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Phase velocity effects of tertiary wave interactions
Oceanographic Abstracts
955
paper, by a slightly different method, the interaction is calculated in detail for the simplest possible case: when two of the three primary wave-numbers are equal (k~ = kl). It.is found that, when k~, and kz are parallel or antiparallel, the interaction vanishes unless kl = k2. Generally, if O denotes the angle between kl and k.~, the rate of growth of the tertiary wave with time is a maximum when 0 - 17"; the rate of growth with horizontal distance is a maximum when 0 - 24 °. The calculations show that it should be possible to detect the tertiary wave in the laboratory.
LONGUETHIGGINS,M. S. and O. M. PHILLIPS,1962. Phase velocity effects of tertiary wave interactions. J. Fluid Mech, 12: 333-336. Also in: Coll. Reprints, Nat. Inst. Oceanogr., WOrmley, 10. It is shown that, when two trains of waves in deep water interact, the phase velocity of each is modified by the presence of the other. The change in phase velocity is of second order and is distinct from the increase predicted by Stokes for a single wave train. When the wave trains are moving in the same direction, the increase in velocity AC2 of the wave with amplitude a2, wave-number kz and frequency az resulting from the interaction with the wave (at, kl, el) is given by Ac2 = alZktax, provided k~ < k,_. If kt > kz, then Ae, is given by the same expression multiplied by kz/k~. If the directions of propagation are opposed, the phase velocities are decreased by the same amount. These expressions are extended to give the increase (or decrease) in velocity due to a continuous spectrum of waves all travelling in the same (or opposite) direction. LOPEZ, J., 1963. Edad de la sardina (Sardina pilchardus, Walb.) de Barcelona. (In Spanish, English summary). Inv. Pesq., Barcelona, 23: 133-157. 4053 specimens of sardines (Sardina pilchardus Waib.) were studied. The material was collected at Barcelona during 1961. The total length of the catch was between 80 and 200ram. The age of the sardines was determined from their scales. The length when the hibernal rings were formed was: I~
12
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14
Is
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139 156 166 174 182 187 mm In comparison with sardine from other localities in the Western Mediterranean, their growth off Barcelona is more rapid than in the Gulf of Valencia and less rapid than in Alicante, Baleares and South of the Peninsula, but very similar to the growth observed in the Gulf of Lyons. Ninety per cent of the commercial catch belongs to the 0-1II age class. The quantitative relation between t he length and weight is stated for whole fishes and for eviscerated fishes. Soawning occurs in winter, chiefly from December to February. The females are generally larger than the males: 51 per cent males and 49 per cent females. The mean number of vertebra is 51-59. According to the characteristic of populations, the exploited area can be divided in two zones, north and south, respectively, of the river Llobregat. 119
MANNING,P,.. B., 1963. A new species ofLysioaquilla (Crustacea, Stomatopoda) from the northern straits of Florida. Bull. Mar. Sci., Gulf Caribb., 13 (1): 54--57. Ly~iosquilla insolita, nov. sp., closely related to L. insignis Kemp from the Indian Ocean, is described and illustrated. The distribution of these two species is similar to that observed in L. microps Manning and its ally, L. crassispinosa Fukuda. MARR, J. W. S., 1963. Unstalked crinoids of the Antarctic continental shelf. Notes on their natural history and distril:ution. Phil. Trans. Roy. Soc., Lond., (Ser. B. Biological Science), 246 (734): 327-379. An account is given of the natural history, distribution and relative abundance of the comatulids of the Antarctic continental shelf. On the whole they form a distinctive geographical assemblage, that, cut off from northern influence, has evidently evolved in isolation since at least from the beginning of the Pleistocene or Quaternary Period. Where large enough numbers have been encountered the distribution of six of the seventeen known shelf species has been shown to be circumpolar, and at least one of the six, ihe largest and most mobile, appears to have spread, or perhaps even now is spreading, northwards to lowe~" latitudes via the submarine ridges that radiate outwards from Antarctica. M~mss, FI. W. and R. H. MELLEN,1963. Underwater sound propagation in the Arctic Ocean.
J. Acouat. Soc. Amer., 35 (4): 552-563.
Some results of a 4 yr experimental study of sound propagation in the Arctic are presented and interpreted. The duration, form, and intensity of waves received at distances up to 1400 km are explained using ray theory and modes, in which source characteristics, refraction, scattering at the ice surface, and bottom effects are important.
955
paper, by a slightly different method, the interaction is calculated in detail for the simplest possible case: when two of the three primary wave-numbers are equal (k~ = kl). It.is found that, when k~, and kz are parallel or antiparallel, the interaction vanishes unless kl = k2. Generally, if O denotes the angle between kl and k.~, the rate of growth of the tertiary wave with time is a maximum when 0 - 17"; the rate of growth with horizontal distance is a maximum when 0 - 24 °. The calculations show that it should be possible to detect the tertiary wave in the laboratory.
LONGUETHIGGINS,M. S. and O. M. PHILLIPS,1962. Phase velocity effects of tertiary wave interactions. J. Fluid Mech, 12: 333-336. Also in: Coll. Reprints, Nat. Inst. Oceanogr., WOrmley, 10. It is shown that, when two trains of waves in deep water interact, the phase velocity of each is modified by the presence of the other. The change in phase velocity is of second order and is distinct from the increase predicted by Stokes for a single wave train. When the wave trains are moving in the same direction, the increase in velocity AC2 of the wave with amplitude a2, wave-number kz and frequency az resulting from the interaction with the wave (at, kl, el) is given by Ac2 = alZktax, provided k~ < k,_. If kt > kz, then Ae, is given by the same expression multiplied by kz/k~. If the directions of propagation are opposed, the phase velocities are decreased by the same amount. These expressions are extended to give the increase (or decrease) in velocity due to a continuous spectrum of waves all travelling in the same (or opposite) direction. LOPEZ, J., 1963. Edad de la sardina (Sardina pilchardus, Walb.) de Barcelona. (In Spanish, English summary). Inv. Pesq., Barcelona, 23: 133-157. 4053 specimens of sardines (Sardina pilchardus Waib.) were studied. The material was collected at Barcelona during 1961. The total length of the catch was between 80 and 200ram. The age of the sardines was determined from their scales. The length when the hibernal rings were formed was: I~
12
13
14
Is
16
17
139 156 166 174 182 187 mm In comparison with sardine from other localities in the Western Mediterranean, their growth off Barcelona is more rapid than in the Gulf of Valencia and less rapid than in Alicante, Baleares and South of the Peninsula, but very similar to the growth observed in the Gulf of Lyons. Ninety per cent of the commercial catch belongs to the 0-1II age class. The quantitative relation between t he length and weight is stated for whole fishes and for eviscerated fishes. Soawning occurs in winter, chiefly from December to February. The females are generally larger than the males: 51 per cent males and 49 per cent females. The mean number of vertebra is 51-59. According to the characteristic of populations, the exploited area can be divided in two zones, north and south, respectively, of the river Llobregat. 119
MANNING,P,.. B., 1963. A new species ofLysioaquilla (Crustacea, Stomatopoda) from the northern straits of Florida. Bull. Mar. Sci., Gulf Caribb., 13 (1): 54--57. Ly~iosquilla insolita, nov. sp., closely related to L. insignis Kemp from the Indian Ocean, is described and illustrated. The distribution of these two species is similar to that observed in L. microps Manning and its ally, L. crassispinosa Fukuda. MARR, J. W. S., 1963. Unstalked crinoids of the Antarctic continental shelf. Notes on their natural history and distril:ution. Phil. Trans. Roy. Soc., Lond., (Ser. B. Biological Science), 246 (734): 327-379. An account is given of the natural history, distribution and relative abundance of the comatulids of the Antarctic continental shelf. On the whole they form a distinctive geographical assemblage, that, cut off from northern influence, has evidently evolved in isolation since at least from the beginning of the Pleistocene or Quaternary Period. Where large enough numbers have been encountered the distribution of six of the seventeen known shelf species has been shown to be circumpolar, and at least one of the six, ihe largest and most mobile, appears to have spread, or perhaps even now is spreading, northwards to lowe~" latitudes via the submarine ridges that radiate outwards from Antarctica. M~mss, FI. W. and R. H. MELLEN,1963. Underwater sound propagation in the Arctic Ocean.
J. Acouat. Soc. Amer., 35 (4): 552-563.
Some results of a 4 yr experimental study of sound propagation in the Arctic are presented and interpreted. The duration, form, and intensity of waves received at distances up to 1400 km are explained using ray theory and modes, in which source characteristics, refraction, scattering at the ice surface, and bottom effects are important.