One numerical method was designed to solve the time-dependent, three-dimensional, incompressible Navier–Stokes equations in turbulent thermal channel flows. Its originality lies in the use of several well-known methods to discretize the problem and its parallel nature. Vorticy-Laplacian of velocity formulation has been used, so pressure has been removed from the system. Heat is modeled as a passive scalar. Any other quantity modeled as passive scalar can be very easily studied, including several of them at the same time. These methods have been successfully used for extensive direct numerical simulations of passive thermal flow for several boundary conditions.

This article studies the linear stability of a thermoconvective problem in an annular domain for different Bond (capillarity or buoyancy effects) and Biot (heat transfer) numbers for two set of Prandtl numbers (viscosity effects). The flow is heated from below, with a linear decreasing horizontal temperature profile from the inner to the outer wall. The top surface of the domain is open to the atmosphere and the two lateral walls are adiabatic. Different kind of competing solutions appear on localized zones of the Bond-Biot plane. The boundaries of these zones are made up of co-dimension two points. A co-dimension four point has been found for the first time. The main result found in this work is that in the range of low Prandtl number studied and in low-gravity conditions, capillarity forces control the instabilities of the flow, independently of the Prandtl number.This work was supported by a generous grant of computer time from the supercomputing center of the UPV.Publicad

Bifurcation Diversity in an Annular Pool Heated from Below: Prandtl and Biot Numbers Effects - Volume 13 Issue 2 - A. J. Torregrosa, S. Hoyas, M. J. Pérez-Quiles, J. M. Mompó-Laborda

This Brief Report studies the linear stability of a thermoconvective problem in an annular domain for relatively low ($$\sim${}$1) Prandtl (viscosity effects) and Biot (heat transfer) numbers. The four possible patterns for the instabilities, namely, hydrothermal waves of first and second class, longitudinal rolls, and corotating rolls, are present in a small region of the Biot-Prandtl plane. This region can be split in four zones, depending on the sort of instability found. The boundary of these four zones is composed of codimension-two points. Authors have also found two codimension-three points, where some of the former curves intersect. Results shown in this Brief Report clarify some reported experiments, predict new instabilities, and, by giving a deeper insight into how physical parameters affect bifurcations, open a gateway to control those instabilities.

The behavior of turbulent flows remains a significant unsolved problem in physics. Recently, a large quantity of effort has been directed toward understanding the non-linear interactions of the different flow structures in order to address this challenge. In this paper, different implementations of one exact method for identifying these structures are analyzed. This includes two sequential algorithms and a parallelizable one, developed to handle large-scale data efficiently. The new parallel algorithm offers significant advantages in handling the computational demands of large simulations, providing a more scalable solution for future research.