Planetary Climate Dynamics

Abstract:

Abstract In the aftermath of the Moon-forming giant impact, the Hadean Earth’s mantle and surface crystallized from a global magma ocean blanketed by a dense volatile-rich atmosphere. While prior studies have explored the thermal evolution of such early-Earth scenarios under idealized, oxidizing conditions, the potential feedback between tidal heating driven by Earth–Moon orbital forcing and variable redox scenarios have not yet been explored in detail. We investigate whether tidal heating could have prolonged this early magma ocean phase and supported quasi-steady state epochs of global radiative equilibrium: periods of thermal balance between outgoing radiation and interior heat flux. Using the PROTEUS simulation framework, we simulate Earth’s early evolution under a range of plausible tidal power densities, oxygen fugacities, and volatile inventories. Our results suggest that feedback between tidal heating and atmospheric forcing can induce substantial variation in magma ocean lifetimes, from ∼30 Myr up to ∼500 Myr, sensitive to interior redox conditions. Global radiative equilibrium epochs commonly arise across this range, lasting from ∼2 to ∼320 Myr, and typically occur from 24 Myr after the Moon-forming impact. Under oxidizing conditions, late-stage H 2 O degassing promotes melt retention and sustained heating due to its significant contribution to greenhouse forcing. Weak tides increase the atmospheric abundance of H 2 S and NH 3 and deplete CO. Therefore, the feedback between tides and atmospheric forcing induces a disequilibrium signature in the magma ocean atmosphere.

Abstract:

We experimentally measure geostrophic turbulence in a rotating, differentially heated fluid annulus, which is bounded by convectively driven warm and cold flows at the outer and inner boundaries, respectively. The horizontal kinetic energy spectra exhibit a range at low wavenumber which scales as 𝑘−3, where k denotes the horizontal wavenumber, with spectral amplitude that correlates with the square of the Brunt–Vaisala frequency at the same heights as the velocity measurements. The observed turbulent state exhibits a forward enstrophy cascade across all scales along with bidirectional energy transfer, which is evidenced by a reversal in the sign of the spectral energy flux at a scale proportional to the internal Rossby radius of deformation. These findings highlight the role of baroclinic instability in shaping the distribution of energy across scales with implications for synoptic-scale turbulent flows near Earth’s tropopause.

Abstract:

Abstract Small, low-density exoplanets are sculpted by strong stellar irradiation, but their primordial compositions and subsequent evolution are still unknown. Two often-considered scenarios hold that they formed with rocky interiors and H 2 –He atmospheres (‘gas dwarfs’) or alternatively with bulk compositions dominated by H 2 O phases (‘water worlds’). Here we constrain the possible range of evolutionary histories linking the birth conditions of low-density super-Earth L 98-59 d to recent observations using a coupled atmosphere–interior evolutionary model. We find that the observations can be explained by in situ photochemical production of SO 2 in an H 2 background, indicative of a chemically reducing mantle and substantial (>1.8 mass%) early sulfur and hydrogen content, inconsistent with both the gas-dwarf and water-world scenarios. L 98-59 d’s interior comprises a permanent magma ocean, allowing long-term retention of volatiles within its mantle over billions of years, consistent with California-Kepler Survey trends. Our analysis reveals an evolutionary pathway in which planets host volatile-rich atmospheres sustained by long-term magma-ocean degassing, shaped by secular cooling, atmospheric erosion and photochemistry. Internal and environmental processes contribute to the observed diversity of super-Earth and sub-Neptune exoplanets.

Abstract:

The circulation of the Earth’s atmosphere and those of many other planets is dominated by turbulent interactions in a baroclinically unstable, rotating, stratified flow. Even for the Earth, which has been well observed for many years, the energy spectrum and complex properties of the anisotropic and inhomogeneous turbulent cascades of energy and enstrophy remain poorly understood and difficult to model accurately. Here we measure geostrophic turbulence energised by baroclinic instability in a rotating, differentially heated fluid annulus in the laboratory, which is bounded by convectively-driven warm and cold flows at the outer and inner boundaries, respectively (see Fig. 1a). Horizontal velocity fields (Fig. 1b-c) are obtained via particle image velocimetry of neutrally buoyant particles suspended in the flow, while the temperature structure is sampled using a vertical array of thermocouples located in the middle of the channel. The horizontal kinetic energy spectra exhibit a wavenumber range at relatively large length scales which scales as k−3, where k denotes the horizontal wavenumber (see Fig. 1d-e). Moreover, the spectral amplitude is found to correlate with the square of the Brunt–Vaisala frequency N at the same heights as the velocity measurements. The observed turbulent state exhibits a net forward enstrophy cascade across all scales, along with bidirectional kinetic energy transfer, which is indicated by a reversal in the sign of the spectral energy flux. The change of sign of the kinetic energy cascade occurs at a scale proportional to the internal Rossby radius of deformation Ld. These findings highlight the role of baroclinic instability in shaping the distribution of energy across scales with implications for synoptic- and meso-scale turbulent flows in the atmospheres of the Earth and other terrestrial planet atmospheres and oceans.FIG. 1. (a) Schematic plot of the convective tank. Snapshots of vorticity ζ for thermal Rossby number RoT = 5.41 (b) and RoT = 0.03 (c). On the scale bar, Lid = 2.4 cm and Liid = 22.6 cm are the Rossby radius of deformation for (c) and (b), respectively. (d) Kinetic energy spectra, E(k), for various values of RoT. The arrow indicates the wave number kp corresponding to the peak of E(k) when RoT = 0.03. Inset: radial profiles of temporal- and zonal-averaged azimuthal velocity, Uθ. (e) Kinetic energy spectra compensated by k−3 and normalised by N2 versus LRk. The dashed line indicates the plateau segment for LRk ∈ [2, 10] and has a magnitude of ∼ 0.5. Data are for height h = 0.18 m.

Abstract:

The midlatitude atmospheres of gas giant planets are characteristic of strong and persistent zonal jets; however, the processes governing their formation and the associated energy pathways remain less understood. To investigate these mechanisms, we conducted a laboratory study of zonal jets driven by thermal forcing in an annular cylindrical tank partially filled with distilled water as the working fluid. Heating is applied at the outer boundary, cooling at the inner boundary, the bottom is thermally insulated, and the top is a free surface. An array of laser diodes embedded in the inner cylinder generates an annular laser sheet, enabling the measurement of velocity fields at a fixed height using particle image velocimetry. By systematically varying the rotation rate and the imposed temperature contrast, we adjusted the steepness of the free surface, thus the topographic β effect, and the thermal forcing strength, respectively. The non-dimensional controlling parameter, thermal Rossby number, RoT, ranges from 0.0012 to 0.01 and Taylor number, Ta, from 2.3 × 1010 to1.7 × 1011. We discerned the emergence of robust zonal jets, of which the zonal-mean kinetic energy accounts for up to 70% of the total kinetic energy, corresponding to a zonostrophic index of 2.7. In this regime, two coherent and persistent prograde jets form near the inner and outer boundaries. The radial profile of the potential vorticity develops toward a pronounced staircase-like structure, consistent with previous numerical studies (Scott and Dritschel, J. Fluid Mech., 2012). Analysis of the inter-scale energy transfer reveals a dominant interaction between the zonal-mean flow and eddies, while the kinetic energy spectrum of the zonal-mean component exhibits k−5 (where k denotes the wavenumber), in agreement with the theory of zonostrophic turbulence (Sukoriansky and Galperin, PRL, 2002).                                     Figure 1: A snapshot of azimuthal velocity contour for RoT = 7.1 × 10−3, Ta = 1.44 × 1011 and β =49.7 m−1 s−1.