Assessment of open thermodynamic system concepts for fluviokarst temperature calculations – an example, the Cent-Fonts resurgence (Hérault, France)

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

Label, patrimoine, population et gouvernance, la cohabitation du meilleur et du pire ; l’exemple de Saint-Guilhem-le-Désert

La notion de territoire ne peut se découpler de la société des individus qui y vivent. C’est là que se fondent les racines du patrimoine qui construit le lien entre la population, son histoire, ses traditions et l’administration locale. À plusieurs reprises, les interventions des habitants de Saint-Guilhem-le-Désert ont permis de sauver et de transmettre un patrimoine qui aurait été dispersé. La puissance passée de l’abbaye avait permis de rassembler ces trésors aujourd’hui protégés par de multiples labels. Ceux-ci favorisent une économie touristique qui permet son entretien. Pourtant les labels ont aussi des influences normatives susceptibles de réduire l’originalité des sites. Cet effet est d’autant plus important que les contraintes ou les instances d’évaluation sont découplés de la population.The notion of territory cannot be separated from that of local-level human society. This is where we find the roots of heritage, linking a given population to its history, its traditions, and the local administration. Several times in the past, the actions of the population of Saint-Guilhem-le-Désert, succeeded in directly saving and passing on precious heritage that would otherwise have been lost. The past power of the abbey meant that it accumulated many treasures through time, which today are protected by various heritage labels. This boosts the economy of tourism, which in turn, funds restoration works and opening the site to the general public. However, conforming to labels can also induce standardisation and possibly reduce the originality of a site. The further the constraints and evaluation criteria are from the concerns of the local community, the more perverse the effect can be

Les pulsations de la Terre

Depuis l'origine des temps géologiques, la surface de la Terre est en perpétuel bouleversement. Après les avoir fait apparaître, la tectonique des plaques promène les continents d'un bout à l'autre de la Terre dans une danse qui ne doit rien au hasard. Tremblements de Terre, éruptions volcaniques, tsunamis... les manifestations les plus visibles des colères actuelles de la Terre font peur. Toutes sont dues à la dynamique du manteau de la Terre dont les couches les plus profondes sont continuellement brassées avec les plus superficielles. Dans l'histoire de la Terre, les lents mouvements du manteau terrestre ont quelquefois été pris dans des événements d'avalanches catastrophiques qui ont successivement créé et détruit les supercontinents. Les conséquences de ces événements se mesurent à l'échelle de la planète entière qu'ils ont modelée de manière irréversible par des phénomènes volcaniques et tectoniques dont l'ampleur n'a rien a voir avec ceux que nous connaissons aujourd'hui

Revisiting Cent-Fonts Fluviokarst Hydrological Properties with Conservative Temperature Approximation

We assess the errors produced by considering temperature as a conservative tracer in fluviokarst studies. Heat transfer that occurs between karstic Conduit System (CS) and Porous Fractured Matrix (PFM) is the reason why one should be careful in making this assumption without caution. We consider the karstic aquifer as an Open Thermodynamic System (OTS), which boundaries are permeable to thermal energy and water. The first principle of thermodynamics allows considering the enthalpy balance between the input and output flows. Combined with a continuity equation this leads to a two-equation system involving flows and temperatures. Steady conditions are approached during the recession period or during particular phases of pumping test experiments. After a theoretical study of the error induced by the conservative assumption in karst, we have applied the method to revisit the data collected during a complete campaign of pumping test. The method, restricted to selected data allowed retrieving values of base flow, mixing of flow, intrusions of streams, and aquifer answer to drawdown. The applicability of the method has been assessed in terms of propagation of the temporal fluctuations trough the solving but also in terms of conservative assumption itself. Our results allow retrieving the main hydrological properties of the karst as observed on field (timed volumetric samplings, geochemical analyses, step pumping test and allogenic intrusion of streams). This consistency argues in favor of the applicability of the conservative temperature method to investigating fluviokarst systems under controlled conditions

Convection dans le manteau terrestre, etude en geometrie spherique

SIGLECNRS T Bordereau / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc

Revisiting Cent-Fonts Fluviokarst Hydrological Properties with Conservative Temperature Approximation

We assess the errors produced by considering temperature as a conservative tracer in fluviokarst studies. Heat transfer that occurs between karstic Conduit System (CS) and Porous Fractured Matrix (PFM) is the reason why one should be careful in making this assumption without caution. We consider the karstic aquifer as an Open Thermodynamic System (OTS), which boundaries are permeable to thermal energy and water. The first principle of thermodynamics allows considering the enthalpy balance between the input and output flows. Combined with a continuity equation this leads to a two-equation system involving flows and temperatures. Steady conditions are approached during the recession period or during particular phases of pumping test experiments. After a theoretical study of the error induced by the conservative assumption in karst, we have applied the method to revisit the data collected during a complete campaign of pumping test. The method, restricted to selected data allowed retrieving values of base flow, mixing of flow, intrusions of streams, and aquifer answer to drawdown. The applicability of the method has been assessed in terms of propagation of the temporal fluctuations trough the solving but also in terms of conservative assumption itself. Our results allow retrieving the main hydrological properties of the karst as observed on field (timed volumetric samplings, geochemical analyses, step pumping test and allogenic intrusion of streams). This consistency argues in favor of the applicability of the conservative temperature method to investigating fluviokarst systems under controlled conditions

Evaluation of First Order Error Induced by Conservative-Tracer Temperature Approximation for Mixing in Karstic Flow

Fluid dynamics in karst systems is complex due to the heterogeneity of hydraulic networks that combine the Porous Fractured Matrix (PFM) and the interconnected drains (CS). These complex dynamic systems often need to be treated as “black boxes” in which only input and output properties are known. In this work, we propose to assess the first-order error induced by considering the temperature as a conservative tracer for flows mixing in karst (fluvio-karst). The fluvio-karstic system is treated as an open thermodynamic system (OTS), which exchanges water and heat with its surrounding. We propose to use a cylindrical PFM drained by a water saturated cylindrical CS, connected on one side to a sinkhole zone and, on the other side, to a resurgence flowing at the base level of the karstic system. This framework allows us to develop the equations of energy and mass conservation for the different parts of the OTS. Two numerical models have been written to solve these equations: 1) the so-called AW (for Adiabatic Wall) configuration that assumes a conservative tracer behavior for temperature with no conductive heat transfer, neither in the liquid, nor in the PFM or even through the wall separating the CS from the PFM; and, 2), the CW (for Conductive Wall) configuration that takes into account the heat and mass transfers in water and from water to aquifer rocks both in the CS and in the PFM. Looking at the large variability of karstic system morphologic properties, dimensionless forms of the equations have been written for both AW and CW configurations. This approach allows us to gather the physical, hydrological and morphological properties of karstic systems into four dimensionless numbers: the Peclet, Reynolds, Prandtl and dimensionless diffusivity numbers. This formalism has been used to conduct a parametric exploration across several orders of magnitude based on the Peclet and the Reynolds numbers. The final errors, between the AW and CW configurations, remain less than 1% across the entire parametric range. The combination of error curves bounds a closed volume in error space that gives a first upper bound of the error made by considering the temperature as a conservative tracer. Applying the method to an illustrative example of karst allows us to reach a first order error within a few degrees °C

Evaluation of First Order Error Induced by Conservative-Tracer Temperature Approximation for Mixing in Karstic Flow

Fluid dynamics in karst systems is complex due to the heterogeneity of hydraulic networks that combine the Porous Fractured Matrix (PFM) and the interconnected drains (CS). These complex dynamic systems often need to be treated as “black boxes” in which only input and output properties are known. In this work, we propose to assess the first-order error induced by considering the temperature as a conservative tracer for flows mixing in karst (fluvio-karst). The fluvio-karstic system is treated as an open thermodynamic system (OTS), which exchanges water and heat with its surrounding. We propose to use a cylindrical PFM drained by a water saturated cylindrical CS, connected on one side to a sinkhole zone and, on the other side, to a resurgence flowing at the base level of the karstic system. This framework allows us to develop the equations of energy and mass conservation for the different parts of the OTS. Two numerical models have been written to solve these equations: 1) the so-called AW (for Adiabatic Wall) configuration that assumes a conservative tracer behavior for temperature with no conductive heat transfer, neither in the liquid, nor in the PFM or even through the wall separating the CS from the PFM; and, 2), the CW (for Conductive Wall) configuration that takes into account the heat and mass transfers in water and from water to aquifer rocks both in the CS and in the PFM. Looking at the large variability of karstic system morphologic properties, dimensionless forms of the equations have been written for both AW and CW configurations. This approach allows us to gather the physical, hydrological and morphological properties of karstic systems into four dimensionless numbers: the Peclet, Reynolds, Prandtl and dimensionless diffusivity numbers. This formalism has been used to conduct a parametric exploration across several orders of magnitude based on the Peclet and the Reynolds numbers. The final errors, between the AW and CW configurations, remain less than 1% across the entire parametric range. The combination of error curves bounds a closed volume in error space that gives a first upper bound of the error made by considering the temperature as a conservative tracer. Applying the method to an illustrative example of karst allows us to reach a first order error within a few degrees °C

Comment on “Stability of the Earth with respect to the spin axis for the last 130 million years” by J.A. Tarduno and A.Y. Smirnov [Earth Planet. Sci. Lett. 184 (2001) 549–553]

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