We consider height-integrated equations of an advection-dominated accretion flow (ADAF), assuming that there is no mass outflow. We include convection through a mixing length formalism. We seek self-similar solutions in which the angular velocity and sound speed scale as R, where R is the radius, and consider two limiting prescriptions for the transport of angular momentum by convection. In one...

It is widely believed that if monotone difference schemes are applied to the linear convection equation with discontinuous initial data, then solutions of the monotone schemes are closer to solutions of their parabolic modified equations than that of the original convection equation. We will confirm the conjecture in this paper. It is well known that solutions of the monotone schemes and their ...

We investigate the early stages of mass convection in a colloidal suspension at high solutal Rayleigh number Ras. From the time evolution of shadowgraph images and by assuming a diffusive growth of the boundary layers we obtain an indirect measurement of the concentration boundary layer thickness delta* at the onset of convection. We show that the dimensionless boundary layer thickness delta=de...

The Canadian Centre for Climate Modelling and Analysis atmospheric general circulation model (AGCM4) is used to study the role of shallow convection in the hydrologic and energy cycles of the atmosphere. Sensitivity tests with AGCM4 show a marked effect of the parameterization of shallow convection in the model. In particular, including the parameterization of shallow convection produces consid...

We investigate the response of convection to idealized perturbations in the thermodynamic environment in simulations which parameterize the large-scale circulations using the weak temperature gradient (WTG) approximation. The perturbations include a combination of modifying the environmental moisture and atmospheric stability via imposing anomalies in reference moisture and temperature profiles...

This essay concerns precipitating convective cloud systems and convectively-driven mesoscale circulations (“mesoscale convection”) and their role in the large-scale structure of the atmosphere. Mesoscale convection is an important and ubiquitous process on scales of motion spanning a few kilometers to many hundreds of kilometers. It plays a role in the input of energy to the climate system thro...

Results of thermal convection experiments in a rotating uid with a geometry similar to the Earth's core tangent cylinder are presented. We nd four di erent regimes of convection. In order of increasing heat ow, these are: (1) subcritical (no convection), (2) helical plumes (hetons) around the tangent cylinder, (3) hetons throughout the tangent cylinder, and (4) fully three-dimensional convectio...

5 The aim for a more accurate representation of tropical convection in global circulation models 6 is a long-standing issue. Here, we investigate the relationships between largeand convective 7 scales in observations and a Stochastic Multicloud Model (SMCM) to ultimately support 8 the design of a novel convection parametrization with stochastic elements. Observations of 9 tropical convection ob...

A global nonlinear stability analysis is performed for a couple-stress fluid layer heated from below saturating a porous medium with temperature-pressure dependent viscosity for different conducting boundary systems. Here, the global nonlinear stability threshold for convection is exactly the same as the linear instability boundary. This optimal result is important because it shows that lineari...