  We consider the Harder-Narasimhan formalism on the category of normed
isocrystals and show that the Harder-Narasimhan filtration is compatible with
tensor products which generalizes a result of Cornut. As an application of this
result, we are able to define a (weak) Harder-Narasimhan stratification on the
$B_{\mathrm{dR}}^+$-affine Grassmannian for arbitrary $(G, b, \mu)$. When $\mu$
is minuscule, it corresponds to the Harder-Narasimhan stratification on the
flag varieties defined by Dat-Orlik-Rapoport. And when $b$ is basic, it's
studied by Nguyen-Viehmann and Shen. We study the basic geometric properties of
the Harder-Narasimhan stratification, such as non-emptiness, dimension and its
relation with other stratifications.
