Abstract
Within the vast array of variants encompassed by thermal (buoyancy) convection, the particular interest of the present work is on the specific dynamics which are enabled when standard steady gravity is replaced by a time-periodic body force induced by vibrations. The study is designed as a set of separate problems, where each exemplar aims to unravel the implications of the fundamental properties of this type of flow. These include the symmetry of the emerging pattern as perceived by a real observer and as seen in a “time-averaged space”, the synchronous or non-synchronous response of the velocity field to the applied forcing, the magnitude of the so-called Thermofluid-dynamic (TFD) distortions and the peculiar route of evolution towards chaos. A kaleidoscope of previously unknown solutions is reported giving emphasis to some still poorly known aspects such as the complex nature of the textural transitions that take place in the flow as the Gershuni number is increased (from 3.30 × 102 to 5.00 × 107 for Pr = 15). It is shown that the low-frequency regime is relatively stable over this range. In addition to the standard quadrupolar pattern, in such a case peculiar convective structures emerge where the time-averaged rolls display a very regular columnar arrangement, which has been rarely observed in earlier studies. Chaotic states are enabled when larger frequencies of vibration are considered. While for intermediate frequencies concurrent aspects of the Feigenbaum and Manneville and Pomeau mechanisms can be recognized, the hallmark of the high frequency regime is its adherence to the standard Ruelle-Takens scenario.
Highlights
Since its beginnings, convection of natural origin hasn’t ceased to amaze us with its peculiarity and counter-intuitive behaviors
Assuming the classical differen tially heated square cavity as reference case, the following questions are tackled here: the existence and the dynamics of regimes of regular fluid motion characterized by different degrees of spatial symmetry, the reverberation of these symmetries and their violation on the underlying temperature field, the influence of the frequency of vibrations on such symmetries and the peculiar path taken by this system in its progression towards chaos
When the Gershuni number is increased by two orders of magnitude, the convective struc ture with central symmetry is taken over by a diagonal mode, i.e. a flow displaying reflectional symmetry with respect to one of the diagonals of
Summary
Convection of natural origin hasn’t ceased to amaze us with its peculiarity and counter-intuitive behaviors. For the case of steady gravity and horizontal temperature difference (differentially heated cavity with vertical isothermal walls), many interesting numerical analyses have been produced for different values of the Prandtl number (ratio of the fluid kinematic viscosity and thermal diffusivity, Pr=ν/α) [3,4,5,6,7,8]; it is known that the flow can even develop turbulence [9,10,11,12,13,14,15,16,17,18,19,20] These findings have been instrumental in understanding the role played by the (square) shape of the cavity and revealing the possible modes of convection and their peculiar path of progression as the control parameter (the Rayleigh number) is increased (steady→periodic→quasi-periodic→turbulent flow). Assuming the classical differen tially heated square cavity as reference case, the following questions are tackled here: the existence and the dynamics of regimes of regular fluid motion characterized by different degrees of spatial symmetry, the reverberation of these symmetries and their violation (or rupture) on the underlying temperature field (leading to the so-called thermofluid-dy namic “distortions”), the influence of the frequency of vibrations on such symmetries and the peculiar path taken by this system in its progression towards chaos (an aspect still almost completely unknown for what concerns thermovibrational convection)
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
