Thesis:

Turbulent convective flows in a differentially heated cavity: a global and local analysis

This study examines turbulent natural convection in a three-dimensional differentially heated cavity with no-slip boundary conditions using direct numerical simulation. Unlike commonly used periodic configurations, the presence of physical walls enables the development of fully three-dimensional structures that significantly alter the flow stability and turbulent dynamics. The vertical and horizontal aspect ratios are 4 and 1, respectively. Simulations are performed using the Nek5000 spectral element solver, while scripts are written in Python and MATLAB for post-processing. Instability onset occurs at critical Rayleigh numbers of Ra_c ≈ 2.8 × 10⁸, substantially higher than in periodic domains, demonstrating the strong stabilizing effect of no-slip boundaries. At Ra = 10¹⁰, the flow is turbulent but not fully developed: the boundary layers lack a logarithmic region, and spectral analysis reveals only a limited inertial subrange. Compared to periodic configurations, global heat transfer is reduced, while the mean temperature profile remains consistent, suggesting that discrepancies with experiments are more likely attributable to thermal radiation effects. The vertical boundary layer exhibits a progression from multimodal behavior through an intermediate monoperiodic state to chaotic dynamics. The intermediate regime is dominated by a frequency approximately four times higher than that of Tollmien-Schlichting waves. Turbulence is concentrated in the detachment region, where shear production dominates and buoyancy plays a secondary role. The PDFs of the velocity-gradient invariants exhibit the characteristic teardrop shape, indicating a predominance of tube-like vortex stretching and rare but intense biaxial strain events. Coherent structures originate in the boundary layer, are advected upward, and are intermittently ejected into the stratified core, where they dissipate and excite internal gravity waves at the Brunt-Väisälä frequency. These results provide insight into the mechanisms governing turbulent natural convection, highlight the critical role of confinement and wall boundary conditions in shaping transition and turbulence in buoyancy-driven flows, and establish a reference dataset for the validation of turbulence models in non-periodic geometries.