arXiv subjects

Marc A. Hesse

Publications and source records attributed to Marc A. Hesse.

7 recordsLinked to original sources

arXiv2026

HydroFirn: A numerical model for large-scale multidimensional firn hydrology

Observations show the multidimensional dynamics of meltwater and distribution of ice layers in the firn on the Greenland Ice Sheet. However, state-of-the-art large-scale models for firn hydrology are essentially one-dimensional, limiting their ability to explain observed datasets and failing to reduce uncertainty in surface mass balance and sea-level rise estimates. Here, we present a large-scale, multidimensional, multiphase, and thermomechanical model to simulate firn hydrology. The model is highly efficient due to a novel algorithm in which an extra equation for pressure is solved only in saturated regions. Furthermore, the model can apply spatially heterogeneous boundary conditions to the unsaturated-saturated domain and allows for the dynamic formation of fully impermeable ice layers. The numerical results show excellent comparisons against analytic solutions to one- and two-dimensional problems that involve coupled unsaturated-saturated flows, thermodynamics, and phase change. We further apply the model to investigate field data from southwest Greenland and find that lateral heterogeneities strongly influence the depth of melt percolation and ice layer formation. Improved understanding of these local, multidimensional processes will provide physics-based constraints on firn densification, reduce uncertainty in converting altimetric elevation change to mass change, and improve estimates of freshwater fluxes to the ocean under a warming climate.

physics.geo-ph↗

arXiv2021

Convective carbon dioxide dissolution in a closed porous medium at high-pressure real-gas conditions

We combine modeling and measurements to investigate the dynamics of convective carbon dioxide (CO$_2$) dissolution in a pressure-volume-temperature cell, extending a recent study by Wen et al. (J. Fluid Mech., vol. 854, 2018, pp. 56--87) at low-pressure under ideal-gas conditions to high-pressure and real-gas conditions. Pressure-dependent compressibility and solubility are included to model the evolution of CO$_2$ concentration in the gas phase and at the interface, respectively. Simple ordinary-differential-equation models are developed to capture the mean behavior of the convecting system at large Rayleigh number and are then verified by using both numerical simulations and laboratory experiments. The prefactor for the linear scaling of convective CO$_2$ dissolution is evaluated -- for the first time -- by using pressure-decay experiments in bead packs at reservoir conditions. The results show that our models could quantitatively predict the process of the convective CO$_2$ dissolution in pressure-decay experiments. Moreover, the results also reveal that for increasing gas pressure in closed systems, the negative feedback of the pressure drop -- resulting from the dissolution of CO$_2$ in the liquid -- is weakened due to the decrease of the solubility constant at real-gas conditions. Our analysis provides a new direction for determination and validation of the convective dissolution flux of CO$_2$ in porous media systems.

physics.flu-dyn↗

arXiv2020

New insights into temperature-dependent ice properties and their effect on ice shell convection for icy ocean worlds

Ice shell dynamics are an important control on the habitability of icy ocean worlds. Here we present a systematic study evaluating the effect of temperature-dependent material properties on these dynamics. We review the published thermal conductivity data for ice, which demonstrates that the most commonly used conductivity model in planetary science represents a lower bound. We propose a new model for thermal conductivity that spans the temperature range relevant to the ice shells of ocean worlds. This increases the thermal conductivity at low temperatures near the surface by about a fifth. We show that such an increase in thermal conductivity near the cold surface can stabilizes the ice shell of Europa. Furthermore, we show that including temperature dependent specific heat capacity decreases the energy stored in the conductive lid which reduces the response timescale of the ice shell to thermal perturbations by approximately a third. This may help to explain surface features such as chaotic terrains that require large additions of energy to the near-surface ice.

astro-ph.EP↗

arXiv2020

Bayesian Poroelastic Aquifer Characterization from InSAR Surface Deformation Data. Part I: Maximum A Posteriori Estimate

Characterizing the properties of groundwater aquifers is essential for predicting aquifer response and managing groundwater resources. In this work, we develop a high-dimensional scalable Bayesian inversion framework governed by a three-dimensional quasi-static linear poroelastic model to characterize lateral permeability variations in groundwater aquifers. We determine the maximum a posteriori (MAP) point of the posterior permeability distribution from centimeter-level surface deformation measurements obtained from Interferometric Synthetic Aperture Radar (InSAR). The scalability of our method to high parameter dimension is achieved through the use of adjoint-based derivatives, inexact Newton methods to determine the MAP point, and a Matérn class sparse prior precision operator. Together, these guarantee that the MAP point is found at a cost, measured in number of forward/adjoint poroelasticity solves, that is independent of the parameter dimension. We apply our methodology to a test case for a municipal well in Mesquite, Nevada, in which InSAR and GPS surface deformation data are available. We solve problems with up to 320,824 state variable degrees of freedom (DOFs) and 16,896 parameter DOFs. A consistent treatment of noise level is employed so that the aquifer characterization result does not depend on the pixel spacing of surface deformation data. Our results show that the use of InSAR data significantly improves characterization of lateral aquifer heterogeneity, and the InSAR-based aquifer characterization recovers complex lateral displacement trends observed by independent daily GPS measurements.

physics.geo-ph↗

arXiv2018

Convection in porous media with dispersion

We investigate the effect of dispersion on convection in porous media by performing direct numerical simulations (DNS) in a two-dimensional Rayleigh-Darcy domain. Scaling analysis of the governing equations shows that the dynamics of this system are not only controlled by the classical Rayleigh-Darcy number based on molecular diffusion, $Ra_m$, and the domain aspect ratio, but also controlled by two other dimensionless parameters: the dispersive Rayleigh number $Ra_d = H/α_t$ and the dispersivity ratio $r = α_l/α_t$, where $H$ is the domain height, $α_t$ and $α_l$ are the transverse and longitudinal dispersivities, respectively. For $Δ= Ra_d/Ra_m > O(1)$, the influence from the mechanical dispersion is minor; for $Δ\ll 1$, however, the flow pattern is controlled by $Ra_d$ while the convective flux is $F\sim Ra_m$ for large $Ra_m$, but with a prefactor that has a non-monotonic dependence on $Ra_d$. Our DNS results also show that the increase of mechanical dispersion, i.e. decreasing $Ra_d$, will coarsen the convective pattern by increasing the plume spacing. Moreover, the inherent anisotropy of mechanical dispersion breaks the columnar structure of the mega-plumes at large $Ra_m$, if $Ra_d < 5000$. This results in a fan-flow geometry that reduces the convective flux.

physics.flu-dyn↗

arXiv2018

Rayleigh fractionation in high-Rayleigh-number solutal convection in porous media

We study the fractionation of two components between a well-mixed gas and a saturated convecting porous layer. Motivated by geological carbon dioxide (CO$_2$) storage we assume that convection is driven only by the dissolved concentration of the first component, while the second acts as a tracer with increased diffusivity. Direct numerical simulations for convection at high Rayleigh numbers reveal that the partitioning of the components, in general, does not follow a Rayleigh fractionation trend, as commonly assumed. Initially, increases in tracer diffusivity also increase its flux, because the diffusive boundary layer penetrates deeper into the flow. However, for $D_2\geq 10\, D_1$, where $D_1$ and $D_2$ are, respectively, the diffusion coefficients of CO$_2$ and the tracer in water, the transverse leakage of tracer between up- and down-welling plumes reduces the tracer flux. Rayleigh fractionation between components is only realized in the limit of two gases with very large differences in solubility and initial concentration in the gas.

physics.flu-dyn↗

arXiv2018

Dynamics of convective carbon dioxide dissolution in a closed porous media system

Motivated by geological carbon dioxide (CO$_2$) storage, many recent studies have investigated the fluid dynamics of solutal convection in porous media. Here we study the convective dissolution of CO$_2$ in a closed system, where the pressure in the gas declines as convection proceeds. This introduces a negative feedback that reduces the convective dissolution rate even before the brine becomes saturated. We analyse the case of an ideal gas with a solubility given by Henry's law, in the limits of very low and very high Rayleigh numbers. The equilibrium state in this system is determined by the dimensionless dissolution capacity, $Π$, which gives the fraction of the gas that can be dissolved into the underlying brine. Analytic approximations of the pure diffusion problem with $Π>0$, show that the diffusive base state is no longer self-similar and that diffusive mass transfer declines rapidly with time. Direct numerical simulations at high Rayleigh numbers show that no constant flux regime exists for $Π> 0$; nevertheless, the quantity $F/C_s^2$ remains constant, where $F$ is the dissolution flux and $C_s$ is the dissolved concentration at the top of the domain. Simple mathematical models are developed to predict the evolution of $C_s$ and $F$ for high-Rayleigh-number convection in a closed system. The negative feedback that limits convection in closed systems may explain the persistence of natural CO$_2$ accumulations over millennial timescales.

physics.flu-dyn↗