  We establish spectral expansions of homogeneous and isotropic random fields
taking values in the $3$-dimensional Euclidean space $E^3$ and in the space
$\mathsf{S}^2(E^3)$ of symmetric rank $2$ tensors over $E^3$. The former is a
model of turbulent fluid velocity, while the latter is a model for the random
stress tensor or the random conductivity tensor. We found a link between the
theory of random fields and the theory of finite-dimensional convex compacta.
