The Power Spectrum of Internal Gravity Waves

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Mar 5, 1985 - Dewan (1979) proposed a hy- pothesis of co-existence of gravity waves and turbulence. Gage. (1979) compared the spectra with a -5/3 power ...
WRI MAP Research Note-6

WRI MAP Research Note-6

The Power Spectrum of Internal Gravity Waves : Stratospheric Balloon Observations

MARG

and Interpretations Manabu D. YAMANAKA

MIDDLE ATMOSPHERE RESEARCH GROUP WATER RESEARCH INSTITUTE

March, 1985

NAGOYA UNIVERSITY Furo-cho, Chikusa-ku Nagoya 464 JAPAN

MIDDLE ATMOSPHERE

RESEARCH

GROUP WATER RESEARCH INSTITUTE NAGOYA UNIVERSITY

WRI MAP Research Note:

The Power Spectrum of Internal Gravity Waves: Stratospheric Balloon Observations and Interpretations

By

Manabu D. Yamanaka

Water Research Institute, Nagoya University Chikusa- ku, Nagoya 464, Japan

5 March 1985

INTRODUCTION To quantitize the gravity-wave momentum budget is one of the most important targets of MAP, of

mainly because theoretical models

weak zonal wind around the mesopause request momentum

ferred 1981;

from the troposphere by internal gravity waves Matsuno, 1982).

trans-

(Lindzen,

The gravity-wave momentum must contribute

also to maintenance of weak zonal wind in the middle stratosphere (Tanaka and Yamanaka, 1985). the

mean

flows,

Such gravity waves interacting with

either by Lindzen's wavebreaking

process or by Matsuno's dissipation mechanism,

(saturation)

must have a spec-

trum of small intrinsic frequency predominance (see Yamanaka

and

Tanaka, 1984a). However,

the

spectrum of middle-atmospheric gravity waves,

which is necessary to quantitize the momentum flux, clarified airplanes, review). horizontal any is

although not a few studies were done rockets

has not been

using

and radars (see Fritts et al.,

For example,

Matsuno (1982) assumed a

balloons,

1984,

for a

Gaussian-shape

phase velocity spectrum at the -bottom (20 km) without

observational facts. essential

Such zero phase velocity predominance

to act on the general circulation

as

a

Rayleigh

friction (Dunkerton, 1982). There frequencies

have (or

been often observed nearly -5/3 power

horizontal wavenumbers) in the mesoscale

zontal wind power spectra (Mantis, al.,

1982;

Balsley and Carter,

Nastrom and Gage,

laws

1983).

1963;

of

hori-

Dewan, 1979; Larsen et

1982; Lilly and Petersen, 1983;

Identification of them ·with the

-5/3

power law of wavenumber in 3D isotropic turbulence theory may not be

reasonable,

because

the

observed spatial scales

l

are

much

greater

than

the JD-turbulence inertial

subrange.

r---------~----"""16

Bretherton

\

(1969) considered this due to the mesoscale topography which is a possible

origin of gravity waves.

Dewan (1979) proposed a

pothesis of co-existence of gravity waves and (1979)

turbulence.

compared the spectra with a -5/3 power law of

wavenumber

\

hy-

>Eulerian, 65°N, B&C'82 \ . \ 8km,Jun.-Aug. \ \ \ \ \

\

Gage

horizontal

in the reverse-cascading energy inertial range of the

2D turbulence theory.

However,

\

complete to explain why such a power low is realized so commonly.

out

stratosphere and Tanaka,

1984a, c; Yamanaka et al., 1985c).

type (0.005 m/s),

(1985a,

middle

We developed and

b).

al.

Four zero-pressure balloons loading these anemome-

ters were launched during 1982-84 at Sanriku (39°N, 142°E). these observations

( .) ...__... ..--..

4

0)

~

\

J ...__... ....._.

\

\

Lagrangian Mantis '63 rv 40-45°N 24-30km Jul.-Sep.

0.9 m/s) and of

which are described in Yamanaka et

\

I

by balloons and balloon-borne anemometer~ (Yamanaka

used anemometers of propeller type (sensitivity: ionic

\

Y & T'84 25km,Sep.

----CJ)

Lagrangian, 39°N

we have carried

a series of high resolution wind observations in the

...-.. ..--..

\

these approaches do not seem

As an activity of the Japanese MAP project,

5

..--.. 3 ...__...

V

::,

3

u..

0)

0

From

u

we can obtain information on the gravity-wave

2

spectrum, which is the context of this brief note.

• i-----..,__----------1 -5 -4 -3 -2

OBSERVED POWER SPECTRA As shown in Yamanaka and Tanaka (1984c) and Yamanaka et

al.

(1985c), we can obtain two kinds of wind data by balloon tracking

log w(c/s)

and balloon-borne anemometers. On one hand, ridional altitude; data

Lagrangian power spectra of the zonal and

winds obtained by level-flight balloon tracking (25 20-21 September 1982) are shown in Fig.

analyzed

1.

here and the observation circumstance

published in Yamanaka and Tanaka (1984c).

mekm

The wind have

been

Higher frequency por-

Fig. 1

Lagrangian

power

meridional

(v)

t ra eking.

Spectra

1963;

spectrum ("Y & T")

component winds obtained from a obtained by other

authors

( u)

and

balloon (Mantis,

Balsley and Carter, 1982) and the ideal power laws

are also indicated.

Modified from VanZandt

vate communication).

3 2

for zonal

(1984;

pr1-

tions

of

the spectra may not be reliable because of

errors of the tracking antenna (in particular,

mechanical

meridional one is r-i

worse since the balloon moved almost eastward). The Vaisala-Brunt frequency

and

the Coriolis factor are 3xlo-;

and

2x10-s

C

c/s,

Therefore, the spectra correspond nearly to those

respectively.

I s::::

of the internal gravity waves. The

(1)

u

(Mantis,

1963;

noted

that

It should be

our and Mantis' spectra are based on Lagrangian

ob-

in

the middle stratosphere

using

balloons

whereas

observations

is

a Eulerian spectrum obtained from IS

in the upper troposphere.

Also note that

radar Mantis'

Balsley-Carter's are in summer (the mean winds are

and westerly,

easterly

respectively) and ours are in autumn (weak wester-

It is very interesting that all the spectra are similar not

only in respect of form but also in point of magnitude. the balloon-borne anemometer data showed

a "hierarchical structure" in the stratospheric turbulence (Table 1).

The

fluctuations

listed in the class (i) may be

also by rawinsondes or radars (e.g.,

detected

Cadet and Teitelbaum, 1979;

and Woodman,

1982),

whereas (iv) and (v) can be

detected

only

by the ionic anemometers (Barat,

1985a).

We

scanned

Yamanaka et

such microstructures vertically

by

al., using

balloon-borne winches (Matsuzaka et al., 1984, 1985).

propellor

anemometer (Yamanaka et al.,

1985b) leads to a

power

spectrum in terms of the vertical wavenumber as shown in Fig. It

is a problem to determine whether those classes are of

4

2.

waves

b.O

(1) .::

.:: Q.)

b.O

Q.)

> (1) (1) ~::::: I'...

.::

H

>,

"tl

(/)

.... Cl)

Cl)

-I->

-I->

Cl)

u

E: 0 E:

-I->

Cl)

Cl)

"tl :::

s::::

Cl)

Cl)

::s

4-l 0

Q.) .,I,) Q.)

Q.) (.)

Q.) (.)

C

C C

s 0 s Q.) .::

"d I'... 0

(.) Q.)



b.O C C 0 0

r-i ;:i

.,I,) (/J

4-l ;:i Q.)

..Q

....... 0

Cl)

. .....

s::::

Q.) .,I,)

Q.)

(.)

0.. r-i 0 0..

r-i . ..,

Q.) .,I,) Q.)

Q.) .,I,)

"d

.:: ;:i

C ;:i

> r-i

b{) s::::

. .....

"d

00

""'~ "d Q.) Q.)

Q.)

"d

(/)

;:i

..,I,)..,

"d

r-i

.C..,

s0..

:::::

-,

'"'--1