Spatio-temporal Patterns in Inclined Layer Convection

TL;DR

This paper provides a comprehensive theoretical and numerical analysis of complex spatio-temporal patterns in inclined layer convection, revealing the interplay of buoyancy and shear mechanisms and matching experimental observations.

Contribution

It introduces a detailed phase diagram of 3D convection patterns and highlights the role of Fourier mode interactions in pattern formation.

Findings

Pattern phase diagram matches experiments

Resonant Fourier mode interactions are key to pattern morphology

Competition between buoyancy and shear drives pattern diversity

Abstract

This paper reports on a theoretical analysis of the rich variety of spatio-temporal patterns observed recently in inclined layer convection at medium Prandtl number when varying the inclination angle $\gamma$ and the Rayleigh number $R$. The present numerical investigation of the inclined layer convection system is based on the standard Oberbeck-Boussinesq equations. The patterns are shown to originate from a complicated competition of buoyancy-driven and shear-flow driven pattern forming mechanisms. The former are expressed as \rm{longitudinal} convection rolls with their axes oriented parallel to the incline, the latter as perpendicular \rm{transverse} rolls. Along with conventional methods to study roll patterns and their stability, we employ direct numerical simulations in large spatial domains, comparable with the experimental ones. As a result, we determine the phase diagram of the characteristic complex 3D convection patterns above onset of convection in the $\gamma-R$ plane, and find that it compares very well with the experiments. In particular we demonstrate that interactions of specific Fourier modes, characterized by a resonant interaction of their wavevectors in the layer plane, are key to understanding the pattern morphologies.