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1/1
1/30
1/200
0
Temperature (°C)
1700
Figure 7.8. Plumes from three numerical models with different ratios of minimum
plume viscosity to ambient viscosity, respectively, 1, 1 / 30 and 1 / 200. The tail is
thinner for lower-viscosity plumes. The models are axisymmetric about the left-
hand side of the panels. Several lines of tracers mark fluid initially from different
levels near the base of the box. The initial configuration is shown in the right-hand
panel. A secondary instability has developed in the 1 / 200 model.
U
R
δ
φ p
Figure 7.9. Sketch illustrating thermal entrainment into a hot plume head. The
dashed line outlines a thermal boundary layer formed as heat conducts out of the
head. As the plume head rises, some of the newly heated material is swept into the
head by the internal circulation of the head. The black patches are fluid initially
from the thermal boundary layer. Symbols show the head radius, R , a typical
thermal boundary layer thickness, δ , the upward velocity of the head, U , and the
volumetric flow rate up the tail, φ p .
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