Abstract. We develop a model for describing water flow in a porous medium under the effect of thermal and pressure gradients. The model simulates geothermal systems in calderas. Given the boundary conditions and the fluid-dynamical properties of the medium, the model allows computation, in fluid-dynamical stationary states, of parameters characterizing the flow, such as flow velocity and temperature and pressure distributions at depth. The model is applied to investigate the effects of the local geothermal system on the unrest episodes at Campi Flegrei caldera. Using experimentally determined fluid-dynamical parameters for the caldera rocks, we show that changes of water flow in shallow aquifers under the effect of pressure and/or temperature variations within the geothermal system can be very important in the genesis and evolution of unrest crises. In particular, they can strongly amplify the effect of pressure increase in the magma chamber on ground uplift. They can also explain the timescales of evolution of ground movements in terms of transit times of the water front and of the connected temperature fronts due to advective transport. On such grounds an integrated mechanic-thermal fluid-dynamical model was built, allowing us to give a semiquantitative, global explanation to the genesis and evolution of unrest phenomena. Results obtained here can be generalized to other similar calderas.

We have employed a simple Galerkin-approximation scheme to calculate nonequilibrium temperature and concentration fluctuations in a binary fluid subjected to a temperature gradient with realistic boundary conditions. When a fluid mixture is driven outside thermal equilibrium, there are two instability mechanisms, namely a Rayleigh (stationary) and a Hopf (oscillatory) instability, causing long-ranged fluctuations. The competition of these two mechanisms causes the structure factor associated with the temperature fluctuations to exhibit two maxima as a function of the wave number q of the fluctuations, in particular, close to the convective instability. In the presence of thermally conducting but impermeable walls the intensity of the temperature fluctuations vanishes as q goes to zero, while the intensity of the concentration fluctuations remains finite in the limit of vanishing q. Finally, we propose a simpler small-Lewis-number approximation scheme, which is useful to represent nonequilibrium concentration fluctuations for mixtures with positive separation ratio, even close to (but below) the convective instability.

In the present article it is shown how a series of experimental evidences and theoretical developments on liquid modelling, gathered for the first time, can all be framed in a mesoscopic view of liquids that are hypothesized as constituted by a population of wave packets, responsible for the propagation of elastic and thermal perturbations, and of dynamic aggregates of molecules, in continuous re-arrangement, diving in an ocean of amorphous, disordered liquid. This model, dubbed Dual Model of Liquids, is complementary to the Phonon theory of Liquid Thermodynamics, recently proposed by an independent group. The pseudo-crystalline dynamic structures, whose presence in liquids is evidenced by high energy inelastic scattering experiments, interact with a statistical population of harmonic elastic waves and anharmonic wave-packets propagating within and among the structures themselves, respectively. The expression for the interaction term is derived from “first principles” based on general considerations related to the pressure exerted by elastic waves travelling in condensed media. The anharmonic character of the interaction allows the exchange not only of energy but also of momentum between wave packets and clusters, thus determining both the displacement of the latter within the medium, and the redistribution of the energy between external, or translatory degrees of freedom of the clusters, and internal collective, vibratory degrees. Using these concepts it is possible to calculate some dynamic and thermodynamic quantities concerning the dynamics of liquids. Moreover, the interpretation of the relaxation times of the processes involved in momentum and energy transport is given, their Order-of-Magnitude is calculated, and the way in which these times are involved in the different phases of the collective dynamics of liquids is discussed. A comparison is provided with results obtained in the frame of PLT and with the forecasts for the visco-elastic transition regions. In the last part of the paper, some experiments are suggested that should be performed to provide additional details to the model.

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