In this work, we study advection-robust Hybrid High-Order discretizations of
the Oseen equations. For a given integer k≥0, the discrete velocity
unknowns are vector-valued polynomials of total degree ≤k on mesh elements
and faces, while the pressure unknowns are discontinuous polynomials of total
degree ≤k on the mesh. From the discrete unknowns, three relevant
quantities are reconstructed inside each element: a velocity of total degree
≤(k+1), a discrete advective derivative, and a discrete divergence. These
reconstructions are used to formulate the discretizations of the viscous,
advective, and velocity-pressure coupling terms, respectively. Well-posedness
is ensured through appropriate high-order stabilization terms. We prove energy
error estimates that are advection-robust for the velocity, and show that each
mesh element T of diameter hT contributes to the discretization error with
an O(hTk+1)-term in the diffusion-dominated regime, an
O(hTk+21)-term in the advection-dominated regime, and
scales with intermediate powers of hT in between. Numerical results complete
the exposition