Double cosets of stabilizers of totally isotropic subspaces in a special unitary group II

In the article (N. Gordeev and U. Rehmann. Double cosets of stabilizers of totally isotropic subspaces in a special unitary group I, Zapiski Nauch. Sem. POMI, v. 452 (2016), 86–107) we have considered the decomposition $\mathrm{SU}(D,h)=\cup_iP_u\gamma_iP_v$ where $\mathrm{SU}(D,h)$ is a special unitary group over a division algebra $D$ with an involution, $h$ is a symmetric or skew symmetric non-degenerated Hermitian form, and $P_u,P_v$ are stabilizers of totally isotropic subspaces of the unitary space. Since $\Gamma=\mathrm{SU}(D,h)$ is a point group of a classical algebraic group $\widetilde\Gamma$ there is the “order of adherence” on the set of double cosets $\{P_u\gamma_iP_v\}$ which is induced by the Zariski topology on $\Gamma$. In the current paper we describe the adherence of such double cosets for the cases when $\widetilde\Gamma$ is an orthogonal or a symplectic group (that is, for groups of types $B_r,C_r,D_r$).