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.     

Phase velocity of semi-diurnal internal waves at Ocean Weather Station T

Phase velocity of semi-diurnal internal waves is determined from differences between phases at three stations which were situated to form a triangle in the vicinity of sta. T (29N, 135E). The wave phases are estimated from temporal variations in depths of isotherms obtained from serial measurements of vertical temperature profiles at these stations. The measurements were carried out in cooperative operation of two vessels, the R. V.Tansei-maru and theNojima, during the period from 30 July to 1 August 1965. Wave propagation with the speed of about 2 m/s in the direction from east to west is obtained as an average over several isotherms of temperature from 19C to 23C. The area of measurement is to the west of Izu-Mariana ridge and the distance from the ridge to the station is about 500 km, which would be about 5 times as large as the wave length of the internal waves under consideration, and so it is possible to suppose that the internal waves observed generated at the ridge and propagated to the area without being subjected to serious refraction, scattering, reflection and decay.     

A description of short period temperature fluctuations in the upper ocean

Dynamical properties of short-period temperature fluctuations are studied. Water temperature was measured continuously at several depths at the following stations: at 38°29.5′N, 141°35.8′E (100 m depth) on the continental shelf off Miyagi Prefecture in the summer of 1967, at 35°01.8′N, 139°0.8.5′E (100 m depth) in Sagami Bay in the summer of 1968, and at 32°32.2′N, 129°53.7′E (74 m depth) in Tachibana Bay in the summer of 1970. These measurements were made with a thermistor array laid down from the R. V.Tanseimaru (Ocean Research Institute, University of Tokyo) which was fixed with bow and stern anchors. Significant temperature fluctuations found at the first and the third stations are thought to be due to first mode internal waves having amplitude 3 to 5 m and period 5 to 20 minutes. The wave length of the waves is estimated to be 25 m to 400 m from the observed density structure. At the second station, we found second-mode internal waves. The period, amplitude and wave length of the waves are about 30 minutes, 1.3 m and 600 m, respectively. In all cases, the spectral density of the temperature fluctuations decreases with increase in frequency. However, the decrease obey neither the ?3 power law nor the ?5/3 power law. Coherences in the temperature fluctuations between two depths of measurement in the seasonal thermocline are significantly high in the range of frequencies lower than the local Brunt-Väisälä frequency, but are low in the higher frequency range. At the first and the third stations, the difference in the level of coherences between the lower frequencies and the higher frequencies are large. Phase differences between two depths in the thermocline are small in the lower frequency range. This suggests that the first-mode internal waves are predominant over higher-mode internal waves and over other disturbances.     

Coastal trapped waves in a two-layer ocean: Wave properties when the density interface intersects a sloping bottom

Properties of coastal trapped waves when the pycnocline intersects a sloping bottom are studied using a two-layer model which has slopes in both layers. In this system there is an infinite discrete sequence of modes, and four different sorts of waves exist: the barotropic Kelvin wave, the upper shelf wave, the lower shelf wave and the internal Kelvin-type wave. They all propagate with the coast to their right in the Northern Hemisphere. The upper and lower shelf waves are due to the topographic-effect on the upper-layer and lower-layer slopes, respectively. Their motions are dominant in the respective layers being accompanied by significant interface elevations. The properties of the upper (lower) shelf wave are almost unaffected by the existence of a lower-layer (upper-layer) slope. The motion of the internal Kelvin-type wave is confined to the region around the line where the density interface intersects the bottom slope.The modes, except that with the fastest phase speed (the barotropic Kelvin wave), are assigned mode numbers in order of descending frequency. Characteristics of Mode 1 change with wavenumber; the upper shelf wave for small wavenumbers and the internal Kelvin-type wave for large wavenumbers (high frequencies). The higher modes of Mode 2 and above can be classified into the upper and lower shelf waves.     

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.     

Very low frequency Ocean Bottom ambient seismic noise and coupling on the shallow continental shelf

Sources of very low frequency (0.01 to 1.0 Hz) ambient seismic noise in the shallow (<100 m) water continental margin sediments are investigated using Ocean Bottom Seismometers (OBS). The predominant seismic motions are found to be due to surface gravity (water) waves and water-sediment interface waves. Actual experimental measurements of seabed acceleration and hydrodynamic pressure are given, including side by side comparisons between buried and plate-mounted OBS units. OBS-sediment resonant effects are found to be negligible at the low frequencies under investigation. Wherever there exists relative motion between the seabed and the water, however, an exposed OBS is subject to added mass forces that cause it to move with the water rather than the sediments. Calculations based on measured seabed motions show that a neutral density, buried seismometer has superior sediment coupling charactersitics to any exposed OBS design.     

Wave particle velocities measured with a Doppler current meter

A newly developed three-dimensional Doppler current meter is described and the results of preliminary field experiments are presented where simultaneous measurements of surface elevation and water velocity associated with wave orbital motion were made. The phase difference between the surface elevation and the vertical velocity measured at 1.0 and 0.45 meters below the mean water level is found to be approximately 90, in accord with the theory for surface waves of infinitesimally small amplitudes. The spectral (frequency) density distribution for velocity is also found to agree with that we would expect from the linear theory for the observed frequency distribution of surface elevation. However, the amplitude of velocity is consistently smaller (about 10 %) than that we would expect. This reduction of amplitude is more pronounced in cases where waves are high and the water depth is shallow.     

Reflection and breaking of internal waves on a sloping beach

The reflection and breaking of internal waves on a sloping beach were studied in a small wavetank filled with water and petroleum. The dependence of the reflection coefficient of the internal waves on wave steepness and on beach slope is found to be very similar to that of surface waves. The reflection coefficient is small for the very gentle slope, increases rapidly as the slope increases, and becomes almost constant for the steep slope. The reflection coefficient decreases with increase of the wave steepness. Also, the transition slope at which the coefficient curve has the maximum gradient increases with increase of the wave steepness. Breaking pattern of the internal waves is classified into four types; breaking, semi-breaking, wrinkle-generating, and non-breaking. Their dependence on beach slope and wave steepness is examined. The regular sequence of the four breaking types from breaking to non-breaking is observed with decrease of wave steepness or with increase of beach slope.     

基于光学遥感MODIS的安达曼海内波时空分布与传播特性研究

This paper describes investigations of the internal waves in the Andaman Sea using Moderate Resolution Imaging Spectroradiometer(MODIS) imagery over the period of June 2010 to May 2016. Results of the spatial and temporal distribution, generation sources and propagation characteristics of internal waves are presented. The statistical analysis shows that internal waves can be observed in almost the entire area of the Andaman Sea. Most internal waves are observed in the northern, central and southern regions of the Andaman Sea. A significant number of internal waves between 7°N and 9°N in the East Indian Ocean are also observed. Internal waves can be observed year-round in the Andaman Sea, while most of internal waves are observed between February and April, with a maximum frequency of 15.03% in March. The seasonal distribution of the internal waves shows that the internal waves have mostly been observed in the dry season(February to April), and fewer internal waves are observed in the rainy season(May to October). The double peak distribution for the occurrence frequency of internal waves is found. With respect to the lunar influence, more internal waves are observed after the spring tide, which implies the spring tide may play an important role in internal wave generation in the Andaman Sea. Generation sources of internal waves are explored based on the propagation characteristics of internal waves. The results indicate that six sources are located between the Andaman Islands and the Nicobar Islands, and one is located in the northern Andaman Sea. Four regions with active internal wave phenomenon in the Andaman Sea were presented during the MODIS survey, and the propagation speed of internal waves calculated based on the semidiurnal generation period is smaller than the results acquired from pairs of the images with short time intervals.     

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.     

Mean Vertical Distribution of the Dissipation Rate of Turbulent Energy in the Black Sea. Comparison with the Existing Models

We compare the results obtained by using theoretical and semiempirical models developed for the evaluation of the dissipation rate of turbulent energy in a stratified ocean with independent distribution of this quantity established by the authors for the active layer of the Black Sea (50–300 m) by using a one-dimensional model taking into account the balance of heat, salt, and fluid inside the layer. It is shown that, in a layer with gradual variation of the Väisälä–Brunt frequency N as a function of depth, the predominant sink of the energy of motion into dissipation N ² is ensured by the flow of energy through the spectrum of internal waves toward low frequencies and small vertical scales. On the contrary, in layers with abrupt drops of density as a function of depth (layers with jumps of density), an important role is played by the interface-type waves and the dependence of on N transforms into N .     

A field study of the development of wind-waves

This paper presents the results of observation on the development of wind-waves which were generated in a lake water about 420 cm deep with a fetch 12 km long. Measurements of surface elevation were carried out at the end of an observational pier where the water depth was 80 cm. The wave momentum flux, i.e., the growth rate of the wave momentum, was estimated from both significant waves and power spectral densities for the wave records. The values obtained by the two ways accorded fairly well and they were 57 % as large as the wind stress measured simultaneously. The exponential growth rate of spectral densities for a frequency component was in good accord with that observed bySnyder andCox (1966) and by others. If these growth rates are applied to all the components of the spectrum, the wave momentum flux must exceed the wind stress. This cannot explain the experimental results nor can be physically accepted. The difference of spectral densities between the two successive runs showed that the increase of spectral densities was. limited in several bands of frequency. The phenomena are discussed in relation with the overshoot-undershoot effects studied byBarnett andSutherland (1968).Observational results suggest that the spectral growth of a certain component is closely related to the spectral densities of other components. Energy exchange among componented waves has not been considered in the theories for generation and development of wind-waves established by Phillips, Miles and others.New generation mechanism suggested byLonguet-Higgins (1969) was found to be able to describe the observed growth rates of the form(f)={(1/2)(t–t_1/2)}²: the spectral density(f) was proportional to the square of durationt. However, the mechanism can not explain the overshoot-undershoot effects peculiar to the equilibrium spectrum of windwaves.Three frequencies characterizing the discrete distributions of frequency bands where spectral densities increased were examined and three waves corresponding to these frequencies were found to be satisfying the resonance conditions for the wave-wave interactions among three sinusoidal wave trains as studied byPhillips (1960),Longuet-Higgins (1962) andBenny (1962). The interactions are suggested to predict well both the spectral growth proportional to squares of duration and the ceaseless oscillations of spectral densities in an equilibrium spectrum.     

Geostrophic adjustment near the coast

Geostrophic adjustment of a two-layer fluid near a straight coast is investigated for an initial pressure disturbance which has no closed geostrophic contours by using a reduced gravity (divergent barotropic) model. Propagation of a volume of water along the coast due to the internal Kelvin wave allows a non-zero solution for the final geostrophic state. Energy partitions among geostrophic motion, the internal Kelvin wave and internal Poincaré waves are obtained and compared with the result of the classical problem of geostrophic adjustment without the coast. It is found that energy partition to the geostrophic motion (EPG) with the coast is always smaller than that without the coast (EPG ), while the scale of the initial disturbance is the same. The difference betweenEPG andEPG is smaller than the energy partition to the internal Kelvin waves (EPK) and approachesEPK as the scale of the initial disturbance increases.     

Internal Tides in the Coastal Waters of NE Arabian Sea: Observations and Simulations

Time series of temperature and salinity collected from a station in the NE Arabian Sea during March, April, May, October, and November was utilized to explain the behavior of internal tides. Analysis revealed the existence of semi-diurnal internal tides and high frequency (HF) internal waves (IW). It was observed that the amplitudes of HF IWs were determined by the degree of stratification in the thermocline. Corresponding to an increase in the density gradient in thermocline (0.016 kg/m⁴ in April to 0.14 kg/m⁴ in October), the temperature fluctuations due to internal tides increased from <0.2°C to >1.5°C, respectively. Brunt-Vaiisala frequency also showed similar variations (～10 cph to 22 cph). Within the thermocline, semi-diurnal internal tides caused fluctuations of >10m in the isotherm depths. A linear regression equation was fitted to parameterize the amplitude of HF IWs and its upper frequency limit in terms of thermocline gradient. The IW and one-dimensional models simulated the presence of internal tides and diurnal cycling in the temperature field, respectively. Coupling of these models showed improvement in the simulation of temperature.     

Observations of cnoidal internal waves and their effect on acousticpropagation in shallow water

Distinctive packets of periodic internal waves were observed during an experiment in the Gulf of Mexico. There was a 65-m-deep mixed layer overlying a thin strong density interface. A layer of weaker density stratification extended below the interface to the bottom, at a depth of 185 m. The waves had 2-10-m amplitudes, narrow frequency bandwidths with central frequencies of 8.5 cph, and they propagated in the upslope direction. The wave packets were observed on three consecutive days. They lasted about 3 h and were always observed at the same time of day, clearly in response to tidal forcing. A model of the time/space structure of the waves was tuned to match that of the observations, showing that the data are consistent with a cnoidal wave hypothesis. Observations of low-frequency acoustic propagation along two baselines show fluctuations that we hypothesize are due to interactions with the cnoidal waves. The fluctuations have spatial correlation scales (in the slantwise direction) on the order of 76 m. We simulate these effects using a time-step PE approach. We find that a mode-coupling resonance with the internal wave field results in elevated acoustic variability along a set of discrete spokes, emanating from the acoustic source. While acoustic variability tends to increase with range and with internal wave amplitude, tangential and radial correlation scales do not show a systematic dependence. The patterns in tangential and radial correlation scales show strong anisotropic patterns in azimuth, but little systematic trend in range     

Transformation of a Baroclinic Tide in the Process of Motion over an Unevenness of the Sea Bottom

Within the framework of the linear theory of long waves, we study the process of incidence of a baroclinic tide on an unevenness of the sea bottom simulating an oceanic ridge. The liquid is assumed to be stratified and the action of the Coriolis force is taken into account. We determine the characteristics of wave disturbances in the region of the ridge induced by the incident baroclinic waves depending on the parameters of the bottom topography and tidal period. Thus, in particular, over the ridge, we reveal the existence of both the regions, where the amplitudes of internal waves are much higher than the amplitude of the incident baroclinic tide, and shaded regions, where the opposite phenomenon is observed.__________Translated from Morskoi Gidrofizicheskii Zhurnal, No. 6, pp. 3–9, November–December, 2004.     

Large amplitude, leaky, island-generated, internal waves around Palau, Micronesia

Three years of temperature data along two transects extending to 90 m depth, at Palau, Micronesia, show twice-a-day thermocline vertical displacements of commonly 50–100 m, and on one occasion 270 m. The internal wave occurred at a number of frequencies. There were a number of spectral peaks at diurnal and semi-diurnal frequencies, as well as intermediate and sub-inertial frequencies, less so at the inertial frequency. At Palau the waves generally did not travel around the island because there was no coherence between internal waves on either side of the island. The internal waves at a site 30 km offshore were out-of-phase with those on the island slopes, suggesting that the waves were generated on the island slope and then radiated away. Palau Island was thus a source of internal wave energy for the surrounding ocean. A numerical model suggests that the tidal and low-frequency currents flowing around the island form internal waves with maximum wave amplitude on the island slope and that these waves radiate away from the island. The model also suggests that the headland at the southern tip of Palau prevents the internal waves to rotate around the island. The large temperature fluctuations (commonly daily fluctuations ≈10 °C, peaking at 20 °C) appear responsible for generating a thermal stress responsible for a biologically depauperate biological community on the island slopes at depths between 60 and 120 m depth.     

Observations of internal tides in Uchiura Bay

Remarkable tidal currents associated with temperature fluctuations in the subsurface layer have been observed in Uchiura Bay. In order to study the characteristics of these tidal currents, we carried out current measurements in November 1972 and October 1974. It was confirmed from the first set of observations in 1972 that the tidal currents above and below the seasonal thermocline oscillate out of phase with each other and the tidal currents are associated with internal tides.In the second set of observations in 1974 not only current measurements but also serial BT lowerings were made. The phase of the thermocline displacements lagged behind the tidal currents by 81 for the semidiurnal constituent and by 83 for the diurnal constituent, and it is thus concluded that the internal tides in Uchiura Bay behave as standing waves.     

相同尺度地形与背景流共振生成内孤立波机制

为研究内孤立波的地形和背景流共振机制,用地形和背景流共振机制计算了3个潜标观测的内孤立波(不同模态、不同波长)的流速和传播速度,并与观测到的内孤立波进行比较。潜标观测的第一模态内孤立波(波长分别为6.4和3.3km)都是下凹型内孤立波,2个内孤立波的传播速度约为1.4m/s、最大振幅约为48m,水平流向结构都是上层西北向、下层东南向,波长3.3km 的内孤立波波峰前后有更明显的下降流和上升流。用共振机制计算出的第一模态和第二模态纬向流速的垂向结构与观测相同,最大纬向流速出现的深度与观测一致,分别相差5和12m。用共振机制计算出的内孤立波传播速度与用 KdV 方程计算的传播速度相当,共振机制计算波速为0.66~1.21m/s,KdV 方程计算波速为0.79~1.40m/s。     

Large-scale ripple marks on the shelf margin of the Northern Okinawa Trough

Trains of large-scale ripple marks (megaripples and sand waves) were found on the Amakusa and East China Sea shelves bordering the northern Okinawa Trough. Side-scan sonar surveys were carried out in 1974 and 1976 to investigate sea-floor features lying along a proposed submarine cable line. Megaripples were found on the outer margin of the Amakusa shelf between depths of 140 and 200 m. The megaripples were especially well developed at a depth of 167 m. They were typically straight-transverse crested with asymmetrical profiles, and measured 7 to 15 m in wavelength and 0.4 to 1.4 m in waveheight. Formation of the megaripples on the Amakusa shelf is probably controlled by relatively complex oceanographic conditions. A secondary circulation associated with the Gotô-nada clock-wise Current may be responsible for formation of the ripple marks. Local vorticities generated in the coastal boundary layer as a result of curvature of the Gotô-nada Current are known to cause the complex flow pattern at the Gotô and Amakusa shelf margins. The main semidiurnal (M₂) tidal current may also interact with these fluid processes.On the East China Sea shelf, megaripples and sand waves were found between depths of 140 and 220 m. Sand waves (200 m in wavelength) were observed in seismic reflection profiles. Large-scale lunate megaripples were observed at a depth of 154 m by the side-scan sonar. They had wavelengths of 10 to 30 m and waveheights of 1 to as high as 3 m. It appears from the types and nature of distribution of the megaripples that they are responding to the present-day flow regime, and it is partly ascertained from our observations over an interval of two years that the megaripples appear to be short-term response elements compared wit hteh sand waves. We conclude that the megaripples on the East China Sea shelf are current-formed during peak typhoon flow in August to November. From their distribution, the long term path of the main flow of the Tsushima Current is inferred at the edge of the East China Sea shelf. An area of low sediment mud content (less than 20 per cent) coincides with this path giving further support to our interpretation.