The Journal of the Oceanographical Vol. 17, No. 4 December 1961 Society of japan Drop Production by Bursting of Air Bubbles on the Sea Surface. III St

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1 The Journal of the Oceanographical Vol. 17, No. 4 December 1961 Society of japan Drop Production by Bursting of Air Bubbles on the Sea Surface. III Study by Use of a Wind Flume (Short Report) Yoshiaki TOBA Abstract : A wind flume experiment and studies based on it, on the air entrainment in wind waves and the droplet production from them, are described. When the wind speed exceeds about 13 m Esec-1 (at 10 m level), small wavelets in which surface tension exerts to a considerable degree and which have a profile that peaks downward, begin to enclose air bubbles at their troughs on crests of underlying gravity waves. Small droplets measured in the air above wind waves are confirmed to be produced by bursting of the air bubbles entrained in wind waves, and the production rate of droplets of each size grade is determined. Droplets carried up into the upper air or transported for long distances are shown to be produced mostly by shuttering of film of bubbles of several mm, and they have diameters smaller than a few tens micron, while droplets produced through jet mechanism are large and fall shortly. Concentration-size distribution of the droplets in the air directly above the sea surface, and salt mass density-salt mass distribution of sea-salt nuclei at various heights, are derived theoretically from the results of the experiment. After some modification, it nearly represents the actual distribution of giant sea-salt nuclei in the atmosphere. The production rate of droplets of each size grade, and its dependence on wind speed, are checked also by data of a field observation. The dependence on wind speed u (m Esec-1 at 10m level) is expressed by exp (0.40u) for u between 15 and 23 m Esec-1. Also, the coefficient of mixing in wind waves is estimated from the distribution of the entrained air bubbles in wind waves. Geophysical Institute, Kyoto University.

2 Table 1. Summarized relation between bubbles and droplets produced from them.

3

4 172 日本 海 洋 学 会 誌 れ,毛 第17巻 第4号 よ う に 見 え る の で あ る こ の 極 の 収 束 は,重 細波 は つ ぎつ ぎ後 の重 力 波 へ と送 られ る 力波 風 が 強 くな つ て 重 力 波 が 大 き くな る と,水 面 は い の 峰 で 小 波 の 波 形 勾配 を高 め る こ れ ら の 小 波 た る と こ ろ重 力 波 に対 し て相 対 的 に後 へ 進 む 小 波 は,Fig.1に (wavelets)で お お わ れ る 一 見,お み られ る よ う に,重 力 波 とは 逆 に 谷 の と こ ろ で と が つ た 断 面 を も ち,水 もな重力波連 面を裏か ら が あ る速 さで 進 行 し,そ の 上 に小 波 が で た らめ に 見 る と 鐘 乳 洞 の 天 井 の よ う に 見 え る これ は 表 面 存 在 して い る よ うに 見 え るが,重 張 力 波 の 断 面 に 関 す るCRAPPERの 力波連をはなれ て 小 波 の パ タ ー ンに 目を つ け る と,そ れ が 重 力 波 理 論10)か ら 推 定 さ れ る と こ ろ で あ り,CRAPPERが 示 唆 した よ の 波 速 よ りお そ い あ る速 さで 進 行 して い る の を 見 う に,そ の 谷 で 空 気 が と じ込 め られ て 気 泡 と な り, い だ す で あ ろ う そ の パ タ ー ンの 間 を 重 力 波 が 通 波 中 の 乱 れ に よつ て水 中 に 入 つ て ゆ くの で あ る り抜 け て ゆ く ので あ る が,小 波 の パ タ ー ンは重 力 し か し,こ 波 の 峰 の と こ ろで 収 束 し,谷 の と ころ で 発 散 す る な く,数cm以 の が 見 られ る ち よ うど,小 波 の パ タ ー ンの媒 質 力 が と もに 重 要 で あ る程 度 の波 で あ る この 機 構 中 を 縦 波 が 重 力波 連 の 波 速 で 進 行 して い るか の で 気 泡 が 捕 捉 さ れ る 場 合,大 Fig. 1. Various phases of the entrainment left lower photograph was taken a stalactite grotto. The inset lines indicate a length 風 波 中 で は,気 こ の 現 象 の お こ る 最 低 風 速 は,Fig.2に 見 られ 上 で 風 路 断 面 平 均7.5 度 で13m/sec)程 度 で あ り,こ れ を 越 え る と,海 の比較的小 さな重力波の峰の上で 力 と表 面 張 きな 重 力 波 自体 は決 of 10cm. 泡 のx方 は ほ と ん ど な い か ら,単 布 は,同 m/sec(10m高 も,い 下 の 波 長 を も つ た,重 of air bubbles in wind waves. The from beneath: it looks like a ceiling of し て くず れ て は い な い る よ う に 吹 走 距 離13mm以 の 小 波 は決 して 純 粋 の表 面 張 力波 で は 向 の全 体 と して の 輸 送 位 体 積 中 の 気 泡 数 θの 分 じ大 きさの 泡 の ク ラス に つ い て 次式 で 表 わ され る す な わ ち, た る と こ ろ 気 泡 が 生 成 さ れ る に い た り,微 (7) 水 滴 生 成 率 の急 激 な 増 加 が 期 待 され る した が つ て こ の 風 速 は,大 気 海 洋 の 境 界 過 程 に お け る一 つ の 重 要 な 臨 界 風 速 と考 え ら れ る 3.3. 風 波 中 の 気 泡 分 布 と混 合 係 数 こ こ に,wは 気 泡 の 水 中 上 昇 の 終 速 度,η 中 の 混 合 係 数 で あ り,z軸 は水 面 か ら下 方 に 正 に と つ て あ る 境 界 条 件 は こ の 場 合, ( 4 ) は風波

5 Fig. 2. Values of the percentage of crests of main gravity waves that are entraining air bubbles (ƒ ). A mean wind speed in the tunnel section (w) of 7.5 m/sec corresponds to 13 m/sec at 10m level. Table 2. Coefficient of mixing in wind waves, estimated from vertical distribution of the entrained air bubbles.

6 Fig. 3. Examples of the distribution of droplet concentration (e) in the flume, observed and calculated, for W =12.1m/sec and for fetch=13.6m. The broken line is the calculation by the equation (4).

7 Fig. 4. Production rate of droplets from wind waves (F1) when the wind speed is 22.8m/sec (at 10m level). Values are shown for each 10p size band of droplets. Fig. 5. Salt mass density-saltmass distribution of sea-salt particles at di- fferent heights. M is the otal mass of sea salt contained in droplets, per unit volume of air, with salt con- tent less than m.

8 Fig. 6. Ratio ľ0(x)/ľ0(0), calculated by the equation (6) for five grades of droplet diameter, for a wind speed of 23m/sec.

9 Fig. 7. Salt fallout near the coast for a wind speed of 23 m/sec. The full line is calculated by the equation (12) by use of the value F1, and the broken line represents the formula by KITA and AYA (1959). 3) MASON, B. J. (1955): Bursting of air bubbles at the surface of sea water. Nature, 174,

10 7) MAY, K. R. (1950): The measurement of airborne droplets by the magnesium oxide method. Jour. Sci. Instr., 27, ) WOODCOCK, A. H. and M. M. GIFFORD (1949): Sampling atmospheric sea-salt nuclei over the ocean. Jour. Mar. Res., 8, ) MUNK, W. H. (1955): High frequency spectrum of ocean waves. Jour. Mar. Res., 14, ) CRAPPER, G. D. (1957): An exact solution for progressive cappillary waves of arbitrary amplitude. Jour. Fluid Mech., 2, ) DATTA, R. L., D. H. NAPIER and D. M. NEWITT (1950): The properties and behaviour of gas bubbles formed at a circular orifice. Trans. Inst. Chem. Engrs., 28, ) LANE, W. R. and H. L. GREEN (1956): The mechanics of drops and bubbles. Surveys in Mechanics, Cambridge University Press, ) HAYAMI, S. and H. KUNISHI (1959): A wind flume study on the generation of waves. International Oceanogr. Congress, Preprints, ) BROCKS, K. (1959): Measurements of wind profiles over the sea and the drag at the sea surface. Ibid., ) ERIKSSON, E. (1959;1960): The yearly circulation of chloride and sulfur in nature; meteorological and pedological implications. Tellus, 11, ; 12, ) MASON, B. J. (1957): The physics of clouds. Oxford at the Clarendon Press, 481 pp. 17) ODDIE, B. C. V. (1960): The variaiton in composition of sea-salt nuclei with mode of formation. Quart. Jour. Roy. Met. Soc., 41, ) SUGAWARA, K., S. OANA and T. KOYAMA (1949): Separation of the components of atmospheric salt and their distribution. Bull. Chem. Soc. Japan, 22, KOYAMA, T. and K. SUGAWARA (1953): ditto (continued).ibid., 26,

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