Wind-wave coupled downward-bursting boundary layer (DBBL) beneath the sea surface

By synthesizing data of the turbulent structure beneath wind waves in laboratory tanks, with some re-analyses, we propose the existence of a particular turbulent boundary layer which is directly coupled with wind waves, a downward-bursting boundary layer (DBBL) in water beneath wind waves. The data set indicates that the depth of this layer is from 3 to 7, or about 5 times the significant wave height of wind waves. The data observed in laboratory tanks agree with data of acoustic observations of bubble clouds under breaking wind waves in the sea made by Thorpe (1986, 1992). It is inferred that DBBL is formed in equilibrium with the local wind waves, as a common feature from initially generated wind waves, young laboratory wind waves to mature wind waves in the sea.     

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.     

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.     

Turbulent structure in water under laboratory wind waves

The structure of the turbulent boundary layer underneath laboratory wind waves was studied by using a combination of a high-sensitivity thermometer array with a two-component sonic flowmeter. The temperature fluctuations are used to detect movements of water parcels, with temperature as a passive quantity. The turbulence energy was dominant in the frequency range (0.01 0.1 Hz), which was much smaller than the wind-wave frequency (2 5 Hz), and in which the turbulence was anisotropic. There was a frequency range (0.2 2 Hz for velocity, 0.2 5 Hz for temperature fluctuation) where the turbulence was isotropic and had a –5/3 slope in the energy spectrum. These points are the same as those in previous works. However, by analyses of the time series by using a variable-interval time-averaging technique (VITA), it has been found that conspicuous events in this main turbulence energy band are the downward bursting from the vicinity of the water surface. Thus the structure of the water layer underneath the wind waves has characters which are similar to the familiar turbulent boundary layer over a rough solid wall, as already conceived. It has been found that, at the same time, the turbulence energy can be related to quantities of the wind waves (the root mean squared water level fluctuation and the wave peak frequency), for different wind and wave conditions. That is, the turbulence underneath the wind waves develops under a close coupling with the wind waves.     

Detailed observation of the wind-exerted surface flow by use of flow visualization methods

Detailed observations were performed of the wind-exerted surface flow, before and after the generation of wind waves. As flow visualization techniques, 6 classes of polystyrene beads of from 0.33 mm to 1.93 mm in diameter, with a specific gravity of 0.99, and also, hydrogen bubble lines, were used. Experiments were carried out at three ranges of the wind speed: 4.0, 6.2 and 8.6ms^–1 in the mean in the wind-wave tunnel section, and the observations were made at 2.85 m in fetch. In the case of 6.2 m s^–1, when the initial surface skin flow attains 0.22 cm in the scale thickness and 16 cm s^–1 in the surface velocity in about 3 second from the onset of the wind, regular waves of about 1.7 cm in wave length appear on the water surface. In one second after that, the downward thrust of the surface flow and the consequent forced convection commences, and the transition of the surface layer to a turbulent state occurs. Ordinary wind waves begin to develop from this state. In developed wind waves the viscous skin flow grows on the windward side of the crests, frequently producing macroscopic skin flows, and these skin flows converge to make a downward thrust at the lee side, and the viscous skin layer disappears there. The velocity of the downward flow has a maximum at the phase of about 30, and the value is of the order of 10 cm s^–1 at 4-mm depth after the orbital velocity of the sinusoidal wave is subtracted. As the process through which the wind stress acts on the water surface, it is considered that the following particular one may be real: the skin friction concentrated at the windward side of the crest produces skin flows, which thrust into the inner region to make the forced convection, carrying the acquired momentum. The viscous shearing stress just before the generation of the surface undurations was about 1/4 of the total shearing stress under the existence of wind waves. It is considered that the increase of the wind stress by wind waves is caused by this mechanism.     

Internal flow structure of short wind waves

The internal flow structure of wind waves in a wind-wave tunnel was investigated on the bases of the measured vorticity distributions, streamline patterns, internal pressure fields, and stress distributions at the water surface for some waves in the field. In part I the experimental method and the internal vorticity structure relative to the individual wave crests are described. The measured vorticity distributions of distinct waves (waves with waveheight comparable with or larger than that of significant wavesH _1/3) in the field indicate that the surface vorticity layer is extraordinarily thickened near the crest, and the vorticity near the water surface shows a particularly large value below the crest. The flow near the crest of distinct waves is found to be in excess of the phase speed in a very thin surface layer, and the tangential stress distribution has a dominant peak near the crest. It is argued that the occurrence of the region of high vorticity in distinct waves is associated with the local generation of vorticity near the crest by tangential stress which attains a peak, under the presence of excess flow.     

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.     

Occurrence of coprostanol, 24-ethylcoprostanol and 5α-stanols in the marine sediments

The present study deals with the elucidation of sterol composition of the marine sediments in Kagoshima Bay. The identification of each sterol was performed by gas-liquid chromatography, Ag⁺ impregnated column chromatography, mass spectrometry, and nuclear magnetic resonance spectrometry. The sediment obtained near the estuary of River Koutsuki contained large portions of 5-stanols such as coprostanol and 24-ethylcoprostanol basides 5-stanols such as cholestanol, 24-methylcholestanol, and 24-ethylcholestanol in the sterol fraction. These 5-stanols in the marine sediment may be derived from the fecal contamination by domestic sewages.     

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.     

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).     

Response of a two-layer ocean with a baroclinic current to a moving storm,part I

A storm moves with a constant speed parallel to a stationary geostrophic current which flows only in the upper layer of a two-layer, infinite ocean. It is assumed that the lower layer is motionless. The quasi-geostrophic approximation is valid for a moving speed less than 4 ms^–1 for a storm radius of 100 km. The primary change of the upper layer thickness is caused by the wind stress divergence and the time integral of the wind stress curl. A cyclonic storm generates upwelling in its wake. The effect of the stationary flow similar to a western boundary current is minor by an order of magnitude and noticeable only on the left edge of the flow. Scaling of equations of motion and continuity for a more general upper geostrophic flow leads to expansion with a parametera ²=gH _m(fL)^–2, whereg is reduced gravity,H _m is the maximum thickness of the upper layer,f is Coriolis' parameter andL is the storm radius. The zeroth order perturbations of transport and thickness do not include the stationary flow which appears only in the first order perturbations ina ². When there is a coast, the change of the interface near the coast is dependent on the time integral of the wind stress component parallel to the coast, thus leading to upwelling or downwelling according to the center being to the left or right of the coastline.     

A note on a critical wind speed for air–sea boundary processes

Wind and wind-generated waves were measured in a wind-wave tank. A clear transition was found in the relation between the wind speed U ₁₀ and the wind friction velocity u _* near u _* = 0.2 m/s, where U ₁₀ is the wind speed at 10 m height extrapolated from the measured wind profile in a logarithmic layer, and u _* = 0.2 m/s corresponds roughly to U ₁₀ = 8 m/s in the present measurement. Quite a similar transition was found in the relation between the spectral density of high frequency wind waves and u _*. These results suggest the existence of the critical wind speed for air–sea boundary processes, which was proposed by Munk (J Marine Res 6:203–218, 1947) more than half a century ago. His original idea of the critical wind speed was based on the discontinuities in such phenomena as white caps, wind stress, and evaporation, which commonly appear at a wind speed near 7 m/s. On the basis of the results of our present study and those of earlier studies, we discuss the phenomena which are relevant to the critical wind speed for the air–sea boundary processes. The conclusion is that the critical wind speed exists and it is attributed to the start of wave breaking rather than the Kelvin–Helmholtz instability, but the air–sea boundary processes are not discontinuous at a particular wind speed; because of the stochastic nature of breaking waves, the changes occur over a range of wind speeds. Detailed discussions are presented on the dynamical processes associated with the critical wind speed such as wind-induced change of sea surface roughness and high frequency wave spectrum. Future studies are required, however, to clarify the dynamical processes quantitatively. In particular, there is a need to further examine the gradual change of breaking patterns of wind waves with the increase of wind speed, and the associated change of the structure of the wind over wind waves, such as separation of the airflow at the crest of wind waves, the turbulent stress, and wave-induced stress. Studies on the dynamical structure of the high frequency wave spectrum are also needed.     

Two layer model of the steady ocean response to large-scale heating and cooling

Steady response of a linear, two-layer baroclinic ocean to a steady thermal forcing was investigated on a mid-latitude -plane. Surface heat flux and its relaxation processes were parametrized as a form of heating function and Newtonian cooling term of cross interfacial velocityw in the continuity equation. Ageostrophic linear drag terms were employed to represent the western boundary layer for accomplishment of the steady circulation in the closed domain. In the interior, the dynamics belongs to thef-plane regime. The flow in the upper layer is zonal and eastward, which is the same as that expected in the channel without meridional boundary. The eastern boundary region is the so called Sverdrup region, in which the vortex stretching balances the term, thoughw contains a damping term. It directs the zonal flow southward (northward) in the south (north) followed by upwelling (downwelling) and forms the two gyres. Western boundary region is of the Stommel type except the upwelling (downwelling) in the south (north). The meridional circulation is similar to the Hadley Cell except southern and northern boundary layers. However, its strength is much greater than the latters.     

Branching of the Tsushima Current in the Japan Sea

Three branches of the Tsushima Current are reproduced in a numerical model, and their formation mechanisms are studied. Two types of a two-layer, inflow-outflow model with a bottom slope along the Japanese coast are used. One has a bottom slope only in the lower layer (Model A), and the other has bottom slopes in both layers (Model B). Model B represents the typical situation in the Japan Sea, i.e., the main pycnocline intersects the bottom slope. The onshore side of the line where the pycnocline intersects the bottom slope has only one layer in Model B. Seasonal variation of inflow in the upper layer of the western half in the entrance section (the Tsushima Strait) is incorporated into the model.Three branches are formed in Model B and not in Model A. The first branch is the bottom-controlled steady current due to the topographic-effect on the upper-layer slope which exists in the one-layer region along the Japanese coast. The second branch is a temporal current which is formed along the offshore edge of the coastal one-layer region in association with the variation of inflow. The third branch is the steady western boundary current due to the planetary-effect. These results compare favorably with observations in Part I of this study.The mechanism of formation of the second branch is examined in detail. This branch is caused by the propagation of the lowest two modes of the upper shelf wave caused by the topographic-effect on the upper-layer slope which are generated by the significant increase in inflow from June to August.     

Study on the chemical forms of radionuclides in seawater-III complexes of60Co with amino acids

Stability constants were determined for⁶⁰Co (II)-amino acid complexes in sodium perchlorate media at an ionic strength=0.67, using cation exchange resins. Stability constants were, for Co(II)-phenylalanine, log ₁=4.4, log ₂=8.2, log ₃=11.7, for Co(II)-histidine, log ₁=7.4. for Co(II)-valine, log ₁=4.3, log ₂=8.5, for Co(II)-proline, log ₁=4.1, and for Co(II)-tyrosine, log ₁=7.2, respectively. The abundance of Co(II)-amino acid complexes in seawater was calculated from these stability constants on the basis of chemical equilibrium, assuming the concentration of individual amino acid to be 10^–7 to 10^–8 mol l^–1. It was inferred that the Co(II)-amino acid complexes are probably not formed abundantly in seawater while inorganic species of⁶⁰Co(II) may still be dominant for a short period of time after discharge into seawater as liquid waste.     

Deep convection in a lake triggered by wind: Two-dimensional numerical experiments with a nonhydrostatic model

We have investigated the fundamental processes of deep convection in a lake at high latitudes triggered by wind during spring or autumn and the associated deep water formation, executing vertically two-dimensional numerical experiments with a nonhydrostatic model. The water column in which a relatively cold mixed layer overlies a relatively warm layer becomes unstable, when the Ekman convergence on the shore due to along-shore wind deepens the mixed layer below the compensation depth, where water densities in both layers becomes equal to each other because of the thermobaric effect. At the onset of deep convection, the critical Rayleigh number agrees with that predicted by the linear theory. The onset time of deep convection is inversely proportional to the magnitude of wind stress. On the other hand, the onset time is minimal when water temperature in the mixed layer _m is 3.1°C because a change of _m has two effects oppositely acting on the stability of the water column. After the first onset, deep convection occurs intermittently for a few days. The sinking of the mixed layer water occurs in a thermal-like shape, and its amount is 4184% of the time-integrated Ekman transport when _m 3°C while it decreases to less than 10% for _m lower than 1.5°C. The present process can explain 30% of the amount of deep water renewal which is expected from the observation in Lake Baikal.     

The evolution of isolated vortices interacted with steep slope

Numerical solutions are examined for isolated, intense vortices as influenced by western bounding bottom topography through the use of a rigid-lid, two-layer primitive -plane numerical model. Systematic studies are made of the sense of rotation (cyclonic/anticyclonic), the consequence of varying the gradient of bottom slope, and the different vertical shear in a two layer ocean. In the basin with a bottom slope, the nearly barotropic anticyclonic vortex forms a modon-like vortex for S with fixedRo ₂<O(1) (where is the ratio between the variation of the Coriolis parameter across the eddy to the Coriolis parameter in the center, S the topographic effect and,Ro ₂ the Rossby number in the lower layer) and its generation is due to a compound effect of the planetary beta, topographic beta, avvection, and mirror image. The formation of the modon-like vortex and the propagation of the original vortex onto the bottom slope depends on the strength of slope gradient and the baroclinicity of the vortex. The nearly barotropic anticyclonic vortex evolves into the stronger upper ocean one with increasing S: the gradient of the bottom slope becomes steeper. Then the original vortex lives longer because the barotropic component of the energy is converted to the baroclinic one and it moves toward southeast in forming a modon-like vortex in the lower layer. The evolution of a vortex in the model results are compared to observational results of a Kuroshio warm core ring (KWCR) obtained from hydrographic data (June, 1985) and from NOAA satellite infrared images (April, 1985 to July, 1985). It is shown that a KWCR (June, 1985) is influenced by the western continental slope/shelf of the East Japan.     

Intrusive Stratification of the Gulf-Stream Frontal Zone According to the Results of Investigations Performed during Cruise 43 of the R/V Akademik Vernadskii

We analyze the data of investigation of the intrusive structure of the Gulf-Stream frontal zone obtained in making frequent drift sections with the help of an MGI-8102 probing complex, study the regularities of variation of temperature, salinity, and density along separate intrusions, and present a series of results connected with the specific features of initiation and development of intrusions and the types of exchange processes determining their transformations. It is shown that the T-diagrams of all intrusions are well separated into segments with different slopes. Moreover, by comparing the slopes and locations of these segments with each other and with the T-diagrams of the Gulf Stream and slope waters, we can fairly reliably attribute the corresponding segments of intrusions to one of the following four types: initial dynamic folds of the frontal zone, layers of domestic water separating the intrusive segments of foreign water from each other, intrusive segments characterized by the penetration of ambient water, and segments not intrusive initially but getting the required slope as a result of interaction with upper and lower intrusive segments. For segments of the last two types, it is possible to specify the predominant type of exchange.     

Numerical experiment on the circulation in the Japan Sea

By using a two-dimensional barotropic model on a-plane, the effect of the bottom topography on the path of the Tsushima Current is investigated. The rectangular model ocean with continental slopes has two openings: one is located at the southern boundary and the other at the eastern boundary. In a steady state, most of the water supplied into the model ocean through the inflow opening, flows along the continental slope with the coast to the right. Continental shelf waves play an important role in the process of adjustment to a steady state. It is suggested that the nearshore branch of the Tsushima Current might be largely topographically controlled.     

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.