  The potential habitability of tidally locked planets orbiting M-dwarf stars
has been widely investigated in recent work, typically with a non-dynamic ocean
and without continents. On Earth, ocean dynamics are a primary means of heat
and nutrient distribution. Continents are a critical source of nutrients,
strongly influence ocean dynamics, and participate in climate regulation. In
this work, we investigate how the size of a substellar land mass affects the
oceans ability to transport heat and upwell nutrients on the tidally locked
planet Proxima Centauri b using the ROCKE-3D coupled ocean-atmosphere General
Circulation Model (GCM). We find that dayside ice-free ocean and nutrient
delivery to the mixed layer via upwelling are maintained across all continent
sizes. We also find that Proxima Centauri bs climate is more sensitive to
differences among atmospheric GCMs than to the inclusion of ocean dynamics in
ROCKE-3D. Finally, we find that Proxima Centauri b transitions from a lobster
state where ocean heat transport distributes heat away from the substellar
point to an eyeball state where heat transport is restricted and surface
temperature decreases symmetrically from the substellar point when the
continent size exceeds about 20 percent of the surface area. Our work suggests
that both a dynamic ocean and continents are unlikely to decrease the
habitability prospects of nearby tidally locked targets like Proxima Centauri b
that could be investigated with future observations by the James Webb Space
Telescope (JWST).
