a wide range of CDM halo and neutrino masses. This invalidates
earlier claims of the technique's applicability. We then compute the exact
phase space distribution of relic neutrinos in our neighbourhood at Earth, and
estimate the large scale neutrino density contrasts within the local
Greisen--Zatsepin--Kuzmin zone. With these findings, we discuss the
implications of gravitational neutrino clustering for scattering-based
detection methods, ranging from flux detection via Cavendish-type torsion
balances, to target detection using accelerator beams and cosmic rays. For
emission spectroscopy via resonant annihilation of extremely energetic cosmic
neutrinos on the relic neutrino background, we give new estimates for the
expected enhancement in the event rates in the direction of the Virgo cluster.
