Chapter 5. SPATIALLY-COHERENT STRUCTURES
anomalies produced by internal forcing as well. In the latter case, parcels of
heavier water would spread along the bottom of the mixed layer (in contrast
to the parcels of lighter water spreading along the ocean surface).
During heavy rainfalls, low-salinity lenses of the order of c
L ~ 10 km
diameter form at the surface (see Section 4.1.5). The initial buoyancy
anomalies produced by convective rains tend to spread due to pressure
gradient forces and produce frontal structures due to nonlinear interactions.
On horizontal scales comparable to the thickness of the upper ocean
boundary layer, the density inhomogeneities are three-dimensional and
dissipate due to turbulent mixing. On these spatial scales, the boundary-layer
mechanisms that eliminate horizontal density anomalies can be enhanced or
suppressed due to the effects of wind stress crossing sharp frontal interfaces
(see Section 5.4). Rotation effects are important on the horizontal scales
comparable to the baroclinic Rossby radius L f (or to its equatorial version
L E ).
Since there is frequent influx of buoyancy from convective rainfalls,
there is a continuous creation, evolution, and dissipation of the density
anomalies in the warm pool area. Here we hypothesize that there is a
wavelength range, h << O << min {L c , O IG , L E , L f }, in which the spectrum of
horizontal buoyancy inhomogeneities in the warm pool area,
B
E k , can be
saturated. Analysis of equation (5.9) suggests that the equilibrium buoyancy
spectrum in this subrange will depend on horizontal wavenumber vector k
G
,
mixed layer depth h, vertical homogenization time W, and a parameter
characterizing the horizontal variability of the density field, B B
.
A standard dimensional analysis then leads to the following formulation
for the horizontal wavenumber spectrum of buoyancy:
4
( )/
( , , )
B
B
k
B B k f
kh
D
P
<
G
,
(5.11)
where D denotes the direction of the wavenumber vector k
G
(the polar angle
relative to wind direction, for instance), B
f is a function, and parameter kh is
associated with the turbulent boundary layer processes. For horizontal scales
exceeding 1 km parameter kh is very small and formally can be dropped
from the number of determining parameters in (5.11). Parameter P is given
by
4
B B
P W .
(5.12)
Under the assumption of directional isotropy, the one-dimensional
wavenumber buoyancy spectrum is obtained by integration over angle D:
303
anomalies produced by internal forcing as well. In the latter case, parcels of
heavier water would spread along the bottom of the mixed layer (in contrast
to the parcels of lighter water spreading along the ocean surface).
During heavy rainfalls, low-salinity lenses of the order of c
L ~ 10 km
diameter form at the surface (see Section 4.1.5). The initial buoyancy
anomalies produced by convective rains tend to spread due to pressure
gradient forces and produce frontal structures due to nonlinear interactions.
On horizontal scales comparable to the thickness of the upper ocean
boundary layer, the density inhomogeneities are three-dimensional and
dissipate due to turbulent mixing. On these spatial scales, the boundary-layer
mechanisms that eliminate horizontal density anomalies can be enhanced or
suppressed due to the effects of wind stress crossing sharp frontal interfaces
(see Section 5.4). Rotation effects are important on the horizontal scales
comparable to the baroclinic Rossby radius L f (or to its equatorial version
L E ).
Since there is frequent influx of buoyancy from convective rainfalls,
there is a continuous creation, evolution, and dissipation of the density
anomalies in the warm pool area. Here we hypothesize that there is a
wavelength range, h << O << min {L c , O IG , L E , L f }, in which the spectrum of
horizontal buoyancy inhomogeneities in the warm pool area,
B
E k , can be
saturated. Analysis of equation (5.9) suggests that the equilibrium buoyancy
spectrum in this subrange will depend on horizontal wavenumber vector k
G
,
mixed layer depth h, vertical homogenization time W, and a parameter
characterizing the horizontal variability of the density field, B B
.
A standard dimensional analysis then leads to the following formulation
for the horizontal wavenumber spectrum of buoyancy:
4
( )/
( , , )
B
B
k
B B k f
kh
D
P
<
G
,
(5.11)
where D denotes the direction of the wavenumber vector k
G
(the polar angle
relative to wind direction, for instance), B
f is a function, and parameter kh is
associated with the turbulent boundary layer processes. For horizontal scales
exceeding 1 km parameter kh is very small and formally can be dropped
from the number of determining parameters in (5.11). Parameter P is given
by
4
B B
P W .
(5.12)
Under the assumption of directional isotropy, the one-dimensional
wavenumber buoyancy spectrum is obtained by integration over angle D:
303