Annals rifGlaciology 19 1994
© International Glaciological Society
Bent icicles and spikes
N.
MAENO,
instilule of Low T emperalure Science, Hokkaido University, Sa/J/Jo ro 060, ] aj}(1n
L.
MAKKONEN ,
Laborat01) of Structural Engineering, T echnical Research Center
of Finland, 02150 Espoo,
Finland
T. T AK AHASHl
Hokkaido University of Education , Sapporo 002, ] a/Jan
ABSTRACT.
Formati on mec ha ni sms of bent icicl es a nd thin spikes were studi ed
by observatio ns o f na tura l icicl es a nd by a rtifi cia ll y growin g icicl es in a co ld
labo ra tory, a nd th e res ults a re disc ussed with reference to th e ge neral growth process o f
icicl es . It is shown th a t icicl es can be bent by th e displ ace ment o f th eir roo ts, cha nge in
water suppl y ra tes, and wind . Spikes were observed to g row by th e freez in g ofa wa ter
column captured at th e centre of icicles a fter th eir length a nd di a m eter growth
stopped.
INTRODUCTION
Th e physical process of icicl e growth has been in ves tigated extensively by G eer (1981 ), Maeno a nd T a ka hashi
(1984a, b ), M a kkon en (1988 ) a nd M ae no a nd oth ers (in
press). However , th ere rem ain several importa nt phenom ena, whi ch were no ted in th eir studi es but have not
bee n surveyed in d etail. Maeno a nd Taka has hi ( 1984b )
tri ed to clarify mechanisms for th e bending of icicl es a nd
for th e formation of thin spikes often found on th e surface
of a n icicl e. This pa per d escribes furth er studi es o n bent
icicl es a nd spik es .
BENT ICICLES
Ben ti cicl es a re often o bserved to grow from roofs a nd
trees (Fig. I). Maeno a nd Taka has hi ( 1984 b) showed th a t
a t least three fac tors can result in th e form a tion of ben t
icicles . Th e first is an y inclina ti on of roo ts of icicles, e.g. b y
th e creeping d eform a tion of ice/snow on a roof edge or b y
bending of a tree bra nch from whi ch icicl es a re growing.
Su ch ben t icicl es are often obse rved to grow fro m trees
exposed to spray a nd waves of ri ve r, la ke 0 1" sea wa ter.
Th e second is th e cha nge o f wa ter suppl y conditi ons
during icicle growth . A d ecrease in water supply ra te by
a n y meteorological cause will lead to a vari ation of waterflow pattern ; a single fl ow pa th on th e icicle wall will
res ul t in a ben t icicle, a nd two fl ow pa th s, forked icicl es .
In o ur icicle growth experim ents th e a bove two types of
ben t icicles could easily be p rod uced .
Th e third fac tor to bend icicles is th e effec t of wind. To
study various effec ts of wind on icicle form a ti on, a n icicl e
growth d evi ce was constru cted in a co ld la boratory, th e
138
tempera ture of whi ch was va ri ed between 0 a nd - 30°C .
Th e d evice was simil a r to th a t used by M ae no a nd
T a kahas hi (1984a ) a nd M ae no a nd o th ers (in press ), in
whi ch icicl es could be grown from a horizonta l meta l ba r
wrapped by wet gauze, to whi ch pure wa ter just a bove
th e melting tempera ture of ice was suppli ed a t a co nsta nt
ra te betwee n 0 a nd 50 mg s I . Wind speed co uld be vari ed
between 0 a nd 6.0 m S I. During th e growth process th e
icicl e's leng th a nd di am eter were measured , a nd rela tive
humidity, mainta in ed a t a bou t 80 % , was a lso monito red.
It was found th a t wind affec ts icicl e growth in two
ways: it in creases th e h ea t excha nge and cha nges the
wa ter fl ow a t the wa ll a nd tip. In our experiments th e
la tter effect was mo re impo rtant tha n th e fo rmer ; it i
observed th a t th e horizon ta l cross-sec ti on of a n icicl e
grown in wind y co nditions becom es "anti-streamlined "
Fig. 1. N atural bent icicles growing from a roo]. All the
icicles are bent loward the righhand side by wind. The
horizontal width of the photograph is 2.5 m.
Mamo and others: Benl icicles and spikes
80
on ly slig htl y with water suppl y rate a nd is kept consta nt
a t 2.44 mm in ave rage irresp ective of temperature and th e
R ey nold s number (R e = 2ParU f ry , ry: d ynami c viscosity
of a ir) . R e is roughl y in th e ra nge of 350 to 3500 in th e
expe rim ental conditions, when U = I 10ms 1. The drag
coeffi cient is a fun ction of R eynolds number a nd can be
empiri ca ll y ex pressed as follows (Morsi and Alexander,
I
0/
Cl)
/
ID
/
~ 60
/
/
Cl
ID
/
/
"'0
I
/
/
/
ID
Cl
40
)3/
C
ctI
"'0
c
20
/
.- /
""
19 72 ) :
CD = 98.33Re-
"
Q)
-
2778Rc- 2
+ 0.3644
(2)
for 100 < R e < 1000, and
/
CD = 148.62Re- 1
g!eO"O
en
t
-
4.75 x 104Re- 2
+ 0.357
(3)
I rTfRl';;U;
0
0
246
Wind speed
8
10
-I
ms
Fig. 2. Nfeasured bend angle versus wind speed. 0:
present results ( temperature around - 9°C and water-su/Jply
ra le around 10 mg s \). 0 : dala from M akkonen and
Fujii ( 1993). The dashed and solid curves refer
respectively to the empirical (rP = 0.684rP+ 0.140+
4.0 degrees, 0 in 111S- 1 and calculated (Equation (1 ) )
bend angles.
with th e sharper end windward, the lee end becoming
blunter a nd thi cker du e to th e more ac tive growth of ice.
The faster growth is attributed to the wind-driven film
Oow of water, which is coo led effecti vely by th e wind ,
toward s leewa rd at th e wall, leading to an ti-streamlined
or Oa t icicl es . l\1i croscop e observation of thin crosssec tion of these icicles und er pol a rized light showed th a t
crystal g rains a re generall y mu ch sma ll er and contain
more tin y a ir bubbl es at the lee, suggesting faster freezing
of water.
"Vh en wind was sta rted a fter some growth of an icicle ,
mostly 20 cm, th e icicle began to bend sha rpl y. The angle
of bend, measured from vertical, was found to increase
with th e wind sp eed in th e ra nge studi ed ; in th e
meas urement th e air temperature a nd water supply rate
were ma in tained at abou t - 9°e a nd 10 mg s- \ res pecti vely. Figure 2 gives th e m easured bend a ngle plotted
aga inst wind speed together with th e result by Makkon en
a nd Fujii ( 1993), who grew icicles on a horizontal wire in
an icing wind tunnel. In the fi gure th e d ash ed lin e is a
curve fitted to th e m eas ured d ata.
Th e general increase in bend a ng le with wind speed is
r easo nab le beca use an aerod yna mi c force acts on th e
pendant drop a t th e tip where th e icicl e is g rowing
lengthwi e. rf we ass um e th at a spherical pend a nt drop
(radius r ) is in a mech a ni cal ba la nce between gravity and
drag force due to a steady wind (hori zo nta l speed U ), a
force balance equation leads a pproxim a tely to
(1)
wh ere c/J is the bend a ngle, Pa a nd Pw a re th e d ensities of
air a nd water respectively , CD is th e drag coeffi cient, a nd
9 is the acce leration o f g rav ity. According to th e
o bserva ti on of Maeno a nd oth ers (in press), r increases
for 1000 < R e < 5000. Th e solid lin e in Figure 2 gives th e
bend a ng le of a n icicl e at va rio us wind speed s calcul a ted
by Eq ua tion ( I) togeth er with Eq uations (2) a nd (3) .
Equ a tion ( I ) can explain on ly th e genera l tend ency of
in crease in th e measured bend angle with wind speed.
The m agn itud es of th e meas ured a ng les a re much la rger
than those calc ul a ted , impl ying that th e bend of icicles is
ca used by wind ac ti on but not onl y through the simple
mechanical aerodynamical force actin g on a pend a nt
drop given by Equation ( I) .
In wind y co nditions, part of wind -dri"en flow of
effec tively coo led water freezes a t th e leewa l-d wa ll
formin g a n anti -streamlin ed icicle, as stated above, and
th e res t ([nally enters into a pend a nt drop preferentially a t
the lee, which leads to faster g r o wth there a nd
co nseq uentl y a llows th e icicl e to bend. At this stage of
study, howeve r, the d eta iled flowin g and freezing process
can no t be fo rmul a ted reasonab ly, because more quantita ti" e info rm a ti o n is need ed on sevel-a l important pmcesses
involved such as rh e a ir Oow a round a n icicle which
controls th e water flow a nd heat exch a nge, th e viscous
flow of a thin , rou ghl y 100 j1m , water film in which radial
(hori zonta l) temperature a nd velocity di stributions are
se t up, a nd so on.
FORMA TION MECHANISM OF SPIKES
The photographs in Fig ure 3 show na tural icicles with
spikes. Spikes a loe thin ice needl e. typicall y I mm in
di amete r and 5 to 20 mm in leng th. Some, however , are
mu ch thicker and shorter. Under th e pol a ri zed light,
microscope observations were mad e of spikes prod L1 ced on
na tura l and a rtifi ciall y form ed icicl es . Th e sp ikes were
fo und to be composed of two or a few sing le crys tals. Th e
growt h direct io n of spikes is ra nd o m a nd shows no
sys temat ic rela ti on to that of main icicl e g rowth. Som e
icicl es have several spikes a nd some none, d ependin g on
how their g rowth stops , as ex pl ained below .
I t was found from observations of natura l icicles a nd
tho. e formed in a co ld labo rato r y that spikes a re no t a
peculiar or unu sua l ph eome non. In o ur icicle form a tion
experim ent most icicles were observed to produce sp ikes
a fter th e cessa tion of th eir grow th of leng th a nd dia meter
and th e su bseq uen t slow freezing of a wa ter column
capt u red at the ce n tre of eac h icicle. Th ese spik e
production eve nts so metim es took p lace a few hours
a ft er th e ove ra ll growth of a n icicl e depending on its
growth history , size a nd su rro unding temperature .
139
Gold: Elastic modulus oJfresh-water ice
confin ed with a th in ice shell after the cessation of growth.
It was noticed that spikes a re more frequently form ed at
the tip than near th e root, a nd in th e late afternoon when
most icicles stop growth by th e relative decrease in the
water supply rate a nd increase in the freezing rate.
The formation mecha nism of spikes on icicles is
esse ntially the same as th e growth of tubu lar or columnar
ice, which develops from an ice layer covering supercooled water (Dorsey, 1921 ; Bally, 1935; Blanchard ,
195 1; Hayward , 1966; Kra usz a nd others, 1967; Tusim a
a nd Suzuki, 1972; Wascher, 1991 ).
ACKNOWLEDGEMENTS
The work was partly supported by G rants-in-Aid for
R esearch in Natural Disaster, Co-operative R esearch a nd
Scientific R esearch of the Ministr y of Education , Science
a nd Culture. The authors th a nk a nonymous referees for
their helpfu l comm ents.
Fig. 3. Natuml icicles with spikes. The vertical length
the jJhotogmph is 180 mm.
of
REFERENCES
As shown by M ae n o and Takahashi ( 1984a ) ,
Makkonen (1988) and Maeno and oth ers (in press), an
icicl e grows by a simu ltaneous freezing of water at the tip
a nd wall , the growth being maintained by a balance
between the suppl y rate and freezing rate of water. When
the balance is d estroyed a nd dripping of water drops at
the tip ceases, the pendant drop begins to freeze from
outside forming a thin ice shell . As freezing proceeds the
press ure inside increases steadil y. Since th e pendant drop
is connected to a water cylind er, 5 mm in diameter and a
rew cm in length , in the central part of a n icicle, its
subsequ ent freezin g produ ces a high internal press ure
which squ eezes out unfrozen water from small holes a nd
cracks. Water exiting from suc h holes and cracks ra pidl y
freezes to form spikes. Th us various forms of spikes can be
produ ced in various directions depending on the mode of
water sq ueezing a nd freezing.
When a n icicle stops growi ng, the water fi lm on th e
wall also begins to freeze from th e outer su rface which is
in contact with th e cold air. In this case, only very fine
needle spikes may be form ed since the volume of confined
wa ter is small so that the pres ure produced is also small.
Spikes are so thin that they easily d isappear by
melting or sublimation . This may be th e reason why
spikes have not been frequently noticed , although th ey
shou ld form in every icicle when unfrozen water is
140
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The accuracy of references in the text and in this list is the
responsibility of the aulhors, to whom queries should be addressed.