Edoardo Bucchignani

Horizontal thermal convection in a shallow cavity: oscillatory regimes and transition to chaos

We develop a numerical analysis of the buoyancy driven natural convection of a fluid in a three dimensional shallow cavity (4 ⋅ 1 ⋅ 1) with a horizontal gradient of temperature along the larger dimension. The fluid is a liquid metal (Prandtl number equal to 0. 015) while the Grashof number (Gr) varies in the range 100,000‐300,000. The Navier‐Stokes equations in vorticity‐velocity formulation have been integrated by means of a linearized fully implicit scheme. The evaluation of fractal dimension of the attractors in the phase space has allowed the detection of the chaotic regime. The Ruelle‐Takens bifurcation sequence has been observed as mechanism for the transition to chaos: the quasi periodic regime with three incommensurate frequencies is the instability mechanism responsible for the transition to chaos. Physical experiments confirm the existence of this scenario.

A Numerical Modeling of Rayleigh–Marangoni Steady Convection in a Non-Uniform Differentially Heated 3D Cavity

A numerical study of a buoyancy driven convection flow in presence of thermocapillarity has been developed. The fluid is a silicone oil (Prandtl number equal to 105) contained in a three-dimensional box bounded by rigid and impermeable walls with top free surface exposed to a gaseous phase. At the lateral box walls a different non-uniform temperature distribution is assumed so to induce horizontal convection and to keep separated thermocapillary and buoyancy effects. The vorticity-velocity formulation of the time-dependent Navier–Stokes equations for a non-isothermal incompressible fluid is used. A procedure based on a linearized fully implicit finite difference second order scheme has been adopted. We obtained very complex steady configurations for several values of the temperature difference at the lateral walls, ΔT=30, 40 and 50°C. Along the direction perpendicular to the lateral walls, for ΔT increasing, we observe a physically meaningful growth of heat transfer. Confidence in these results is supported by a comparison with recent experimental and numerical observations.

A numerical algorithm for the assessment of the conjecture of a subglacial lake tested at Amundsenisen, Svalbard

The melting of glaciers coming with climate change threatens the heritage of the last glaciation of Europe likely contained in subglacial lakes in Greenland and Svalbard. This aspect urges specialists to focus their studies (theoretical, numerical, and on-field) on such fascinating objects. Along this line, we have approached the validation of the conjecture of the existence of a subglacial lake beneath the Amundsenisen Plateau at South-Spitzbergen, Svalbard, where ground penetrating radar measurements have revealed several flat signal spots, the sign of the presence of a body of water. The whole investigation aspects, mathematical modeling and numerical simulation procedure, and the numerical results are presented through a trilogy of papers of which the present one is the last. The time-dependent mathematical model in the background of the numerical algorithm includes the description of dynamics and thermodynamics of the icefield and of the subglacial lake, with heat exchange and liquid/solid phase-change mechanisms at the interface. Critical modeling choices and confidence in the algorithm are granted by the numerical results of the sensitivity analysis versus the contribution of ice water content, of firn and snow layers at top of the icefield and versus the approximation of ice sliding on bedrock. The two previous papers deal with these issues, show successful comparison with local measured quantities, and demonstrate numerically the likelihood of the subglacial lake. In this work, we aim at providing the studied case and the numerical algorithm with a possible paradigmatic value. At this aim, we introduce on-field measurement data related to the physical characteristics of the Amundsenisen Plateau that justify the adoption of significant modeling simplifications, here, focussed from physical viewpoint. Furthermore, we present the numerical algorithm and discuss several representative results from the numerical test to point out the type of results coming from the procedure. Such results might, eventually, provide a support to the decision to undertake drilling operations for tracing the subglacial water bio-chemicals generally present within the accreted ice above the presumed ice/water front.