
The purely conductive state in configurations such as the Rayleigh-Benard is linearly stable for yield stress fluids at all Rayleigh numbers, Ra. Other classical natural convection configurations, such as the differentially heated cavity, only convect for yield stresses below a critical value, above which they too are linearly stable. Other configurations of heated and insulated walls lead to different stability characteristics. In the recent experimental study of Davaille et al. (2013) use of a localised heater configuration resulted in the onset of convective rolls and eventually intermittent pulsing of thermal plumes, as the rate of heating was increased. Here we study an analogous problem both analytically and computationally, from the perspective of an ideal yield stress fluid (Bingham fluid) that is initially stationary in a locally heated rectangular tank. The aim is to understand which features of the observed flows of Davaille et al (2013) can be attributed to the yield stress and which depend on other physical effects not accounted for in simple yield stress models. In doing so we uncover general mechanisms leading to flow onset, which are quite different from the onset of classical hydrodynamic instabilities. In the latter part of the talk we develop our understanding of intermittency in thermal plumes. Joint work with Ida Karimfazli and Anthony Wachs.

The purely conductive state in configurations such as the Rayleigh-Benard is linearly stable for yield stress fluids at all Rayleigh numbers, Ra. Other classical natural convection configurations, such as the differentially heated cavity, only convect for yield stresses below a critical value, above which they too are linearly stable. Other configurations of heated and insulated walls lead to different stability characteristics. In the recent experimental study of Davaille et al. (2013) use of a localised heater configuration resulted in the onset of convective rolls and eventually intermittent pulsing of thermal plumes, as the rate of heating was increased. Here we study an analogous problem both analytically and computationally, from the perspective of an ideal yield stress fluid (Bingham fluid) that is initially stationary in a locally heated rectangular tank. The aim is to understand which features of the observed flows of Davaille et al (2013) can be attributed to the yield stress and which depend on other physical effects not accounted for in simple yield stress models. In doing so we uncover general mechanisms leading to flow onset, which are quite different from the onset of classical hydrodynamic instabilities. In the latter part of the talk we develop our understanding of intermittency in thermal plumes. Joint work with Ida Karimfazli and Anthony Wachs.