Field data support of three-seconds power law andgu *σ−4-spectral form for growing wind waves

Observational data on air-sea boundary processes at the Shirahama Oceanographic Tower Station, Kyoto University, obtained in November, 1969, was analyzed and presented as an example representing the structure of growing wind-wave field. The condition was an ideal onshore wind, and the data contained continuous records of the wind speed at four heights, the wind direction, the air and water temperatures, the tides, and the growing wind waves, for more than six hours. The main results are as follows. Firstly, in both of the wind speed and the sea surface wind stress, rather conspicuous variations of about six-minute period were appreciable. Secondly, the three-seconds power law and its lemma expressed byH ^*=BT ^*3/2 and=2BT ^*–1/2, respectively, are very well supported by the data, whereH ^*(gH/u _* ²) andT ^*(gT/u _*) are the dimensionless significant wave height and period, respectively, the wave steepness,u _* the friction velocity of air,g the acceleration of gravity, andB=0.062 is a universal constant. Thirdly, the spectral form for the high-frequency side of the spectral maximum is well expressed by the form of()= _sgu_*^–4, where is the angular frequency and() the spectral density. The value of _s is determined as 0.062±0.010 from the observational data. There is a conspicuous discrepancy between the spectral shape of wind waves obtained in wind-wave tunnels and those in the sea, the former containing well-defined higher harmonics of the spectral peak, and consequently there is an apparent difference in the values of _s also. However, it is shown that the discrepancy of _s may be eliminated by evaluating properly the energy level of the spectral form containing higher harmonics.     

Local balance in the air-sea boundary processes

A combination of the three-second power law, presented in part I for wind waves of simple spectrum, and the similarity of the spectral form of wind waves, leads to a new concept on the energy spectrum of wind waves. It is well substantiated by data from a wind-wave tunnel experiment.In the gravity wave range, the gross form of the high frequency side of the spectrum is proportional tog u _* ^–4, whereg represents the acceleration of gravity,u _* the friction velocity, the angular frequency, and the factor of proportionality is 2.0×l0^–2. The wind waves grow in such a way that the spectrum slides up, keeping its similar form, along the line of the gross form, on the logarithmic diagram of the spectral density,, versus. Also, the terminal value of, at the peak frequency of the fully developed sea, is along a line of the gradient ofg ^{2 –5}.The fine structure of the spectrum from the wind-wave tunnel experiment shows a characteristic form oscillating around the ^–4-line. The excess of the energy density concentrates around the peak frequency and the second- and the third-order harmonics, and the deficit occurs in the middle of these frequencies. This form of the fine structure is always similar in the gravity wave range, in purely controlled conditions such as in a wind-wave tunnel. Moving averages of these spectra tend very close to the form proportional to ^–5.As the wave number becomes large, the effect of surface tension is incorporated, and the ^–4-line in the gravity wave range gradually continues to a ^–8/3-line in the capillary wave range, in accordance with the wind-wave tunnel data. Likewise, the ^–5-line gradually continues to a ^–7/3-line.Also, through a discussion on these results, is suggested the existence of a kind of general similarity in the structure of wind wave field.     

On the wave dependence of sea-surface wind stress

Analysis is made of wind and wave data, which were obtained during the passage of Typhoon 8013 at an Ocean Data Buoy Station south of Honshu operated by the Japan Meteorological Agency, in order to investigate the wave dependence of sea-surface roughness parameter in the situation where wind waves are dominant with less significant swells. The data fit better the wave-dependent expression of the wind stress,z _{0 p}/u*=, than to Charnock's formula,gz ₀/u*²=, wherez ₀ is the roughness length, _p the angular frequency of the spectral peak of wind waves,u* the friction velocity of air,g the acceleration of gravity, and are non-dimensional constants. The results are very similar to those of our previous study using data from an oil producing platform in the Bass Strait, Australia, although the type of observation system and the synoptic situation of the winds and wind waves were totally different.     

On nondimensional correlation between roughness length and wind-friction velocity

Physical bases for nondimensional parameters,z ₀/(u ² _*/g) andz ₀/(u _*/), characterizing wind-wave interaction are discussed; data selected to support the latter are critically reviewed. Both parameters are herewith unified, with the former describing the primary growth of roughness length with wind and the latter the secondary effects due to waves.     

Analysis of photographic images of the structure of the surface of the sea near a speck of light

Values of root mean square slope ₀ and its variations -₀ are estimated using the brightness field of an image of the surface of the sea near a speck of light. When ₀ and -₀ are defined it is highly important to take into account direct as well as dissipated solar radiation.The space-time analysis of the structure of the image brightness field is performed. This gives an opportunity to estimate dispersion relationship and the running effect of a brightness contrast packet. Comparison of the parameters obtained with the theoretical dispersion ratio of internal waves (IW) allows one to make a conclusion that IW surface manifestations are recorded in a frame.UDK 551.463.5     

Chlorofluorocarbons in the western North Pacific in 1993 and formation of North Pacific intermediate water

Chlorofluorocarbons (CFC-11 and CFC-12) in the intermediate water having between 26.4 and 27.2 were determined at 75 stations in the western North Pacific north of 20°N and west of 175.5°E in 1993. The intermediate water of 26.4–26.6 was almost saturated with respect to the present atmospheric CFC-11 in the zone between 35 and 45°N around the subarctic front. Furthermore, the ratios of CFC-11/CFC-12 of the water were also of those formed after 1975. These suggest that the upper intermediate water (26.4–26.6) was recently formed by cooling and sinking of the surface water not by mixing with old waters. The water below the isopycnal surface of 26.8 contained less CFCs and the area containing higher CFCs around the subarctic front was greatly reduced. However, the CFC age of the lower intermediate water (26.8–27.2) in the zone around the subarctic front was not old, suggesting that the water was formed by diapycnal mixing of the water ventilated with the atmosphere with old waters not containing appreciable CFCs, probably the Pacific Deep Water. The southward spreading rate decreased with depth and it was one sixth of its eastward spreading rate of the North Pacific Intermediate Water (NPIW).     

On the relation between the growth rate of water waves and wind speed

Various wind velocitiesu _*,U _/2,U andU ₁₀ are correlated to the measured growth rate of water waves , whereu _* is the friction velocity of the wind, andU _/2,U andU ₁₀ are the wind speeds respectively at the heights /2, and 10m above sea surface (: wave length). It is shown that within a range of the dimensionless wind speed, 0.1<u _* /C<0.6, there are no appreciable differences in the correlations, whereC is the phase velocity of water waves. The present relation between andU shows qualitatively similar properties as the one obtained by Al'Zanaidi and Hui (1984); the growth rate for waves with rough surface is larger than that with smooth surface. However, our present relations give, for the both waves with different surface roughness, larger values by factors 1.71.8 than those given by Al'Zanaidi and Hui's relation.     

Dilution of North Pacific Intermediate Water studied with chlorofluorocarbons

Assessment was made of residual ratio of North Pacific Intermediate Water (NPIW) produced in subpolar region of the North Pacific using chlorofluorocarbons, CFC-11 and CFC-12 (CCl₃F and CCl₂F₂), along 175°E. NPIW on density horizons less than 26.80 remained more than 80% north of 30°N. It was suggested that new NPIW laterally spreads over the northern North Pacific without hardly being diluted by the surroundings. For density horizons greater than 26.80 north of 30°N, NPIW remained less than 60%. The difference in the residual ratio between <26.80 and >26.80 north of 30°N suggests that NPIW is produced on density horizons less than 26.80, which contacts the atmosphere in the subpolar region, and that NPIW is diluted by upwelling deep water on density horizons greater than 26.80 in high latitude of the North Pacific. NPIW on a density horizon of 26.80 remained about 50% south of 30°N. The decrease in the horizontal distribution of the residual ratio of NPIW suggests that half the new NPIW produced in the subpolar region is laterally spread over the North Pacific with the southward movement of NPIW.     

A Preliminary Study of Oceanic Bomb Radiocarbon Inventory in the North Pacific during the Last Two Decades

Radiocarbon and total carbonate data were obtained near the 1973 GEOSECS stations in the North Pacific along 30°N and along 175°E between 1993 and 1994. In these stations, we estimated radiocarbon originating from atomic bomb tests using tritium, trichlorofluoromethane and silicate contents. The average penetration depth of bomb radiocarbon during the two decades has deepened from 900 m to 1300 m. Bomb radiocarbon inventories above the average value for the whole North Pacific were found widely in the western subtropical region around 30°N both in the 1970s and 1990s, and its area in the 1990s was broader than that in the 1970s. In most of the North Pacific, while the bomb radiocarbon has decreased above 25.4, the bomb radiocarbon flux below 25.4 was over 1 × 10¹² atom m^-2yr^-1 in the subtropical region around 30°N. In the tropical area south of 20°N, the bomb radiocarbon inventory below 25.4 increased from zero to over 10 × 10¹² atom m^-2 during the last three decades. These distributions suggest that the bomb radiocarbon removed from the surface is currently accumulated with bomb ¹⁴C flux of over 1 × 10¹² atom m^-2yr^-1 below 25.4 in the subtropical region, mainly by advection from the higher latitude, and that part of the accumulated bomb ¹⁴C gradually spread southward with about 30 years.     

Tritium in the northwestern North Pacific

Vertical profiles of tritium in seawater were determined for samples collected during the period from 1988 to 1990 at fourteen stations in the northwestern North Pacific (the Oyashio region) including the Okhotsk Sea and the Bering Sea. The profiles usually had a maximum in the surface layer and decreased gradually with depth down to 1,000 m. The water column inventory of tritium averaged 63% of the total atmospheric input in this region.The horizontal distribution of tritium showed a maximum in the region facing the Okhotsk Sea near 45°N for every isopycnal surface of ₀ ranging from 26.60 to 27.40. The ages of the intermediate water were calculated for the respective isopycnal surfaces in the maximum region. This calculation assumed that the intermediate water was formed by the isopycnal mixing of two water masses—the Okhotsk Sea and the Bering Sea Component Waters, which had been produced in wintertime by the diapycnal mixing of the surface and the deep waters in the respective marginal seas. The results show that the intermediate water in this region was formed in the late 1980's for the water which has ₀ of 26.60 to 26.80 and about 1970 for the water which has ₀ of 27.00 to 27.40. Although we have estimated the mean ages of the intermediate water, the horizontal profile of dissolved oxygen suggests that the Okhotsk Sea Component Water is younger than the mean age.     

Water masses and hydrography in the tropical Pacific during Japanese Pacific Climate Study '91 cruise

Hydrographic measurements by CTD were made in the western-central Equatorial Pacific (160°W–147°E) during the Japanese Pacific Climate Study cruise in January–February 1991. InT-S diagram, three water masses are seen in the layer of kg/m³: salinity water corresponding to the Tropical Water of eastern South Pacific origin, less saline water in the North Pacific, and water with salinity between the above two, found on the equator. In three meridional sections (160°W–160°E), the Tropical Water of eastern South Pacific origin extends further equatorward than the climatological data of Levitus (1982).     

Vertical transport and residence time of chlorinated hydrocarbons in the open ocean water column

The vertical transport of PCBs and chlorinated hydrocarbon pesticides such as DDT compounds and HCH (BHC) isomers in the deep sea are discussed on basis of their vertical profiles and the proportion of their adsorbed and dissolved fractions in surface water surveyed in the Western Pacific, Eastern Indian and Antarctic Oceans.All chlorinated hydrocarbons determined were detected with measurable concentrations throughout the water column, even at depths of several thousand meters. The vertical distributions of PCBs and DDT compounds were found to show small variations in concentration throughout the water column, whereas HCH isomer concentrations decreased systematically with depth. A large portion of DDT compounds in surface water was adsorbed on suspended solids, while most of the HCH isomers were present in the filtered water. The proportion of PCBs adsorbed on suspended solids was smaller than the proportion of DDT compounds, but was much greater than that of HCH isomers. These observations suggest that HCH isomers have been slowly scavenged from the surface to the deeper layers in the water column, while PCBs and DDT compounds have been rapidly and abundantly transported downward by sinking particles.The percentages of chlorinated hydrocarbons adsorbed on suspended solids in surface water increased towards the high latitude locations, and the percentage seemed to be proportional to the concentration of suspended solids in the surface water. This implies that the residence time of chlorinated hydrocarbons in the water column will differ significantly among oceans that differ in primary productivity. According to our estimation based on the data presented in this study, the residence time ofHCH in the euphotic zone, the top 100 m of the water column, is more than 2 years, whereas those of PCBs andDDT are less than 1 year. The longest residence time, of from 5 to 10 years, was obtained forHCH in oligotrophic water of the western North Pacific. The shortest value, only 11 to 19 days, was estimated forDDT in the Antarctic Ocean.     

Horizontal Pressure Gradient Errors of the Monterey Bay Sigma Coordinate Ocean Model with Various Grids

A coastal ocean -coordinate model of Monterey Bay (MOB) with realistic bottom topography and coastlines is developed using the Princeton Ocean Model (POM) and grid generation technique (GGT) to study the horizontal pressure gradient errors associated with the MOB steep topography. The submarine canyon in MOB features some of the steepest topography encountered anywhere in the world oceans. The MOB grids are designed using the EAGEAL View and GENIE⁺⁺ grid generation systems. A grid package developed by Ly and Luong (1993) is used in this study to couple grids to the model. The MOB model is tested with both orthogonal and curvilinear nearly-orthogonal (CNO) grids. The CNO grid has horizontal resolution which varies from 300 m to 2 km, while the resolution of the orthogonal grid is uniform with x = 1.25 km and y = 1.38 km. These grids cover a domain of 180 × 160 km with the same number of grid points of 131 × 131. Vertical resolutions of 25, 35 and 45 vertical sigma levels are tested. The error in the MOB are evaluated in terms of mean kinetic energy and velocity against various grids, vertical, horizontal resolution and distributions, and bottom topography smoothing. Simulations with various grids show that GGT can be used as another tool in reducing -coordinate errors in coastal ocean modeling besides increasing resolution and smoothing bottom topography. Topographical smoothing not only reduces topographic slope, but changes realistic topography. A CNO grid with a high grid density packed along steep slopes and Monterey Submarine Canyon reduces the errors by 40% compared to a rectangular grid with the same number of grid points. The CNO grid is more efficient than the rectangular grid, since it has most of its grids over water. The simulations show that the presented MOB -coordinate model can be used with a confidence regarding horizontal pressure gradient error.     

Analytically derived wind-wave directional spectrum part 1. Derivation of the spectrum

In contrast with the usual method to obtain the wind-wave directional spectrum by multiplying the frequency spectrum with an empirical directional function, the authors attempt to derive analytically the directional spectrum by adopting proper spectral form and using effective parameters, namely, the zero order momentm ₀ of the wind-wave frequency spectrumS(), its peak frequency ₀ and the so-called peakness factorP=₀ S(₀)/m ₀, where is angular frequency. The directional spectrum is given in a form of frequency spectrum for each direction. The spectral directionality depends on, in addition to frequency, the wind-wave growth status, for the peakness factorP as introduced by the authors previously is a measure of the wave development stage. The salient features of the directional spectrum, comparison with existing formulas and the verification of the spectrum by observational data are to be given in the Part 2 of the paper.Project supported by the National Natural Science Foundation of China.     

Validation of wind speeds and significant wave heights observed by the TOPEX altimeter around Japan

The wind speeds and significant wave heights observed by the TOPEX altimeter during the first 30 repeat cycles (for about 10 months) are validated by comparing with the data obtained at Japanese Ocean Data Buoy stations. The values of Kuband ⁰ observed by the altimeter show good agreement with those estimated from the buoy wind speed using the modified Chelton-Wentz algorithm. The wind speeds derived from the Ku-band ⁰ using the algorithm agree well with the buoy data with an rms difference of 1.99 ms^–1. The significant wave heights observed by the altimeter have a systematic bias of 0.3 m.     

Bispectra of spike-array type time series and their application to the analysis of oceanic microstructures

Bispectral analysis is applied to records of the vertical profile of the vertical temperature gradient in the oceanic thermocline in the San Diego Trough. The bispectra exhibit three notable features; (1) bispectral peaks at the points (0.2 m^–1, 0.2 m^–1) and (0.2 m^–1, 0.1 m^–1), (2) bispectral ridges along the lines ( ₁= ₀, ₂= ₀ and ₁+ ₂= ₀ corresponding to peak wavenumbers ₀ in power spectra, and (3) array of bispectral peaks of interval of 0.2 m^–1 The results are compared with the bispectra of several modeled time series of spike-array type. The periodicity of 5 m found in the records seems to have two meanings: spacing of predominant spikes and wavelength of predominant sinusoidal wave. If this indicates the existence of internal waves having a vertical wavelength the same as the scale of homogeneous layers, it would suggest the possible importance of internal waves in the formation and maintenance mechanisms of oceanic microstructure.     

Radiation balance and heat budget at the ocean/atmosphere interface in the western North Pacific

The downward short- and long-wave radiation fluxes at the sea surface (S, L) were measured aboard the R/VHakuho Maru, University of Tokyo, for the period of 117 days on six cruises from 1981 to 1985 in the western North Pacific near Japan. The upward fluxes of short- and long-wave radiation (S, L) were calculated by Payne's (1972) table and the Stefan-Boltzmann's law, respectively. The sensible and laten heat fluxes (Q _h ,Q _e ) were also estimated from an aerodynamic bulk method.From April to August, the daily mean value ofS varied with the amplitude of 100200 Wm^–2. The value ofS was estimated approximately 6% ofS in all seasons. The difference betweenL andL was so small that the net radiation flux (Q _n ) was dominated byS. In addition, the net heat flux at the sea surface was also dominated byS due to small values ofQ _h andQ _e , and then the ocean was warmed at the rate of 111 Wm^–2 in April and 63 Wm^–2 in August in the Oyashio Area, and 132 Wm^–2 in May and 164 Wm^–2 in June in the Kuroshio Area, respectively.From September to March, a remarkable negative correlation between the day to day variation ofS and that ofL was observed except when an intense cold air outbreak occurred. It was found that the correlation was caused by the cloud climatological feature of the western North Pacific in this period.S was not a dominant factor in the net heat flux. The value ofQ _h +Q _e in the Kuroshio Area ranged from 260 Wm^–2 to 630 Wm^–2, much larger thanQ _n which ranged from –8 Wm^–2 to 92 Wm^–2 in the leg mean values (each leg period was about 10 days). Then the ocean was cooled at the rate of –160–620 Wm^–2 during this period. The net heat flux in the Kuroshio Area averaged over five legs from late November to February was –473 Wm^–2. This value is 50100% larger than the climatological values reported so far.The temporal and spatial variability of radiation fluxes and heat fluxes during each leg was also discussed.     

Excess CO2 and pHexcess in the Intermediate Water Layer of the Northwestern Pacific

Excess CO₂ and pH_excess showing an increase in dissolved inorganic carbon and a decrease in pH from the beginning of the industrial epoch (middle of the 19th century) until the present time have been calculated in the intermediate water layer of the northwestern Pacific and the Okhotsk Sea. It is concluded that: (1) The Kuril Basin (Okhotsk Sea) and the Bussol' Strait areas are characterized by the greatest concentrations of excess CO₂ at isopycnal surfaces due to the processes of formation and transformation of intermediate water mass. (2) The largest difference in excess CO₂ concentration between the Okhotsk Sea and the western subarctic Pacific (about 8 µmol/kg) is found at the = 27.0. (3) The difference in excess CO₂ between the western subarctic Pacific and subtropical regions is significant only in the upper part of the intermediate water layer ( = 26.7–27.0). (4) About 10% of the excess CO₂ accumulation in the subtropical north Pacific is determined by water exchange with the subarctic Pacific and the Okhotsk Sea.     

Respiration rates of copepod larvae and a ciliate from a tropical sea

The respiration rates of copepod larvae and a ciliate (Placus sp.) from a tropical sea were measured with an oxygen electrode method. The general range of body size of these animals was 40–161m (diameter equivalent to a sphere), and the respiration rate measured was 0.00076–0.00176l O₂ (animal)^–1h^–1 (or 2.02–9.05l O₂ (mg wet weight)^–1h^–1) at 25.5–29.2C. There was no marked difference observed between the respiration rates of copepod larvae and the ciliate. The respiration rates obtained here are relatively higher than the rates of other similar sized protozoans found in the literature, but lower than the rate extrapolated from larger planktonic copepods in tropical seas.The present results and other information available on microzooplankton biomass suggest that microzooplankton respiration is of near equal importance to that of net zooplankton in the study of energy flow through tropical, pelagic ecosystems.     

Some characteristics of the development process of the wind-wave spectrum

The development process of wind-waves of which spectral peak distributes from 0.6 cps to 9.3 cps will be discussed on the basis of the wind tunnel experiments and of the field observations performed at Lake Biwa. The characteristics of power and slope spectra are here presented. The development process of these wind-waves is characterized by three stages;i.e. initial-wavelets, transition stage and sea-waves. In the wind tunnel experiments, the transition from the stage of the initial-wavelets to the transition stage occurs when the wave spectral peak arrives at the line 6.40×10^–4 k ^–2cm²·sec (wherek is wave number) or when the slope spectral density at the frequencyf _max becomes larger than 6.40×10^–4 sec. In the stage of sea-waves, the component wave of a wave-spectral peak is steepest in the component waves. And the wave spectral peak develops along the line 1.02×10² f ^–6 cm²·sec (wheref is the frequency corresponding to the wave numberk) untill it reaches the line 33.3f ^–4cm²·sec, and thereafter develops along the latter line, which indicates the constant density of slope spectrum. It is suggested that the nonlinearity of wind-waves must become stronger as wind-waves develop. The effective momentum flux _ws from the air flow to wind-waves in this stage is evaluated to be about 49% of the total stress ₀.