3. Results: dust-free case
 3.d. Intensity of convection (3): Transition layer

 Figure 8: Vertical one-dimensional "chimney" convective plume model.

According to the argument in Intensity of convection (2), potential temperature difference of the conduction layer in daytime is expected to be more than 6 K. However, the potential temperature deviation of ascending convective plumes in convection layer is about 2 K. This difference is caused by the entrainment of the relatively cold air surrounding an ascending plume during the layer of moderate vertical gradient of temperature between the conduction layer and the convective layer. In the followings, the region where entrainment occurs is referred to as the transition layer.

Let us consider influence of entrainment on the potential temperature deviation of convective plumes. Assume that, at the root of a plume as illustrated by the blue frame in Figure 8, air with the potential temperature of is coming up from the below of the transition layer at the velocity of , and air with the potential temperature of is going out to the convection layer at the velocity of . We have

by considering the heat budget. Now, can be estimated by the buoyancy force of convective plume ascending from the conduction layer and the turbulent diffusion time of the conduction layer, , while can be estimated from the work done by convective plume in the convection layer.

is the depth of the convection layer. If we define , which is the time for the convective plume to travel around the convection layer with its potential temperature deviation kept constant, can be rewritten as

 (5)

The influence of entrainment is determined by the ratio of the travel time of plume to turbulent diffusion time.

By assuming that is given as the potential temperature difference of the conduction layer, we can estimate the potential temperature deviation of a convective plume in the convection layer by the use of (5). Suppose daytime at LT = 14:00. From Figure 7, we can adopt ˜ 40 m and ˜ 6 K. By using these values,

which roughly coincides with those of plumes observed at LT=14:00.

According to the above discussion, potential temperature deviation of ascending convective plumes can be estimated by using heat flux , depth of convection layer , and turbulent diffusion coefficient . Note that this estimation does not describe causality of the whole convection field, since the magnitude of sensible heat flux included in and the value of turbulent diffusion coefficient are determined by the convective motion to be determined itself.

Note also that the estimation by the use of (5) can be applied only for the case where convection is well developed and hence < can be assumed. When > , we have a strange result, > , which means that potential temperature deviation of convective plumes is larger than potential temperature difference in the conduction layer. In such a case, it is more reasonable to assume that entrainment hardly occurs.

A numerical simulation of thermal convection in the Martian lower atmosphere.
Odaka, Nakajima, Ishiwatari, Hayashi,   Nagare Multimedia 2001