ALBERT

Description: We propose to assess the error done when temperature is considered as a conservative tracer in fluviokarst studies. As a matter of fact, heat exchanges occur between karstic Conduit System (CS) and Porous Fractured Matrix (PFM) that prevents from using this approximation without caution. The conservative tracer approximation boils down to consider the cooling of CS water by PFM flow in an open thermodynamic system where the CS is bounded by an Adiabatic Wall (AW). The resulting CS water temperature contrasts with the one obtained from more complete models (CW), which also take into account heat conduction within the CS, within the PFM, and from the CS to PFM through CS a Conductive Wall. In order to assess first orders of this error, the dimensionless equations, characteristic of CS cooling by PFM, have been solved thanks to Alternate Finite Difference Implicit methods both in AW and CW configurations. Four groups of dimensionless numbers appear in the various terms of energy and mass equations among which the Peclet and Reynolds numbers depict the large morphologic and hydrologic variability of natural karstic systems. A parametric exploration of the differences between AW and CW models has then been conducted vs. Peclet numbers (Pe numbers varying from 106 to 109, at constant CS Reynolds number) and vs. Reynolds numbers (Red varying from 103 to 107, at constant Peclet number). The error curves bound finite volumes in the Peclet–Reynolds space that converge uniformly to zero for the extreme values of these parameters. However, for Peclet and Reynolds numbers characteristic of realistic fluviokarst configurations, the errors reach finite values, that give first order information assessing the error done by considering temperatures as conservative tracers. Maximum relative errors around 10−2 (in fact 0.0092) have been found varying Pe; while it remained slightly lower than 0.7 × 10−2 varying Red. An illustrative example of the temperature conservative tracer AW approximation is presented with the data obtained from the main morphologic and hydrologic properties of the Cent–Font resurgence (Hérault, France). According to the results, the error reached at the output of the fluviokarst is 0.00613 (for Pe = 1.4993 × 108 and Red = 4.2969 × 104). When rescaled to the physical domain, this error leads to a temperature difference of 1.77 K between the CW and AW configurations.

Description: We designed a thermo-mechanical numerical model for fast-spreading mid-ocean ridge with variable viscosity, hydrothermal cooling, latent heat release, sheeted dyke layer, and variable melt intrusion possibilities. The model allows for modulating several accretion possibilities such as the "gabbro glacier" (G), the "sheeted sills" (S) or the "mixed shallow and MTZ lenses" (M). These three crustal accretion modes have been explored assuming viscosity contrasts of 2 to 3 orders of magnitude between strong and weak phases and various hydrothermal cooling conditions depending on the cracking temperatures value. Mass conservation (stream-function), momentum (vorticity) and temperature equations are solved in 2-D cartesian geometry using 2-D, alternate direction, implicit and semi-implicit finite-difference scheme. In a first step, an Eulerian approach is used solving iteratively the motion and temperature equations until reaching steady states. With this procedure, the temperature patterns and motions that are obtained for the various crustal intrusion modes and hydrothermal cooling hypotheses display significant differences near the mid-ocean ridge axis. In a second step, a Lagrangian approach is used, recording the thermal histories and cooling rates of tracers travelling from the ridge axis to their final emplacements in the crust far from the mid-ocean ridge axis. The results show that the tracer's thermal histories are depending on the temperature patterns and the crustal accretion modes near the mid-ocean ridge axis. The instantaneous cooling rates obtained from these thermal histories betray these discrepancies and might therefore be used to characterize the crustal accretion mode at the ridge axis. These deciphering effects are even more pronounced if we consider the average cooling rates occurring over a prescribed temperature range. Two situations were tested at 1275–1125 °C and 1050–850 °C. The first temperature range covers mainly the crystallization range that is characteristic of the high temperature areas in the model (i.e. the near-mid-oceanic-ridge axis). The second temperature range corresponds to areas in the model where the motion is mainly laminar and the vertical temperature profiles are closer to conductive. Thus, this situation results in less discriminating efficiency among the crustal accretion modes since the thermal and dynamic properties that are described are common to all the crustal accretion modes far from the ridge axis. The results show that numerical modeling of thermo-mechanical properties of the lower crusts may bring useful information to characterize the ridge accretion structure, hydrothermal cooling and thermal state at the fast-spreading ridges and may open discussions with petrological cooling rate results.

Description: We designed a thermo-mechanical model for fast spreading mid-ocean ridge with variable viscosity, hydrothermal cooling, latent heat release, sheeted dyke layer, and variable melt intrusion possibilities. The model allows to take into account several accretion possibilities as: the "gabbro glacier" (G), the "sheeted sills" (S) or the "mixed shallow and MTZ lenses" (M). Viscosity contrasts of 2 to 3 orders of magnitude between the hot and cold phases have been tested. We also explored hydrothermal cooling according to various cracking temperatures for crustal rocks. Hence, the model allows exploring various near ridge motions and thermal patterns that induce various cooling histories for gabbros. According to the assumed opening-closure temperature range, the cooling rates sample the near-ridge structure or record areas farther from the ridge. As an analogy to experimental petrology we called ICR the cooling rates sampled near the ridge and SRC the cooling rates sampled far from the ridge where the flow tends to laminar and conductive patterns. The results emphasize that the cooling rates may significantly depend on the choice of this opening-closure temperature range. The results show that numerical modeling of thermo-mechanical properties of the lower crust's may bring information to study the hypotheses related to the ridge accretion structure, hydrothermal cooling and thermal state at the fast-spreading ridges.