  We calculate the non-zero Boer-Mulders functions of sea quarks inside the
proton in a meson-baryon fluctuation model. The results show that the
transverse spin effects of sea quarks in an unpolarized nucleon are sizable.
Using the obtained antiquark Boer-Mulders functions, we estimate the $\cos 2
\phi$ asymmetries in the unpolarized $pp$ and $p D$ Drell-Yan processes at FNAL
E866/NuSea experiments. The prediction for the $\cos 2 \phi$ asymmetries in the
unpolarized $pp$ Drell-Yan process at the BNL Relativistic Heavy Ion Collider
(RHIC) is also given.
