Ocean Circulation on Tide-locked Lava Worlds: 3D Modeling with a Simple Boundary Iteration Method

TL;DR

This paper investigates magma-ocean circulation on 1:1 tidally locked lava planets, addressing how rotation and day-night forcing shape ocean structure. It advances from prior 2D analyses by employing full 3D spherical MITgcm simulations with Coriolis effects and a boundary-iteration scheme to handle evolving liquid boundaries, driven by a radiative-equilibrium surface pattern. The results show shallow oceans on the dayside, with depths of about $50$–$300$ m, weak horizontal heat transport relative to stellar insolation, and pronounced western intensification of boundary currents, plus a mid-latitude shift of the deepest ocean under moderate-to-large vertical diffusivity. These findings provide a first coherent 3D picture of thermal-driven magma-ocean circulation on tidally locked lava worlds and set the stage for future inclusion of wind stresses and atmosphere-ocean coupling to assess broader dynamical regimes and observables.

Abstract

Tide-locked lava worlds are surface-melted rocky planets under 1:1 tidally locked orbit (i.e., synchronously rotating) with orbital period being equal to rotation period and with permanent hot dayside and cold nightside. Previous studies on this type of planets employed scaling analyses and two-dimensional (2D) simulations. This work is a continuation of the previous researches but including the effect of the Coriolis force and the simulation domain is extended to a 3D global sphere. We find that under the condition with thermal-only forcing (without surface wind stresses), the area-mean ocean depth is about 50--300 m (depending on vertical diffusivity) and the area-mean effect of horizontal ocean heat transport (in the order of 10$^{3}$ to 10$^{4}$ W m$^{-2}$) is significantly smaller than stellar radiation (in the order of 10$^{6}$ W m$^{-2}$ at the substellar region), being consistent with previous results. Different from 2D results, due to the effect of the Coriolis force, large-scale horizontal gyres form on the dayside, ocean currents near the west boundaries are much stronger than that near the east boundaries (called as ``western intensification''), the deepest ocean is not right at the substellar point but in the middle latitudes as the vertical diffusivity is moderate or large, and meanwhile there exists significant asymmetry between the west and the east of the substellar point. These results establish a first picture for the 3D thermal-driven ocean circulation and confirm that the lava ocean should be shallow on tide-locked lava worlds.

Figures (7)

• Figure 1: Schematic diagram of the boundary iteration method. The red star marks the substellar point. In each panel, the colored region represents the active simulation domain, while the white area is not simulated. Solid and dashed black lines denote the simulation boundaries, and the red curve indicates the 2000 K isotherm (freezing point). At each iteration, the new simulation boundary is defined as the midpoint between the 2000 K isotherm and the previous iteration's boundary. Iterations continue until the simulation boundaries converge. Initial lateral and bottom ocean boundaries are arbitrarily defined (see Figure \ref{['fig2']}).
• Figure 2: Sensitivity tests of the boundary iteration method under four different initial conditions. The top row shows the control case, and the other rows show variations in initial ocean temperature, depth, and current strength. The first column displays the initial condition for each test, while the remaining columns show intermediate and final states during the iteration process. The colored regions represent the active simulation domain; white areas are not simulated. Although the initial conditions vary significantly, all experiments roughly converge to similar equilibrium states with an ocean depth of approximately 200–400 m along the equator. Note: The y-axis range differs in the rightmost column.
• Figure 3: Lava temperature and ocean depth in the control experiment with a vertical diffusivity of $4 \times 10^{-5}$ m$^2$ s$^{-1}$. (a) Sea surface temperature (K, color-shaded) and surface surface height (m, contour lines); (b, c) temperature slices at 99 m and 297 m depth; (d) equatorial cross-section temperature; (e) meridional cross-section temperature at the substellar longitude ($0^\circ$); (f) 3D perspective view of ocean depth (m). On the night side and near the terminators, the ocean depth is zero everywhere. White areas indicate solid regions (temperature below 2000 K), which are not included in the simulation domain (the same applies to all following figures).
• Figure 4: Ocean currents in the control experiment. (a) Horizontal currents ($u$, $v$) at the sea surface; (b) horizontal currents at 99 m depth; (c) zonal-vertical section ($u$, $w$) along the equator; (d) zonal-vertical section at $40^\circ$S; (e) meridional-vertical section ($v$, $w$) along $0^\circ$ longitude; (f) meridional-vertical section along $40^\circ$ longitude, in the west of the substellar point. Note that the color bar range (representing velocity magnitude, $\sqrt{u^2 + v^2 + w^2}$) and the reference vector length vary between different panels.
• Figure 5: Results of the vertical diffusion sensitivity tests. (a) Area-mean ocean depth as a function of the diffusion coefficient, (b) the strength of zonal-mean zonal ocean current, and (c) the divergence of zonal ocean heat transport for the three different diffusion coefficients, $4\times10^{-6}$, $4\times10^{-5}$, and $4\times10^{-4}$ m s$^{-2}$. Note the stellar flux on the planetary surface is in the order of $10^{6}$ W m$^{-2}$, being about two orders larger than the area-mean ocean heat transport. The theoretical lines are from Table 2 in lai2024b. (d--f): Sea surface temperature (SST, color-shading in unit of K) and sea surface height (SSH, contour lines in unit of m) (d), lava temperature along the equator (e), and horizontal ocean currents (vectors) and the strength of the currents (color shading) in the experiment with an diffusivity of $4\times10^{-4}$ m s$^{-2}$. (g--i): Same as panels (d--f) but for the experiment of $4\times10^{-6}$ m s$^{-2}$. The contour interval is 2 m in (d) but 0.2 m in (g), and the reference vector is 1.0 m s$^{-1}$ in (f) but 0.1 m s$^{-1}$ in (i). When the vertical diffusivity is very small, the ocean currents and heat transports are weak and the largest SSH is very close to the substellar point. When the vertical diffusivity increases, the ocean becomes deeper, the ocean currents and associated horizontal and vertical heat transports become stronger, the value of SSH increases, and the largest SSH moves from the equator to the extratropics.