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.     

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.     

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.     

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).     

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.     

A comparison of observed and calculated directional wave spectra in the East China Sea

Directional wave spectra measured by a cloverleaf buoy in the East China Sea during AMTEX '75 have been compared with those calculated with the operational numerical MRI wave model developed at the Meteorological Research Institute of the Japan Meteorological Agency (J.M.A.). It is shown that the numerical wave model MRI can predict rather well, not only the frequency spectrum, but also the angular distribution function of the spectrum. The frequency dependence of the calculated angular distribution function is quite similar to that observed; the angular distribution is narrower for the spectral components near the peak spectral frequency but widens toward high frequencies and approaches the cos²-distribution.     

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.     

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.     

Volume transport of the western boundary current penetrating into a marginal sea

The amount of penetration of a western boundary current into a marginal sea which is connected to an open ocean by two narrow straits is estimated from a linear, steady and barotropic theoretical model. In this model the western boundary current in the open ocean is driven by a wind stress imposed at the sea surface. The inflow of the water of the open ocean into the marginal sea is caused by the pressure difference between two straits produced by the wind-driven circulation in the open ocean.Main external parameters are combined into two non-dimensional parameters; and (the ratio of the depth of the marginal sea to that of the open ocean), whereb is the distance between north and south boundaries of the ocean,D ₀ is the depth of the open ocean, is the latitudinal variation of the Coriolis parameter andR is the coefficient of friction. The friction is assumed to be proportional to the flow velocity.In the limit of infinite the volume transport into the marginal sea is not affected by the width of two straits and . It is mainly controlled by the wind stress and the positions of two straits. For finite values of , however, the volume transport depends considerably on and the width of the straits.Guided by both this model and physical considerations, we obtained a relation between the volume transport into the marginal sea and the external parameters. This relation predicts that about 2 % of the volume transport of the Kuroshio penetrates into the Japan Sea.     

A new expression for the production rate of sea water droplets on the sea surface

A new set of empirical formulas for the production rate and the number concentration of sea-water droplets on the sea surface are proposed, synthesizing past observation data of sea-salt particles in the sea and water droplets in wind-wave tanks. A new levelz _c is introduced as the effective wind-sea surface where seawater droplets are produced. The new formulas are expressed in linear functions in logarithmic scales ofu*²/v _p , a parameter to describe overall conditions of airsea boundary processes, whereu _* is the friction velocity of air,v the kinematic viscosity of air and _p the peak angular frequency of wind-wave part of wave spectra. A model of coexistence of spray droplets and suspended particles near the sea surface is proposed. As for the independent parameter, a comparison between the uses ofu*²/v _p and ofu _* ³ which was the traditional way of parameterization excluding wave measure, shows that the advantage of usingu*²/v _p is statistically significant with a confidence limit 89% in F-test.     

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).     

North Pacific Intermediate Water studied chiefly with radiocarbon

The importance of the North Pacific Intermediate Water as a sink for the anthropogenic carbon dioxide has been examined by mapping chemical and radiochemical properties at two isopycnal surfaces of of 26.6 ad 27.2 obtained in 1970's. Its radiocarbon contents in 1980's were determined for comparison. The isopleths of depth and salinity at the two isopycnal surfaces obviously show that the intermediate layer of the entire mid-latitudes of the North Pacific is occupied by a similar water mass. The distributions of dissolved oxygen contents and Si/N ratios in the intermediate water indicate its source in the northwestern North Pacific and its sink in the eastern Pacific. The ¹⁴C values clearly designate the intrusion of the artificial radiocarbon of mostly 1960's origin into the upper intermediate water of the western North Pacific having its maximum in the subarctic zone of 40–45°N and 160–180°E in 1973. The maximum region for tritium is much broader extending to the north. These suggest that the subboreal region is active in the gas exchange and/or the warm water residing for a long time at the surface and flowing into the region across the subarctic front sinks quickly in winter. At the lower isopycnal surface, the increase ¹⁴C value for 14±4 years was around 27, which is smaller than that expected from the total carbonate increase, indicating an active isopycnal mixing.     

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.     

The statistical distributions for the elevation,velocity and acceleration of the surface of wind waves

Water surface elevations(t), vertical surface velocities and vertical surface acceleration of wind-generated waves have been measured in a laboratory wind wave channel by using resistance-type wave gauges combined with an electronic differentiation circuits. Probability distributions of the values of(t), , and have been determined from the wave records.In an initial stage of wave generation,i.e., when wind waves are generated at short fetches and low wind speeds, the observed distributions for(t), and are appreciately good fit to the distributions given by successive sum of a Gram-Charlier series, which has been derived following the formulation ofLonguet-Higgins (1963), by taking the weakly nonlinear effect into account.However, when wind waves develop with increasing wind speeds and fetches, the observed distributions deviate gradually from the Gram-Charlier series. Particularly, the deviations are remarkable for the distribution of .When the wind speed increases, the observed distributions of(t), and show the following characteristics: (i) the skewnesses of the distributions of(t) and decrease slightly, (ii) the skewness of changes, at some wind speed, from positive small values to relatively large negative values, (iii) the kurtosis of the distribution of(t) decreases slightly but that of increases slightly and these characteristics seem to depend not so much on fetches, (iv) the kurtosis of the distribution of increases rapidly.     

On nonlinear sea waves and the induced mean flow

The nonlinear modulation of water wave groups is investigated and the interaction equations with induced flows are obtained. The analysis is performed up to the third order of the wave steepness a by treating it as a small parameter in the singular perturbation technique by means of the Krylov-Bogoliubov-Mitropolski method. The equation which governs the development of the wave envelope is found by a modification of the ordinary nonlinear Schroedinger equation for the case of uniform depth. The equations governing the behavior of the induced mean flow are examined by deriving the second order flow when the form of the modulated wave train is prescribed. The present theory can describe the mean flow caused by the radiation stress. Some applications containing the monochromatic wave instability are given to confirm the theoretical results.An outline of this paper was presented at The Ocean Surface Symposium (Sendai, 1984).     

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.     

Indirect evidence of deep flow east of a North Pacific seamount

East-west vertical sections centered on Kinmei Seamount (35N, 172E) of potential temperature, salinity, and oxygen, based on recent standard hydrographic measurements, and vertical profiles ofin situ temperature and density ( ₄) east of the seamount, based on STD data, show contrasting variability in the deep water characteristics east and west of the seamount. These data are consistent with horizontal variations in water mass properties (temperature-salinity and temperature-oxygen curves) east of the seamount between 2,600–3,900 m but not west of the seamount. East of the seamount on surfaces of constant potential temperature (or density) salinity and oxygen are higher at a station 200 km from the seamount than at stations on either side. From these relations and from known deep water properties of the North Pacific, it is suggested that east of the seamount, between 2,600–3,900 m, the observations are consistent with northward flow, which is interpreted to be a western boundary current with an east-west scale of about 300 km.