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(a)
(b)
10 -2
10 -2
10 -4
10 -4
10 -6
10 -6
10 -8
10 -8
10 -10
10 -10
T K +T P
T K +T P
10 -12
10 -12
abs(B)
abs(B)
10 -14
10 -14
10 0
10 1
10 2
10 3
10 0
10 1
10 2
10 3
k h
/
Δ k
k h
/
Δ k
Figure 8.7. Horizontal wave number spectra of total energy transfer and buoyancy flux in simulations with fixed Re b
0.2 and
different Fr h and Re, corresponding to Fr h = (a) 0.0069 and (b) 0.0034 (runs C4 and C6). Log-log axes are used for clarity. As a
result, only k h /k
4 are shown, and the absolute value of the buoyancy flux is taken. The buoyancy flux is positive over almost
all k h , but the peaks around k h /k
40 in (a) and 60 in (b) are negative.
(a)
(b)
(c)
Figure 8.8. Vertical ( x , z ) slices of the y component of vorticity in simulations with fixed ν = 0.03125 cm 2 /s and different N (and
hence different Fr h and Re b ), corresponding to Re b = 2.6 (top), 0.69 (middle), and 0.18 (bottom) (runs A6, B6, and C6). Shading
is saturated to white/black at
3s −1 . Fields in (a) and (b) are plotted at the final time of the simulations t = 2000 s. Panel (c) is
plotted at t = 1900 s, which was chosen to illustrate the lone patch of Kelvin-Helmholtz billows visible at this time.
±
 
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