The effect of tidal currents on internal waves

Internal waves were observed by measuring temperature variations of several subsurface layers at the innermost part of Suruga Bay from December 1968 to October 1971. Spectral energy densities of temperature fluctuations were computed from the records of the measurements. In the shorter period range from one minute to one hour, peaks of energy density were found occasionally in the range shorter than the minimum of VÄisÄlÄ periods computed from the vertical distribution of water density. It has been generally understood, however, that the periods of internal waves in a stable stratum should be within the range between the inertial and VÄisÄlÄ periods.The measurements of tidal currents in the surface and lower layers, which were undertaken simultaneously with the temperature measurements, revealed that the short-period oscillations were associated with the increase of current velocity and of vertical shear of current at the pycnocline.It is considered that observed periods shorter than the minimum of VÄisÄlÄ period are not real but apparent periods due to the Doppler effect, because the waves are generated in the velocity shear of tidal current and the source is moving towards the station with the tidal current.     

Some peculiarities of the Black Sea inertial currents

By treating observations involving long-term buoy moorings, numerical characteristics of the periods, amplitudes, phases and orbits of inertial currents in some Black Sea areas have been obtained. The inertial component's contribution to the total velocity field and turbulent exchange has been determined. As a result, the maximal heights of the internal waves generated by the inertial currents have been estimated. Translated by Vladimir A. Puchkin.     

Dynamics of the Crimea shelf waters in summer

In this paper, the main results of field research into the seawater dynamics on the shelf of the Crimea in the summer of 1991 are reported. It is shown that in the weather frequency band, the oscillations with periods of 11–12 days have the greatest amplitude. These represent coastal-trapped waves with a spatial scale of the order of the length of the Black Sea coastline. These waves are generated by distant winds and significantly disturb the response of the Crimea shelf waters to local wind forcing. A transient upwelling-downwelling circulation having a period of 5–7 days is induced by local winds and is not accompanied by the generation of trapped waves at the frequency of forcing. Since the average circulation on the shelf of the Crimea is of cyclonic character, downwelling events are found more frequently and have longer time periods than the upwelling events. The wind-generated trapped waves on the shelves of the Crimea and Kerch Peninsula have an average period of 27 h. The inertial oscillations were well expressed during an experiment resembling long-wave motions.Translated by Mikhail M. Trufanov.     

Is the small-scale turbulence an exclusive breaking product of oceanic internal waves

On the basis of the theoretical research results by the author and the literature published up to date, the analysis and the justification presented in this paper show that the breaking products of oceanic internal waves are not only turbulence, but also the fine-scale near-inertial internal waves (the oceanic reversible finestructure) for inertial waves and the internal solitary waves for internal tides respectively. It was found that the oceanic reversible finestructure may be induced by the effect of the horizontal component f (f = 2Ωcosφ) of the rotation vector on inertial waves. And a new instability of the theoretical shear and strain spectra due to the effect of f occurs at critical vertical wavenumber β c ≈ 0.1 cpm. It happens when the levels of shear and strain of the reversible finestructure are higher than those of inertial waves, which is induced by the effect of f along an "iso-potential-pycnal" of internal wave. If all breaking products of internal waves are taken into account, the average kinetic energy dissipation rate is an order of magnitude larger than the values of turbulence observed by microstructure measurements. The author’s theoretical research results are basically in agreement with those observed in IWEX, DRIFTER and PATCHEX experiments. An important impersonal fact is that on the mean temporal scale of thermohaline circulation these breaking products of internal waves exist simultaneously with turbulence. Because inertial waves are generated by winds at the surface, and internal tides are generated by strong tide-topography interactions, the analysis and justification in this paper support in principle the abyssal recipes Ⅱ:energetics of tidal and wind mixing by Munk & Wunsch in 1998, in despite of the results of microstructure measurements for the turbulent kinetic energy dissipation rate and the diapycnal turbulent eddy diffusivity.     

Statistical estimates of the parameters of non-linear long internal waves off the South Crimea in the Black Sea

Hydrological data covering the South Crimea test area are used to calculate the mean profile of the variable Brunt-Väisälä frequency and the coefficients of the Korteweg-de Vries equation for internal waves at each station. Charts showing internal wave velocity isolines, non-linearity and dispersion parameters, and sea depth have been constructed. The average Brunt-Väisälä frequency profile has been used to calculate the Urcel parameter for internal waves, and non-linear properties of the internal waves observed have been assessed.Translated by Mikhail M. Trufanov.     

On the possible generation of low-frequency microseisms by internal waves in the ocean

The conditions under which the interaction between internal waves and the rough bottom topography may be the reason for synchronous fluctuations of pressure at the bottom have been studied. Disturbances of the depth are assumed to be small compared with the mean depth of the ocean, and the Väisälä-Brunt frequency is constant. It is shown that synchronous fluctuations of pressure exist with a frequency equal to that of internal waves. The amplitude of pulsations can be approximately an order lower than the amplitude of fluctuations generated by standing surface waves. However, local maxima can exist in the low-frequency minimum of the spectrum of microseisms (in the range of 20–1000 s).Translated by Mikhail M. Trufanov.     

Resonance excitation of internal waves by fluctuations of the atmospheric pressure and the tangential wind stress

Resonance excitation of internal waves by running waves of the atmospheric pressure and the tangential wind stress in a continuously stratified rotating ocean is studied in a linear statement. A comparative analysis of the rates of the increase in amplitude of resonance-excited waves for these external disturbances is carried out numerically for the case of the average distribution of the Väisälä-Brunt frequency in the Caribbean Sea.Translated by Mikkail M. Trufanov.     

Generation of long internal waves in the ocean by a moving pressure zone

The generation of plane internal waves in a continuously stratified ocean by a steadily moving anomaly of the atmospheric pressure is studied in a linear statement using a quasi-static approximation. Quantitative estimates for the parameters of internal waves in the wake are obtained for the average distribution of the Väisälä-Brunt frequency in the Caribbean Sea.Translated by Mikhail M. Trufanov.     

Generation of internal waves by moving non-stationary disturbances in a real stratified ocean

The plane problem on the generation of linear internal waves by a moving area of time-harmonic surface pressures in a continuously-stratified ocean of constant depth is considered. An analytical relation has been derived for forced internal waves off the site of their generation in the form of an internal wave field superposition corresponding to individual vertical modes. The possible wave regimes are determined. For the Brunt-Väisälä frequency distribution in the North Atlantic, the generation conditions and amplitudes of diverse radiated waves are numerically determined.Translated by Vladimir A. Puchkin.     

Rotation of orbital currents in the trains of internal solitons in the ocean

We analyze the results of measurements of currents in the trains of internal solitons on the New-York shelf of the Atlantic Ocean performed in the course of the Joint US/Russia Internal Wave Remote Sensing Experiment (JUSREX). It was discovered that the thermocline is characterized by an almost monotonic anticyclonic variation of the direction of orbital currents in the trains of solitons but the direction of waves in each train is practically constant. As a rule, the current significantly deviates to the left from the direction of waves in the leading soliton and approaches the indicated direction in the rear solitons of the train. The angular rotation current velocity corresponded to periods varying within the range 12–24h and, on the average, was close to the local inertial period. It is shown that this rotation cannot be caused by the distorting influence of advection of background shear currents but, most likely, is connected with the unknown properties of internal solitons in the rotating ocean. Translated by Peter V. Malyshev and Dmitry V. Malyshev     

Trapped symmetric disturbances in rotating shear flows

The structure of trapped symmetric disturbances in rotating stratified shear flows is investigated theoretically. It is shown that the arrangement of the trapping region is determined by atmospheric stratification. For example, if the characteristic Brunt-Väisälä frequency is greater (smaller) than the inertial frequency, waves are trapped in the region of anticyclonic (cyclonic) velocity shear. Accordingly, in the first (second) case, the frequencies of trapped waves are smaller (greater) than the inertial frequency. The problem of finding the frequencies of trapped waves is reduced to solving the Schrödinger equation but with a more complex dependence on a spectral parameter. Exact solutions to the problem are obtained for a triangular jet and a hyperbolic shear layer.     

Generation of spatial internal waves in a rotating ocean by moving non-stationary disturbances

In a general linear statement, the kinematic structure of spatial internal waves generated by a uniformly moving area of oscillating surface pressures in a continuously stratified ocean of constant depth is studied. The earth's rotation effects are considered. Possible types of ocean wave fields with a constant Brunt-Väisälä frequency are examined. The wave regimes for individual modes of internal and gyroscopic waves are classified on the basis of estimating the integrals asymptotically.Translated by V. Puchkin.     

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.     

Statistical characteristics and the variability of currents over the western Black Sea shelf

Statistical characteristics and the parameters of the temporal variability of currents are analysed using data on current measurements conducted by five moored autonomous buoy stations over Bulgaria's shelf. Estimates of the specific contribution to the variability of synoptic (60%) and mesoscale (40%) oscillations are derived. The qualitative spectrum of the currents is defined, constituted by synoptic oscillations, short-period synoptic oscillations, inertial oscillations, and internal waves. Estimates of periods and oscillation amplitudes are also derived. The kinetic energy of the currents is calculated and the specific contribution of the energy of different-scale oscillations and their interrelations are determined.Translated by V. Puchkin.     

Trapped quasi-inertial waves in shear oceanic currents

We studied trapped long quasi-inertial waves in horizontally inhomogeneous flows with low Rossby numbers. A simple heuristic derivation of two equations for the wave amplitude is presented. These equations are true for strong and weak density stratifications. A spectral problem is formulated to find the frequencies of trapped waves based on the amplitude equations. Exact solutions of the hyperbolic problem for a free hyperbolic shear layer are found. It is shown that the location of the trapping area principally depends on the stratification. If the buoyancy frequency is greater than the inertial frequency, trapping occurs in the region of anticyclonic velocity shear; if the buoyancy frequency is smaller than the inertial frequency, trapping occurs in the region of cyclonic velocity shear. Thus, in the first case, the frequencies of the trapped waves are smaller than the inertial frequency, while, in the second case, they are greater. The intense wave activity observed in the regions of oceanic fronts and jet currents can be related to the existence of trapped waves.     

Statistics of Wind and Waves off Tsuyazaki, Fukuoka, in the Eastern Tsushima Strait

The variability of the sea surface wind and wind waves in the coastal area of the Eastern Tsushima Strait was investigated based on the hourly data from 1990 to 1997 obtained at a station 2 km off Tsuyazaki, Fukuoka. The annual mean wind speed was 4.84 m s⁻¹, with strong northwesterly monsoon in winter and weak southwesterly wind in summer. Significant wave heights and wave periods showed similar sinusoidal seasonal cycles around their annual means of 0.608 m and 4.77 s, respectively. The seasonal variability relative to the annual mean is maximum for wave heights, medium for wind speeds, and minimum for wave periods. Significant wave heights off Tsuyazaki turned out to be bounded by a criterion, which is proportional to the square of the significant wave period corresponding to a constant steepness, irrespective of the season or the wind speed. For terms shorter than a month, the significant wave height and the wave period were found to have the same spectral form as the inshore wind velocity: white for frequencies less than 0.2 day⁻¹ and proportional to the frequency to the −5/3 power for higher frequencies, where the latter corresponds to the inertial subrange of turbulence. The spectral levels of wave heights and wave periods in that inertial range were also correlated with those of the inshore wind velocity, though the scatter was large. This revised version was published online in August 2006 with corrections to the Cover Date.     

Water surface resonance in the L-shaped channel of seawater exchange breakwater

The resonance period of the L-shaped channel in the caisson is predicted analytically for the seawater exchange breakwater of “Applicability Study of the Seawater Exchange Breakwater (1). Korea Ministry of Maritime Affairs and Fisheries (in Korean) (1999a)”. Hydraulic experiments are conducted for a composite breakwater with a rear reservoir that is one of the seawater exchange breakwaters developed by them. For regular waves, the water surface elevation in the channel and the flow rate through the breakwater are measured. For irregular waves, the flow rate through the breakwater and the reflection coefficient on the breakwater are measured. The resonant maximum values in both the surface elevation and the flow rate, and the resonant minimum values in the reflection coefficient are all at wave periods slightly longer than analytically predicted ones. The measured resonance period for irregular waves is closer to the predicted one than for regular waves. If the resonance period of the L-shaped channel is fitted to the dominant period of incident waves, there would be high efficiency of seawater exchange between inside and outside the harbor.     

Dynamics of Rossby waves in an ocean with inhomogeneous currents

A model for a two-layer ocean is applied to consider, in terms of the geometrical optics approximation, the effect of mean flows propagating within the upper layer upon the dynamics of Rossby waves. The case is theoretically analysed, with the depth of the ocean's upper layer much smaller than that of the underlying layer. In this case, the flow's impact upon the baroclinic mode of Rossby waves is ubiquitous, with the exception of synchronicity. Depending on the parameters, four types of wave packets' behaviour in the vicinity of synchronicity points are singled out, namely, the elimination of the peculiarity, shadowing, and convective/absolute instability. For the mean flow profile simulating cyclonic and anticyclonic gyres, we have obtained wave packet trajectories and have studied the wave packet's interaction with the current. Specifically, it has been demonstrated that, given some modulus of the wave packet, vigorous energy exchange between the wave vector and the flow takes place. Translated by Vladimir A. Puchkin.     

南海西北部半日内潮参量次谐频不稳定生成的近惯性波研究

为了研究非临界纬度上参量次谐频不稳定(parametric subharmonic instability,PSI)过程生成的近惯性波(near-inertial wave,NIW),本文基于国家重点研发项目的 准实时传输深海潜标资料,对内波速度谱、近惯性流速和动能、D2-f(半日频减惯性频)流速和动能、半日内潮流速和...     

Inertial wave loads on horizontal cylinders: A field experiment

A long submerged horizontal circular cylinder of .90 m diameter was assembled off the beach at Reggio Calabria where the wind waves typically have significant height ranging within 0.20 and 0.40 m and dominant period within 1.8 and 2.6 s. Three ultrasonic probes recorded the waves, and two sets of pressure transducers, the first one at the cylinder and the second one in the undisturbed wave field, enabled to compare the force amplitude on the cylinder to the force amplitude on an equivalent mass of water in the undisturbed wave field (Froude-Krylov F-K force). After ten days of measurements, the experiment was repeated with a cylinder of .45 m diameter. The Keulegan-Carpenter number was within 2.5, and the wave forces proved to be inertial. The following general features emerged: (i) the force spectrum is usually very narrow even if the wave spectrum is broad; (ii) the vertical diffraction coefficient is somewhat smaller than the horizontal diffraction coefficient; (iii) the positive extremes of F_z (vertical force referred to the buoyancy force) markedly exceed the negative extremes; (iv) the pressure fluctuations induced by the highest waves at the cylinder are very similar to the measured pressure-surface displacement covariances. In each of the 580 records obtained in the course of the experiment it was found that the propagation speed reduces to about a half at the cylinder, and the amplitude of the pressure fluctuations increases of 10–15% at the upper half of the cylinder and decreases of about the same percentage at the lower half. These phenomena fully explain why the force amplitude on the cylinder is larger than the F-K force amplitude.