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Ocean circulation supplies the surface ocean with the nutrients that fuel global ocean productivity. However, the mechanisms and rates of water and nutrient transport from the deep ocean to the upper ocean are poorly known. Here, we use the nitrogen isotopic composition of nitrate to place observational constraints on nutrient transport from the Southern Ocean surface into the global pycnocline (roughly the upper 1.2 km), as opposed to directly from the deep ocean. We estimate that 62 ± 5% of the pycnocline nitrate and phosphate originate from the Southern Ocean. Mixing, as opposed to advection, accounts for most of the gross nutrient input to the pycnocline. However, in net, mixing carries nutrients away from the pycnocline. Despite the quantitative dominance of mixing in the gross nutrient transport, the nutrient richness of the pycnocline relies on the large-scale advective flow, through which nutrient-rich water is converted to nutrient-poor surface water that eventually flows to the North Atlantic. Much of the nutrient transport from the deep ocean into the ocean’s upper water column occurs through the Southern Ocean, with mixing and advection playing complementary roles, according to a box model analysis of the isotopic composition of ocean nitrate.

Dispersion coefficients and the average solute transport velocity are pivotal for groundwater solute transport modeling. Accurately and efficiently determining these parameters is challenging due to difficulties in directly correlating them with pore‐space structure. To address this issue, we introduced the Physics‐enhanced Convolutional Neural Network‐Transformer (PhysenCT‐Net), an innovative model designed to concurrently estimate the longitudinal dispersion coefficient and average solute transport velocity in three‐dimensional porous media. PhysenCT‐Net exhibited excellent predictive performance on unseen testing datasets and significantly reduced computational demands. Comprehensive evaluations confirmed its robust generalization across various flow conditions and pore structures. Notably, the longitudinal dispersion coefficient predictions closely align with established empirical relationships involving Péclet number, affirming the model's physical interpretability and potential to aid in simulating transport phenomena in porous media. Plain Language Summary The migration of solutes in geological media is a complex process that involves both dispersion and advective motions. Therefore, the dispersion coefficient and advective flow rate are crucial parameters for modeling and predicting solute migration, with the former being determined by the complex flow field and solute diffusion coefficient within the medium. These two parameters are typically obtained through the experiment results of solute concentration distribution or through complex numerical simulations, which take a lot of time and resources. In this letter, we introduce a deep learning model that can provide a more efficient way to determine the two parameters describing substance movements. The model uses three‐dimensional images and properties of the media, the diffusion coefficient of solute and the mean flow speed of water as the inputs. We tested the model under a variety of conditions, and the dispersion coefficients predicted by the trained model agreed well with physical laws. The model can not only improve how we estimate these parameters, but also help us understand the physical laws that govern how substances move through groundwater. This could lead to better ways of modeling and managing these important water resources. Key Points Accurately predicting key parameters of the advection‐dispersion equation for solute transport in porous media Developing direct mapping relationships between three‐dimensional porous media images and parameters by the physics‐enhanced neural network Network demonstrates exceptional prediction accuracy and generalization, providing parameters that align with empirical formulas

Fluids in sedimentary basins exert a crucial influence on various geological phenomena including natural resource formation. Worldwide drilling projects have revealed that the salinity of sedimentary basinal fluids generally increases with depth, irrespective of lithology, age of sediments, or the presence of a halite bed. However, how these vertical salinity variations are produced and what controls the salinity remain unclear. This work examines a new hypothesis that downward‐increasing salinity variations are a natural outcome of the constant chemogravitational potential condition. In a static environment, the salinity is distributed such that the chemogravitational potential of the solute is constant with depth. Once formed, such a distribution would be maintained because no further migration of the solute would occur. To test the hypothesis, a constant chemogravitational potential distribution model was constructed for NaCl–H2O fluids in the sediment column, and NaCl content at each depth was calculated. The results showed that NaCl content monotonically increases with depth, and the variations are similar to the trend of measured data. However, the data were not necessarily completely reproduced by the model, and deviated in some parts from the calculated profile. Such deviation may indicate fluxing of external fluid occurring in these parts, as the constant chemogravitational potential is vulnerable to an advective flow. Therefore, it is proposed that the constant chemogravitational potential condition is a possible endmember theory, influencing natural salinity variations in a static environment. Key Points Vertical variations in salinity of sedimentary basinal fluid were simulated under constant chemogravitational potential conditions The simulation showed that the salinity increases with depth and the salinity gradient is positively dependent on the geotherm The constant chemogravitational potential distribution is roughly coincident with the data of natural sedimentary basinal fluids

We examine the dynamical behavior of accretion flow around XTE J1859+226 during the 1999 outburst by analyzing the entire outburst data (∼166 days) from RXTE Satellite. Towards this, we study the hysteresis behavior in the hardness intensity diagram (HID) based on the broadband (3–150 keV) spectral modeling, spectral signature of jet ejection and the evolution of Quasi-periodic Oscillation (QPO) frequencies using the two-component advective flow model around a black hole. We compute the flow parameters, namely Keplerian accretion rate (m˙d), sub-Keplerian accretion rate (m˙h), shock location (rs) and black hole mass (Mbh) from the spectral modeling and study their evolution along the q-diagram. Subsequently, the kinetic jet power is computed as Ljetobs∼3–6×1037ergs−1 during one of the observed radio flares which indicates that jet power corresponds to 8–16% mass outflow rate from the disc. This estimate of mass outflow rate is in close agreement with the change in total accretion rate (∼14%) required for spectral modeling before and during the flare. Finally, we provide a mass estimate of the source XTE J1859+226 based on the spectral modeling that lies in the range of 5.2–7.9 M⊙ with 90% confidence.

Recent research explored an alternative energy-centred perspective on hydrological processes, extending beyond the classical analysis of the catchment's water balance. Particularly, streamflow and the structure of river networks have been analysed in an energy-centred framework, which allows for the incorporation of two additional physical laws: (1) energy is conserved and (2) entropy of an isolated system cannot decrease (first and second law of thermodynamics). This is helpful for understanding the self-organized geometry of river networks and open-catchment systems in general. Here we expand this perspective, by exploring how hillslope topography and the presence of rill networks control the free-energy balance of surface runoff at the hillslope scale. Special emphasis is on the transitions between laminar-, mixed- and turbulent-flow conditions of surface runoff, as they are associated with kinetic energy dissipation as well as with energy transfer to eroded sediments. Starting with a general thermodynamic framework, in a first step we analyse how typical topographic shapes of hillslopes, representing different morphological stages, control the spatial patterns of potential and kinetic energy of surface runoff and energy dissipation along the flow path during steady states. Interestingly, we find that a distinct maximum in potential energy of surface runoff emerges along the flow path, which separates upslope areas of downslope potential energy growth from downslope areas where potential energy declines. A comparison with associated erosion processes indicates that the location of this maximum depends on the relative influence of diffusive and advective flow and erosion processes. In a next step, we use this framework to analyse the energy balance of surface runoff observed during hillslope-scale rainfall simulation experiments, which provide separate measurements of flow velocities for rill and for sheet flow. To this end, we calibrate the physically based hydrological model Catflow, which distributes total surface runoff between a rill and a sheet flow domain, to these experiments and analyse the spatial patterns of potential energy, kinetic energy and dissipation. This reveals again the existence of a maximum of potential energy in surface runoff as well as a connection to the relative contribution of advective and diffusive processes. In the case of a strong rill flow component, the potential energy maximum is located close to the transition zone, where turbulence or at least mixed flow may emerge. Furthermore, the simulations indicate an almost equal partitioning of kinetic energy into the sheet and the rill flow component. When drawing the analogy to an electric circuit, this distribution of power and erosive forces to erode and transport sediment corresponds to a maximum power configuration.

This paper describes full solutions of the energy and Navier–Stokes equations in the approximate form of Boussinesq. The advective fluid layer flowing within parallel horizontal infinite walls subject to hydro-thermal slip conditions is of the prime interest. The control of the momentum/thermal motion is undertaken by a vertically applied magnetic field towards the parallel walls. The response of the layer to the momentum slip and thermal jump conditions under the applied magnetic field is investigated through solving exactly the idealized system of equations. From the obtained closed-form formulae, behaviour of the velocity and temperature fields as well as the rigid/free and thermally conducting/insulating wall cases is easy to gain. Results clearly imply that hydro-thermal slip enhances both velocity and temperature fields, unlike the suppression effects of magnetic field. Full solutions as presented here can serve as good basic flow for further research including the linear/nonlinear stability issues in regard to the plane or spiral perturbations.

Assessment of the level of activity of advective transport through faults and fractures is essential for guiding the geological disposal of radioactive waste. In this study, the advective flow (active, inactive) of meteoric water through fractures is assessed by comparing stable isotopes (δD and δ18O) between fracture and pore waters obtained from four boreholes in marine deposits in the Horonobe area, Japan. At 27–83-m depth in one borehole and 28–250 m in another, the isotopic compositions of pore and fracture water reflect mixing with meteoric water, with stronger meteoric-water signatures being observed in the fracture water than in pore water of the rock matrix. At greater depths in these boreholes and at all sampling depths in the other two studied boreholes, the isotopic compositions of fracture and pore waters are comparable. These results suggest that the advective flow of meteoric water is active at shallow depths where fossil seawater is highly diluted in the two boreholes. This interpretation is compatible with the occurrence of present or paleo meteoric waters and tritium, whereby present meteoric water and tritium are limited to those depths in the two boreholes. This difference in the level of activity of advective flow is probably because of the glacial–interglacial difference in hydraulic gradients resulting from sea-level change. Although fractures are hydraulically connected to the surface through the sedimentary rock, advective flow through them is inferred to remain inactive so long as sea level does not fall substantially.

The galactic black hole candidate (BHC) XTE J1118+480 during its 2000 outburst has been studied in a broad energy range using the archival data of PCA and HEXTE payloads of Rossi X-ray Timing Explorer. Detailed spectral and temporal properties of the source are studied. Low and very low frequency quasi-periodic oscillations (QPOs), with a general trend of increasing frequency are observed during the outburst. Spectral analysis is done using the combined data of the PCA and HEXTE instruments with two types of models: the well-known phenomenological power-law model and the current version of the fits file of two-component advective flow (TCAF) solution as an additive table model in XSPEC. During the entire period of the outburst, a non-thermal power-law component and the TCAF model fitted to the sub-Keplerian halo rate were found to be highly dominant. We suggest that this so-called outburst is due to enhanced jet activity. Indeed, the ‘outburst’ subsides when this activity disappears. We estimated the X-ray fluxes coming from the base of the jet and found that the radio flux is correlated with this X-ray flux. Though the object was in the hard state in the entire episode, the spectrum becomes slightly softer with the rise in the Keplerian disk rate in the late declining phase. We also estimated the probable mass of the source from our spectral analysis with the TCAF solution. Our estimated mass of XTE J1118+480 is 6.99−0.74+0.50M⊙\\(6.99^{+0.50}_{-0.74}~M_{\\odot }\\) i.e., in the range of 6.25–7.49M⊙\\(7.49~M _{\\odot }\\).

Non-uniform infiltration and subsurface flow in structured soils is observed in most natural settings. It arises from imperfect lateral mixing of fast advective flow in structures and diffusive flow in the soil matrix and remains one of the most challenging topics with respect to match observation and modelling of water and solutes at the plot scale. This study extends the fundamental introduction of a space domain random walk of water particles as an alternative approach to the Richards equation for diffusive flow (Zehe and Jackisch, 2016) to a stochastic–physical model framework simulating soil water flow in a representative, structured soil domain. The central objective of the proposed model is the simulation of non-uniform flow fingerprints in different ecohydrological settings and antecedent states by making maximum use of field observables for parameterisation. Avoiding non-observable parameters for macropore–matrix exchange, an energy-balance approach to govern film flow in representative flow paths is employed. We present the echoRD model (ecohydrological particle model based on representative domains) and a series of application test cases. The model proves to be a powerful alternative to existing dual-domain models, driven by experimental data and with self-controlled, dynamic macropore–matrix exchange from the topologically semi-explicitly defined structures.

The effect of the temporal variation of the hydraulic gradient on the transport of the impurity pulses in a porous column has been studied experimentally. The measurements were made using horizontal columns with different porosity and therefore different permeability. The temporal changes in the hydraulic gradient as well as the intensity of the bulk flow were organized by changing the vertical position of the outlet valve. Only harmonic fluctuations of the filtration flow intensity have been taken into account. It was shown that the effect of the time-varying flow rate is only noticeable when concentration convection develops against the background of the main advective flow. Changing the period and amplitude of the flow pulsations caused by changing the hydraulic gradient at the ends of the column will only change the impurity transport rate, not the amount of impurity leached.