We study natural convection of viscoplastic fluids in 2D domains. A sufficiently large yield stress introduces a static solution to the Navier–Stokes equations that may not otherwise exist. We find conditions that guarantee such motionless regimes and investigate flow development between static and advective states. Considering three problems, we explore the various ways in which the yield stress modifies the hydrodynamics of steady and transient natural convection.

We start by analyzing natural convection in an infinitely long rectangular cavity. Flow is driven by a constant horizontal temperature difference and a stabilizing stratification imposed on the walls. We classify different 1D flow regimes and establish that an arbitrary number of unyielded regions can exist in the domain.

Secondly, considering a square cavity, we investigate conditional and unconditional stability of the stationary state. We study the transition of the fluid between conductive and advective states, revealing the possibility of temporary arrest of the flow at yield stresses less than the critical value.

Finally, we study natural convection of viscoplastic fluids due to a heater of finite width positioned on the bottom wall of a cavity. We show that if the yield stress is less than the critical value, the flow starts after a finite time. We characterize transient flow and explain the processes that result in the observation of pulsing plumes at high Rayleigh.

Overall, we investigate the force balance that governs the existence of steady motion, or lack thereof. When the steady regime is advective, we illustrate that depending on the boundary and initial conditions flow may start immediately or flow onset may be delayed by a finite time. We focus on problems where flow onset is due to dominance of buoyancy stresses and is not a consequence of hydrodynamic instability. In $4 we clarify the difference.

Further, we explore transient flow dynamics and establish that the yield stress can intensify oscillatory transient features. This results in the dominance of different transport methods and corresponding timescales at different stages of flow development. We show that under appropriate conditions, this may lead to temporary flow arrest and create other noteworthy dynamics.