Geoscience Reference
In-Depth Information
Fig. 5 Nondimensional radial velocity of the warm buoyant jet as a function of Rayleigh number
in the double logarithmic scale
Table 2 Overview of the experimental parameters for nonrotating case. The radius of the tank
R
¼
0
:
3 m and the slope angle
a ¼
39
is the same for all experiments
B
(m
3
/s
3
)
Type of markers
q
(Wt/m)
10
9
♦
6.37
ð
3
:
12
3
:
13
Þ
13.1
10
9
ð
6
:
4
6
:
6
Þ
○
25.7
ð
1
:
2
1
:
3
Þ
10
8
4.2 Nonrotating Case
In the nonrotating case, the external dimensional parameters are the same as
described in Sect.
4.1
, excepting the Coriolis parameter (it is absent). Results of
laboratory experiments have shown that the radial propagation velocity of the jet
U
~
B
1/2
and that it is independent of time;
k
T
and
are nearly constant. Therefore,
the main dimensionless parameter is (flux) Rayleigh number, Ra
B
¼
n
BH
3
2
,
where
B
is the buoyancy flux (m
3
/s
3
);
H
the vertical length scale (m);
k
T
the thermal
diffusivity (m
2
/s);
=k
T
n
the viscosity (m
2
/s).
By analogy with Eq.
3
in Sect.
4.1
, we should parameterize the velocity of the
buoyant jet as follows:
n
U
B
1
=
3
Ra
1
=
2
(5)
Thus, the formula for velocity jet is obtained in the final form:
1
=
2
B
1
=
3
H
3
k
T
n
U
(6)
The results are presented in log-log scale in Fig.
5
, which includes the data of
all experimental runs in nonrotating case (Table
2
). The solid line in Fig.
5
is the
best fit of the predicted law (
5
) to the all-laboratory experiments with the high
