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.     

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.     

The roughness height and drag law over the water surface based on the hypothesis of local equilibrium

A series of measurements of winds and wind-waves were carried out in wind-wave flumes. A data analysis based on the hypothesis of local equilibrium yielded a new empirical formula on the controversial quantity of roughness heightz ₀ over the water surface: , where the nondimensional roughness height is defined bygz ₀/u _* ² and the wave-wind parameterũ byω _p u _*/g, g being the gravitational acceleration,u _* the friction velocity of air,ω _p the peak frequency of wind-wave spectra. The obtained formula is compared with Charnock's (1955) and Toba's (1979) proposals; is constant in the former and inversely proportional toũ in the latter. As in Toba's, this formula immediately leads to a practically important conclusion that the drag coefficientC _d depends not merely on the usual variableU ₁₀ (wind velocity at 10m height over the water surface), but also on the surface state represented by wind-waves. An explicit expression is provided for the drag coefficient incorporating the wave-wind parameter; it covers the range ofC _d calculated from most of the previous drag formulas, by varying the wave-wind parameter.     

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.     

A method for evaluating statistical errors associated with logarithmic velocity profiles

A logarithmic velocity profile is often fitted to velocity data in order to calculate the friction velocity (u _*) and typify the surface texture by a roughness length (z _o ). A method is given for estimating the errors in these parameters as calculated by this method. An example is given in which the size of the error is compared with the fluctuations that typically occur in the time seriesu _*(t) andz _o (t).     

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.     

Sea-surface roughness length fluctuating in concert with wind and waves

When the nondimensional aerodynamic roughness parameter for the sea surface (gz ₀/u _* ²,g being the acceleration of gravity,u _* the air friction velocity) is plotted as a function of the wave age, the data points in the diagram are distributed mostly in a triangle area between the Charnock formula and the Toba-Koga formula; the nondimensional roughness perameter is not expressed as a unique function of the wave age, but rather there seem to be multiple regimes. In order to investigate the cause of the data point scattering, a reanalysis was made of the 4.5-hour time series of the wind profile and wind-wave statistics which were obtained at an oceanographic tower station under the conditions of a winter monsoon wind having slightly fluctuating speed and steadily growing wind waves.It is concluded that the averaged variation ofz ₀ is given by the Toba-Koga formula with a constant of value 0.015. However, as a result of the wind fluctuation on the time scales ranging from several minutes to an hour, data points show a conspicuous fluctuation on the nondimensional roughness parameter-wave age diagram in the direction transverse to the averaged variation. The variation inz ₀ directly reflects the degree of over- or under-saturation in the high-frequency range of the wind-wave spectra. Physical interpretation of these variations is also presented.     

Numerical Modeling of Wave-Enhanced Turbulence in the Oceanic Upper Layer

A coupled model of air-wave-sea interaction is modified based on a new roughness formulation and the latest data. The model parameters for aerodynamic roughness from below (ARB) and wave-dependent roughness from above (ARA, z _0a ) are assumed equal. The combined roughness is assumed to be a function of friction velocity, gravity, air and seawater densities, and wave age (c _w ). The model is used in a study of wave-enhanced turbulence under breaking waves to predict turbulent dissipation (), ARA, and drag coefficient (C _d ). Both waves and shear production are considered as sources of ocean turbulent energy. The atmospheric part of the model is used only to specify a correct condition at the interface. Numerical experiments are performed to study the -distribution, z _0a and C _d , and to compare with data. The major achievement is model verification using all available data. The first full application of this model is in conjunction with an ocean circulation model in a coupled circulation-wave system. Simulations show that the -distribution is strongly dependent on local wind-forced wave heights. For each wind and wave state there is a particular wave-dependent depth that is verified by data. The comparison shows that the model predicted agrees well with the observed of the z ^–4 law distribution of Gargett (1989). Simulations also show that waves have an important role in causing to differ from the classical wall-layer theory and z _0a , with a value of 0.30 for the empirical constant a _a . The model-predicted , z _0a , C _d and C _gd agree well with data.     

Vertical mixing in the bottom mixed layer near the continental shelf break in the East China Sea

The strength of the vertical mixing in the bottom mixed layer near the continental shelf break in the East China Sea was directly measured with the Micro-Scale Profiler (MSP). It has been shown that there is no significant statistical relation between the turbulent energy dissipation and the degree of the stratificationN ². It seems that the vigorous turbulence occurs not constantly but intermittently in the bottom mixed layer so that a large variation of is found depending on the time. In contrast to , the coefficient of the vertical eddy diffusivityK _z is mostly determined byN such thatK _z is large in the bottom mixed layer and small in the thermocline. Large value ofK _z in the bottom mixed layer is also found in the time series ofK _z estimated in terms of Richardson number calculated from the data obtained with electromagnetic current meters. The value ofK _z more than 10 cm²s^–1 frequently occur in the layer of 20–25 m thick just above the bottom.     

The dissociation constants of carbonic acid in seawater at salinities 5 to 45 and temperatures 0 to 45°C

The pK₁^* and pK₂^* for the dissociation of carbonic acid in seawater have been determined from 0 to 45°C and S = 5 to 45. The values of pK₁^* have been determined from emf measurements for the cell:

Pt](1 − X)H2 + XCO2|NaHCO3, CO2 in synthetic seawater|AgC1; Ag

where X is the mole fraction of CO₂ in the gas. The values of pK₂^* have been determined from emf measurements on the cell:

Pt, H2(g, 1 atm)|Na2CO3, NaHCO3 in synthethic seawater|AgC1; Ag

The results have been fitted to the equations:

lnK^*₁ = 2.83655 − 2307.1266/T − 1.5529413 lnT + (−0.20760841 − 4.0484/T)S^0.5 + 0.08468345S − 0.00654208S¹

InK^*₂ = −9.226508 − 3351.6106/T− 0.2005743 lnT + (−0.106901773 − 23.9722/T)S^0.5 + 0.1130822S − 0.00846934S^1.5

where T is the temperature in K, S is the salinity, and the standard deviations of the fits are σ = 0.0048 in lnK₁^* and σ = 0.0070 in lnK₂^*.Our new results are in good agreement at S = 35 (±0.002 in pK₁^*and ±0.005 in pK₂^*) from 0 to 45°C with the earlier results of Goyet and Poisson (1989). Since our measurements are more precise than the earlier measurements due to the use of the Pt, H₂|AgCl, Ag electrode system, we feel that our equations should be used to calculate the components of the carbonate system in seawater.     

Internal flow structure of short wind waves

The minimum value of wind stress under which the flow velocity in short wind waves exceeds the phase speed is estimated by calculating the laminar boundary layer flow induced by the surface tangential stress with a dominant peak at the wave crest as observed in previous experiments. The minimum value of the wind stress is found to depend strongly on, the ratio of the flow velocity just below the boundary layer and the phase speed, but weakly onL, the wavelength. For wind waves previously studied (=0.5,L=10 cm), the excess flow appears when the air friction velocityu _* is larger than about 30 cm sec^–1. The present results confirm that the excess flow found in my previous experiments is associated with the local growth of a laminar boundary layer flow near the wave crest.     

Tidal boundary layer measurements in the presence of waves

Measurements of tidal current and wave velocity made at 0.69 and 1.85 m above a rough seafloor exhibit large current gradients (boundary layer) in the water column. The logarithmic boundary layer flow model was fitted to the measurements, and thus roughness (z₀) and friction velocity (u^*) parameters were derived. The roughness parameter values were generally consistent with the observed upstream physical roughness. The values of both parameters for conditions in the rough turbulence flow regime are generally larger (much larger for ebb) than earlier published values for similar measurements of currents in the absence of significant waves but are comparable to values from recent measurements of currents in the presence of storm waves. The high parameter values here appear to relate more to the magnitude of the current and to the upstream physical bottom roughness than to the magnitude of the seastate. Large boundary layers in the flow at the seabed have a profound effect on the design of offshore structures such as offshore pipelines.     

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 method for evaluating statistical errors associated with logarithmic velocity profiles

A logarithmic velocity profile is often fitted to velocity data in order to calculate the friction velocity (u _*) and typify the surface texture by a roughness length (z _o ). A method is given for estimating the errors in these parameters as calculated by this method. An example is given in which the size of the error is compared with the fluctuations that typically occur in the time seriesu _*(t) andz _o (t).     

Formation of the vertical salinity profile in the Black Sea

The vertical distribution of salts brought by the Bosphorus undercurrent is numerically evaluated. By multiplying the average vertical salinity gradient by the diffusion coefficient,K _z , and the cross-section of the sea at the appropriate depth, we can determine the total vertical salt flux,Q(z). The derivative ofQ with respect toz depicts the salt source intensity distribution over depth. The highest intensity, Q/z, matches the 200 m depth level, i.e. the shelf edge. Below 1500 m, Q/z equals merely 0.1% of the value observed at a depth of 200 m. Above 37 m, salts are noted to sink, which corresponds to their outflow with the Bosphorus current. The distribution of Q/z and the respective values of mineral phosphorus and hydrogen sulphide are matched up.Translated by Vladimir A. Puchkin.     

Methane hydrate dissolution rates in undersaturated seawater under controlled hydrodynamic forcing

The dissolution of in-situ generated methane hydrate in undersaturated, synthetic seawater (S = 35) was investigated in a series of laboratory-based experiments at P-/T-conditions within the hydrate stability field. A controlled flow field was generated across the smooth hydrate surface to test if, in addition to thermodynamic variables, the dissolution rate is influenced by changing hydrodynamic conditions. The dissolution rate was found to be strongly dependent on the friction velocity, showing that hydrate dissolution in undersaturated seawater is a diffusion-controlled process. The experimental data was used to obtain diffusional mass transfer coefficients k_d, which were found to correlate linearly with the friction velocity, u. The resulting k_d/u-correlation allows predicting the flux of methane from natural gas hydrate exposures at the sediment/seawater interface into the bulk water for a variety of natural P, T and flow conditions. It also is a tool for estimating the rate of hydrate regrowth at locations where natural hydrate outcrops at the seafloor persist in contact with undersaturated seawater.     

Modeling ocean primary production: Sensitivity to spectral resolution of attenuation and absorption of light

Modeling the vertical penetration of photosynthetically active radiation (PAR) through the ocean, and its utilization by phytoplankton, is fundamental to simulating marine primary production. The variation of attenuation and absorption of light with wavelength suggests that photosynthesis should be modeled at high spectral resolution, but this is computationally expensive. To model primary production in global 3d models, a balance between computer time and accuracy is necessary. We investigate the effects of varying the spectral resolution of the underwater light field and the photosynthetic efficiency of phytoplankton (α^*), on primary production using a 1d coupled ecosystem ocean turbulence model. The model is applied at three sites in the Atlantic Ocean (CIS (60°N), PAP (50°N) and ESTOC (30°N)) to include the effect of different meteorological forcing and parameter sets. We also investigate three different methods for modeling α^* – as a fixed constant, varying with both wavelength and chlorophyll concentration [Bricaud, A., Morel, A., Babin, M., Allali, K., Claustre, H., 1998. Variations of light absorption by suspended particles with chlorophyll a concentration in oceanic (case 1) waters. Analysis and implications for bio-optical models. J. Geophys. Res. 103, 31033–31044], and using a non-spectral parameterization [Anderson, T.R., 1993. A spectrally averaged model of light penetration and photosynthesis. Limnol. Oceanogr. 38, 1403–1419]. After selecting the appropriate ecosystem parameters for each of the three sites we vary the spectral resolution of light and α^* from 1 to 61 wavebands and study the results in conjunction with the three different α^*estimation methods. The results show modeled estimates of ocean primary productivity are highly sensitive to the degree of spectral resolution and α^*. For accurate simulations of primary production and chlorophyll distribution we recommend a spectral resolution of at least six wavebands if α^* is a function of wavelength and chlorophyll, and three wavebands if α^* is a fixed value.     

A quasi-similarity between wind waves and solid surfaces in their roughness characteristics

A formulation for the aerodynamic roughness length of air flow over wind waves $$z_0 = \gamma {\text{ }}u_* /\sigma p$$ which was proposed by Toba (1979) and Toba and Koga (1986) from dimensional considerations with some data analysis, is shown to correspond with a formulation for irregular solid surfaces $$(z_0 /h) = a(h/l)^{1 + \beta } $$ which resulted from work by Woodinget al. (1973) and Kustas and Brutsaert (1986);u _* is the friction velocity,σ _p the spectral peak frequency of wind waves,h the mean height of the solid obstacles,l the mean distance between their crests, andα,Β, andγ are constants. This correspondence is reached by the existence of a statistical 3/2-power law and an effective dispersion relationship for wind waves. Because both approaches of parameterizingz ₀ were arrived at independently, they provide each other mutual reinforcement.     

Dissociation constants of protonated methionine species in seawater media

The dissociation constants (pK₁ and pK₂) for methionine have been measured in artificial seawater as a function of salinity (S = 5 to 35) and temperature (5 to 45 °C). The seawater pK₂ values were lower than the values in NaCl at the same ionic strength while the pK₁ values in seawater were lower only at S = 35. In an attempt to understand these differences, we have made measurements of the constants in Na–Mg–Cl solutions at 25 °C. The measured values have been used to determine the formation of Mg²⁺ complexes and Pitzer interaction parameters for Mg²⁺ with methionine. The seawater model with the interaction parameters accounts for the differences between the value of pK₁ and pK₂ between NaCl and seawater. This study demonstrates that it is important to consider all of the ionic interactions in natural waters when examining the dissociation of organic acids.