A DIAGNOSTIC STUDY OF ATMOSPHERIC BLOCKING
USING ANALOGY BETWEEN JET STREAM AND OPEN CHANNEL FLOW
Yoshikazu Kitano (CRIEPI), Tomohito J. Yamada (Hokkaido Univ.), Yasuo Hattori (CRIEPI)

1. Introduction

Open channel flow

Figure 1 shows the specific energy flux derived by Eq. (5) between 21 February to 3 March 1989. Vertically averaged
data between 2500-12000 m, which is set to exclude influence of terrain and stratosphere, is used. Poleward
boundary of the jet stream (y = -a) is defined by a constant pressure line (p = 395 hPa). Equatorward boundary of thejet stream (y = a) is defined to let V becomes constant (V = 8.7x107 m2/s) by Eq. (3).
High specific energy flux ET1, ET2 in Figure 1 may represent energy
transports from west to east. Figure 2-6 show the horizontal windvelocity and specific energy flux in each time step written by blue dashedlines in Figure 1. On February 22 and 26 (Figure 2, 4), high specific energy
flux characterized by higher kinetic energy exists near Japan and its
surroundings. After that (Figure 3, 4 and 5, 6), area of high specific energy
flux is replaced eastward and Ω-type blockings are formed over central
North Pacific region.

Jet meridional width

Water depth

Atmospheric blocking is one of the important causes ofHydrostatic Equilibrium
meteorological extremes in mid-latitude, such as cold
spells, heat waves, draught, and heavy rainfalls. Rossby(1950) focused on dynamical analogies between thesubcriticalhydraulic jump in open channel flow and theatmospheric blocking in jet stream, and proposed atheoretical formula to explain the two dynamicallypossible states in zonal currents which are compatible
supercriticalwith supercritical and subcritical flow in an open channel
flow. Armi (1989) focused on the specific energy flux inSpecific energy
zonal currents and showed that a dimensionlessparameter, which is called Froude/Rossby number, isanalogous to the Froude number of open channel flow.
AtmosphericJetstreamKitano and Yamada (2017) extended these theories torealistic conditions in atmosphere and showed a
Geostrophic Equilibrium
relationship between typical blocking flow and specificenergy flux in jet stream. However, specific energy flux ishigh potential energy
not conserved quantitatively at jet-width expansion area
because β-plane approximation is not satisfied.
The purpose of this study is to investigate behavior ofhigh kinetic energy
the specific energy flux of jet stream in which Coriolis
parameter approximation is not considered and reveal
the usability of specific energy flux for blocking diagnosis
Specific energy
method.

3. Results

Figure 6
Figure 6: 1989/03/01 00:00 UTC
Figure 5
Figure 4
Figure 3
Figure 2

2. Derivation of the specific energy flux equation
Energy of jet stream is given by/%& '( &+𝐺 = ∫0/ 𝑢+)
,𝑑𝑦 .

(1)

Considering the geostrophic equilibrium, pressure distribution
is given by7
𝑝 𝑦 = 𝑝0/ + 𝜌 ∫0/ 𝑓 𝑢 𝑑𝑌 .
(2)
Unit depth volume transport V over north-south cross-section
is defined by/
𝑉 = ∫0/ 𝑢 𝑑𝑦 = 𝐶𝑜𝑛𝑠𝑡.
(3)
Substituting Eqs. (2) and (3) into (1), the energy equation isrewritten as follow.
//>%& '( &+?@ A
𝐺 = ∫0/ 𝑢
𝑑𝑦 + ∫0/ 𝑢 ∫0/ 𝑓 𝑢 𝑑𝑌 𝑑𝑦 +.
),(4)Here, third term is constant. First and second terms are definedby specific energy of jet stream G0.
//>%& '( &𝐺B = ∫0/ 𝑢𝑑𝑦 + ∫0/ 𝑢 ∫0/ 𝑓 𝑢 𝑑𝑌 𝑑𝑦 .
)(5)

We use Eq. (5) and analyze a Pacific blocking episode utilizing
ERA-Interim reanalysis dataset (Dee et al., 2011).

ueastward wind velocityvequatorward wind velocity

ppressureρdensityy, Yequatorward direction

ahalf width of jet

fCoriolis parameter

VUnit depth volume transport over northsouth cross-section

G, G0

energy of jet stream

Ro=VL/Ωa3

Rossby numberΩrotation speed of the earth

Ldistance between pole and equatorβ

meridional gradient of Coriolis
parameterf0

Coriolis parameter at jet center (y=0)

u’

non-dimensional eastward velocityy’, Y’

non-dimensional poleward direction

α1’, α2’velocity distribution coefficients

Henderson, F. (1966). Open Channel Flow. Macmillan.
Jaeger, C. (1956). Engineering Fluid Mechanics, Blackie & Son Limited, London Glasgow.
Kitano, Y., Yamada, T.J. (2017). Annual journal of Hydraulic engineering JSCE, 61: I_439-I_444.
Lejenäs, H., økland, H. (1983). Tellus A, 35: 350-362.
Long, R. R. (1955). Tellus, 7:341-357.
Rex, D. F. (1950). Tellus. 2(4): 275-301.

Figure 5: 1989/02/27 00:00 UTC

Figure 2: 1989/02/22 18:00 UTC

Figure 4: 1989/02/26 00:00 UTC

4. Summary

References
Armi, L. (1974). Geophys. Fluid Dyn. Notes, WHOI Ref.74-63(2): 1-14.
Armi, L. (1989). J. Fluid Mech., 201:357-377.
Ball, F. K. (1959). Quart. J. R. Meteorol. Soc., 85(363): 24-30.
Chow, V.T. (1959). McGraw-Hill Book Company.
Dee D. P. et al. (2011). Q. J. R. Meteorol. Soc., 137:553-597.
Fultz, D. (1961). Adv. Geophys., 7:1-103.

Figure 1: Specific energy flux derived by Eq. (5) between 21 February to 3
March 1989.

Riffler, M. (2005). University of Innsbruck for the degree of master of science, 1-62.
Rossby, C.-G. (1950). J. Chinese Geophys. Soc., 2:1-13.
Tibaldi, S., Molteni, F. (1990). Tellus A, 42(3):343-365.
Yen, B. C. (1973). J. Engng Mech., Div. ASCE, 99:979-1009.

Figure 3: 1989/02/24 06:00 UTC

KY2017 stated that eastward flow in situation of atmospheric blocking characterized by wide width of jet (2a) andmeridional profile of u theoretically needs high specific energy flux. In Figures 1-6, this feature is clearly observed. Theseresults imply that high specific energy flux could be treated as a blocking diagnosis method. Furthermore, before theoccasion of atmospheric blocking, high specific energy flux is generated over upstream region. This generation could be atrigger of the Pacific blocking episodes.