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fluiddyn
fluiddyn_papers
Commits
b58af7713c85
Commit
b58af7713c85
authored
1 year ago
by
Pierre Augier
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parent
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Topic/default/update strat
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2022strat_polo_proj/review0/input/rebut2.tex
+16
-12
16 additions, 12 deletions
2022strat_polo_proj/review0/input/rebut2.tex
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16 additions
and
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2022strat_polo_proj/review0/input/rebut2.tex
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−
12
View file @
b58af771
...
...
@@ -245,5 +245,5 @@
but upscale in frequency. Do the quoted WWT theories agree with that?
}
We explain how the change of coordinates
$
(
k
_
h, k
_
z
)
\rightarrow
(
\omega
, k
_
z
)
$
is done
after equation (3) by adding
\Add
{
``
... where the change of coordinates is defined by
after equation (3) by adding
``
\Add
{
... where the change of coordinates is defined by
the dispersion relation
$
E
(
\omega
, k
_
z
)
=
E
(
k
_
h,k
_
z
)
\left
(
\partial
\ok
/
\partial
k
_
h
...
...
@@ -249,12 +249,14 @@
the dispersion relation
$
E
(
\omega
, k
_
z
)
=
E
(
k
_
h,k
_
z
)
\left
(
\partial
\ok
/
\partial
k
_
h
\right
)
^{
-
1
}$
.''
}
. The question of energy transfers in anisotropic wave systems is a
subtle question. For example, the direction of the energy cascade depends on the
considered triad for inertial wave turbulence
\cite
[]
{
david
_
locality
_
2023
}
. Generally
speaking, the transfers also depend on the exponents of the energy spectrum. In the
case of stratified flows,
\cite
{
dematteis
_
origins
_
2022
}
argued that the global energy
flux is direct in both
$
k
_
z
$
and
$
\omega
$
for some spectra due to the dominance of
Induced Diffusion (ID) contribution. Yet, the Parametric Subharmonic Instability (PSI)
\right
)
^{
-
1
}$
.
}
''.
The question of energy transfers in anisotropic wave systems is a subtle question. For
example, the direction of the energy cascade depends on the considered triad for
inertial wave turbulence
\cite
[]
{
david
_
locality
_
2023
}
. Generally speaking, the
transfers also depend on the exponents of the energy spectrum. In the case of
stratified flows,
\cite
{
dematteis
_
origins
_
2022
}
argued that the global energy flux is
direct in both
$
k
_
z
$
and
$
\omega
$
for some spectra due to the dominance of Induced
Diffusion (ID) contribution. Yet, the Parametric Subharmonic Instability (PSI)
mechanism is responsible for inverse cascade in
$
\omega
$
as explained in section III.D
(see Figure 15). To our opinion, a complete prediction for energy transfers (based on
WWT or a more general theory) remains to be find.
...
...
@@ -257,9 +259,11 @@
mechanism is responsible for inverse cascade in
$
\omega
$
as explained in section III.D
(see Figure 15). To our opinion, a complete prediction for energy transfers (based on
WWT or a more general theory) remains to be find.
- TODO: oceans: forced waves (inertial waves, M2 and spontaneous generation from
vortices)
$
\omega
/
N
$
small.
Note also that a lot of forcing mechanics known to be important (internal tide,
inertial waves, spontaneous generation from slow vortices) force rather slow waves. It
would be surprising if the
$
\omega
^{
-
2
}$
spectrum down to
$
\omega
=
N
$
could be
explained only with a upscale in frequency energy cascade.
\itemit
{
typo p4 hyper viscosity
}
...
...
@@ -267,7 +271,7 @@
This typo is corrected.
\itemit
{
(20) is an interesting definition. But I don
’
t understand (20b)
}
\itemit
{
(20) is an interesting definition. But I don
'
t understand (20b)
}
(20a) is relevant because we remove one over two degree of freedom of the horizontal
velocity when we removing vortical modes. However, the reviewer's remark make us
...
...
@@ -290,7 +294,7 @@
force with white noise in time?
}
We chose
$
T
_
c
$
to be equal to the wave period to excite frequencies of the same order
than the linear internal gravity
$
\ok
=
N k
_
h
/
k
$
.
O
n
the
contra
ry
, a white noise would
than the linear internal gravity
$
\ok
=
N k
_
h
/
k
$
.
I
n contra
st
, a white noise would
excite all frequencies, favoring the appearance of vortical modes and non linear
structures.
...
...
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