Inertial oscillations over the background of shear currents in the ocean

Inertial oscillations observed in the seas and oceans are frequently characterized by various hodographs of current velocities different from circular anticyclonic motion as follows from the simplest model. It is supposed in [1] on the basis of the data analysis of measurements carried out on the shelf near Gelendzhik in the autumn of 2009 that the observed distortions of hodographs of inertial currents are the consequences of superposition of inertial oscillations and background shear current. In this work we construct a simple model of inertial oscillations over the background of a shear current based on the exact solution of shallowwater equations, which generally confirms the hypothesis suggested in [1].     

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.     

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.     

台风Wayne过后南海北部陆架海域的近惯性振荡

1986年8月18日8616号台风维纳(Wayne)在南海中部生成,其后在南海北部迂回盘旋,前后3次穿越巴士海峡,9月4日在海南岛登陆。布放在海南岛东部陆架上的锚系浮标记录了台风中心过境前后风和近表层的海流响应。分析结果表明,台风中心过境造成海水强烈的近惯性运动,其影响大约持续了6—8d,近惯性振荡的频率为0.029 2周.h-1(周期约34.2h),高出当地的惯性振荡频率(0.028cph)4.3%。带通滤波所提取的惯性运动特征显示,台风过境后惯性振荡逐渐衰减,惯性圆逐渐向西南方向偏移。根据这一个例,探讨了台风条件下近表层流速与风速的关系以及台风尾迹中近惯性流流速衰减过程的经验描述,可为近海海洋工程设计提供参考。     

Structure and variability of current and water temperature fields near the Mascarene Ridge

An anticyclonic mesoscale eddy is found using the current and temperature data obtained at six moorings near the eastern foot of the Mascarene Ridge (Southern Hemisphere). Its spatial parameters radius, depth of penetration, and direction of the vertical axis tilt are given. The volume of water transported by the eddy across its radial section is calculated. Numerical characteristics of the spatial-temporal variability of the current and temperature field in the eddy are obtained. The relative contributions of the variability of mesoscale, tidal and inertial, and high-frequency oscillations are estimated.Translated by Mikhail M. Trufanov.     

上层海洋对热带气旋的响应与反馈研究进展

对60年来有关上层海洋与热带气旋(Tropical Cyclone,TC)的响应与反馈的研究进行了回顾,通过观测手段的完善和改进模式的应用,人们的认识不断提高:TC直接激发的近惯性流最大可达1 m/s,其导致的强烈的剪切造成混合层对下层冷水的夹卷是引起混合层降温的主要原因,并往往伴随着混合层深度的增加,这一影响在TC右侧更为最著,并可延续几天到几十天不等。TC导致的混合层降温会使得海洋输出的热通量减少,反过来削弱TC的强度,形成一个负反馈,而海洋特殊的热力和环流结构(如暖涡、洋流等)则对TC有正反馈。所以了解TC经过前的海洋初始场对研究TC与海洋之间的相互作用、对预测,TC的强度、路径变化等尤其重要;通过准确的初始场结合越来越完善的模式可以对TC进行更真实的模拟和预测,使得对TC准确的预报和预警成为可能。     

Experimental study of the instabilities of alongshore currents on plane beaches

A laboratory experiment on alongshore currents was conducted for two plane beaches, with gradients 1:40 and 1:100, to investigate the instability of alongshore currents. Complicated and strongly unstable alongshore current motions were observed. In order to clearly examine the spatial and temporal variations of the shear instability of the currents, digital images from a charge-coupled device (CCD) recorded the deformations of dye batches released in the surf zone. Some essential characteristics of the shear instability were obtained from analyses of images showing the temporal variation of the dye patches.A high-resolution spectral analysis technique (the maximum entropy method, or MEM) was used to analyze the dominant frequency of the observed oscillation, along with the trigonometric regression method for determining the variations of the oscillation strength in the cross-shore direction. The propagation speed of the dye patch was obtained by tracking the movement over time of fixed locations in the dye patch, such as its peak, in the longshore direction. This data was then fitted linearly.Alongshore and cross-shore velocity time series acquired from sensors showed clearly that large-amplitude, long-period (about 50 s or 100 s) oscillations were present for all sensors deployed in the cross-shore direction under regular and irregular wave conditions. The analysis found that the maximum shear wave amplitude was approximately one-sixth of the maximum for the mean alongshore current, and occurred approximately at the position of the maximum of the mean alongshore current for irregular waves. The spatial structure of the shear waves was studied by analyzing collected images of the dye patches. The phase velocity of the meandering movements was obtained by measuring the magnitude of the oscillations of the dye patches in the alongshore direction with respect to time. The results suggest that the propagation speed of the shear instability was approximately one-half to three-quarters of the maximum mean longshore current for both regular and irregular waves.Linear instability analysis theory was applied to the characteristics of alongshore current instability, which suggested that there are two instability modes related to the observed oscillations: the frontshear mode observed for the 1:100 slope, and the backshear mode observed for the 1:40 slope. Theoretical analyses agreed with the experimental results in both cases. The velocity profile of the mean longshore current was found to affect the instability mode significantly, leading to further investigations on the influence of the velocity profiles and to provide support for the above conclusions.     

Propagation and trapping of inertial gravity waves in shear flows (ray theory)

The process of propagation and trapping of inertial gravity wave (IGW) packets in oceanic shear flows is studied in the geometric-optics approximation (ray theory). It is shown that wave trapping in strong stable stratification occurs in the region of anticyclonic (horizontal) velocity shear in a narrow frequency range on the left side of the inertial frequency. Beyond this range, the packet (ray) is either reflected from a cyclonic shear layer or propagates freely through the shear layer. The basic equations of ray theory are analyzed qualitatively, and analytical expressions are derived for freely propagating and trapped rays. The influence that vertical shear exerts on the ray behavior is also investigated. It is shown that two-dimensional ray focusing occurs as the velocity profile decreases with depth, so that rays concentrate along a specific latitude.     

Inertial Oscillations and the Galilean Transformation

This paper presents a general solution of shallow-water equations on the f-plane. The solution describes the generation of inertial oscillations by wind-pulse forcing over the background of currents arbitrarily changing in time and space in a homogeneous fluid. It is shown that the existence of such a complete solution of shallow-water equations on the f-plane is related to their invariance with respect to the generalized Galilean transformations. Examples of velocity hodographs of inertial oscillations developing over the background of a narrow jet are presented which explain the diversity in their forms.     

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.     

Strong near-inertial oscillations in geostrophic shear in the northern South China Sea

With observational data from three Acoustic Doppler Current Profiler (ADCP) moorings, we detected strong near-inertial oscillations (NIO) in the continental shelf region of the northern South China Sea in July 2008. The amplitude of the near-inertial current velocity is much greater than that of diurnal and semi-diurnal tides. The power of the NIOs is strongest in the intermediate layer, relatively weak in the surface layer, and insignificant in the near-bottom layer. The spectral analysis indicates that the NIOs have a peak frequency of 0.0307 cph, which is 2% lower than the local inertial frequency, i.e., a red-shift. The near-inertial wave has an upward vertical phase velocity, which involves a downward group velocity and energy flux. The estimated vertical phase velocity is about 43 m day⁻¹, corresponding to a vertical wave length of about 58 m. The horizontal scale of the NIOs is at least hundreds of kilometers. This NIO event lasted for about 15 days after a typhoon’s passage. Given the northeastward background flow with significant horizontal shear, both Doppler shift and shear flow modulation mechanisms may be responsible for the red-shift of the observed NIOs. For the shear flow mechanism, the observed negative background vorticity and the corresponding effective Coriolis frequency reduce the lower limit of admissible frequency band for the NIOs, causing the red-shift. Meanwhile, the mooring area with the broadened frequency band acts as a wave-guide. The trapping and amplification effects lead to the relatively long sustaining period of the observed NIOs.     

旋转地球上不可压缩流体惯性重力波的频率方程

用微扰动方法对旋转地球上不可压缩流体的控制方程组进行线性化,得到了扰动解和流体界面上惯性重力波的频率方程。表面惯性重力波和惯性重力内波的相速公式都是这个更普遍的频率方程的特殊情况。     

Estimation of the transports through the Strait of Gibraltar

An acoustic doppler current profiler (ADCP) is used to measure the currents and estimate the transports over the Camarinal Sill at the Strait of Gibraltar. The deepest measurements of the ADCP compare well with an underlying conventional current meter. The exchange interface between the Atlantic and the Mediterranean water is defined as the depth of the maximum vertical shear. The mean depth of the shear interface is 147 m. The time series of the depth of the interface and the currents are used to estimate the transports across the Strait. The resulting values are 0.78 Sv for the Atlantic inflow and −0.67 Sv for the Mediterranean outflow. The time series of the shear interface include fortnightly oscillations of 19 m. The time series of the transports are compared with the pressure and sea level difference records across the Strait. Linear multiple regression is used to estimate the (statistical) contribution of each parameter on the variation of transports. The cross strait sea level difference is well correlated with the Atlantic inflow and accounts for 57% of the variability of the transport records which improves to 78% when the fortnightly and monthly cycles are included in the linear regression. The Mediterranean outflow is best correlated with the along strait sea level difference which accounts for only 10% of the variability of the transport record. Again the addition of the M_sf and the MM cycles improves the percentage of the variance accounted for to 37%. The local, along strait wind component is significantly correlated with, both the Atlantic inflow and the across strait sea level difference.     

Observation of the abyssal current in the West Mariana Basin

In order to investigate long-term variations of deep sea currents and temperature in the western North Pacific, a direct current measurement was made at 12.5°N, 137°E from July 1985 to July 1986. The current meter was moored at a depth of about 4,000 m (bottom depth 4,604 m) in the West Mariana Basin, very close to the deep water passage to the North Pacific Basin. Throughout the observed period, the current flows southward with an average speed of 0.8 cm sec^–1. There are significant variations of both currents and temperature within the period of 60 days. For the shorter time scales, in addition to the tidal oscillations with one day and half day periods, there is a notable spectral peak of the current with a clockwise rotation at a period of 2.2 days, which is slightly shorter than the local inertial period of 2.3 days.The observed southward current seems to indicate that the deep sea water in the West Mariana Basin flows out through the sill which is deeper than 4,000 m and is located about 200 km southeast of the mooring point. A simple analysis of the linear plane wave indicates that the medium time-scale variation with a period of 60 days is associated with the barotropic Rossby wave whose wavelength is 390 km and whose trough direction is 30° clockwise from the north.     

Drifter Observations of Anticyclonic Eddies near Bussol' Strait, the Kuril Islands

Hydrographic surveys and satellite imaging reveal that mesoscale anticyclonic (AC) eddies are common features of the area south of Bussol' Strait, the deepest of the Kuril straits connecting the western North Pacific and Sea of Okhotsk. To examine the velocity structure of these eddies, we deployed groups of 15-m drogued satellite-tracked surface drifters over the Kuril-Kamchatka Trench in the fall of 1990 and late summer of 1993. Drifters in both groups entered large AC eddies centered over the axis of the trench seaward of Bussol' Strait and subsequently underwent a slow northeastward translation. One drifter (Drifter 1315) deployed near the center of the “Bussol' eddy” in 1990, remained in the eddy for roughly 45 days and made five loops at successively greater distances from the eddy center. Large-amplitude (80–100 cm/s) storm-generated inertial oscillations were observed during the first two loops. The vorticity field associated with the eddy resulted in a Doppler “red-shift” of inertial frequency motions such that the “effective” inertial period of 21 hours was roughly 4 hours greater than the nominal inertial period for the drifter latitude (45°N). In 1993, a second drifter (Drifter 15371) was retained in the Bussol' eddy for about 40 days. This eddy had characteristics similar to those of the 1990 eddy but was devoid of significant high-frequency motions until the drifter's final half loop. The observed spatial scales, persistence, and slow poleward translation of the eddies suggests that they play an important role in the dynamics of the East Kamchatka and Oyashio current systems. This revised version was published online in August 2006 with corrections to the Cover Date.     

The effect of oscillations on the flow patterns near a simulated bed

This work investigates the effect of oscillations on the flow near a simulated bed and their impact on erosion. Those oscillations were generated by using wavy lids at the top of a small toroidal channel. Particular attention is dedicated to their influence on the velocity field and turbulence near the bed. The experiments were made in a mini circular flume using a 2D LDA system. It was concluded that such oscillations induce non negligible shear stresses in the flow main stream, becoming more important to the dispersion of entrained matter into the flow than to the initiation of the erosion process.     

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.     

Current spectra under varying stratification conditions in the central North Sea

Given strongly different vertical stratification and not significantly different kinetic energy, ‘internal wave’ band spectral properties were studied using two 8-day representative sets of observations from the central North Sea in winter and summer. The observed similar spectral shape of the internal wave band was due to a combination of deterministic narrow band and intermittent signals. In addition to dominant tidal harmonics, 25% of total kinetic energy was found at inertial and non-linear inertial-tidal interaction frequencies in summer and about the same amount was found in broad-band response to atmospheric forcing in winter. The energy at the (seasonal) non-linear interaction frequencies was proportional to stratification, specifically, to near-inertial shear magnitude. In summer, motions at frequencies (σ) between f<σ<2.5 cpd (cycles per day) appeared in low vertical mode, whilst the power P(σ) of motions at σ>4±1 cpd obeyed canonical internal wave scaling P(σ)∼Cσ⁻², provided the shear magnitude ∣S∣ was used instead of the buoyancy frequency N for the factor C. Motions at 2.5<σ<4±1 cpd appeared as transition between the two regimes. In winter no inertial motions were observed.     

Sub-surface temperature oscillations and associated flow in the western Bay of Bengal

Unusual temperature variations at subsurface depths were noticed while making continuous observations (for 13 h) on temperature, salinity and currents at a point in the vicinity of river Krishna in the western Bay of Bengal. Sharp temperature oscillations recorded at four different levels between 14 and 20·1 m had an average periodicity of about 1·6 h. Similar periodicities were also observed in the case of flow components. Computed Brunt-Vaisälä frequency, vertical shear and Richardson number showed remote possibilities of vertical mixing occurring in this area. These oscillations showed features of internal waves propagating with a speed of about 13·3 cm s⁻¹ and wavelengths between 0·8 and 1·3 km and apparently generated as a result of flood current passing over a submarine obstacle in the presence of stratification.     

Deep slope currents and suspended particle fluxes in and around the Foix submarine canyon (NW Mediterranean)

Deep slope currents and particulate matter concentrations were studied on the Barcelona continental margin in and around the Foix submarine canyon from May 1993 to April 1994. This year-long moored experiment revealed that near-bottom slope currents are strongly influenced by the bottom topography, being oriented along isobaths and along the canyon axis. The deep slope current fluctuations are controlled by the local inertial motion (18.3 h) and also by low-frequency oscillations at periods of 6–10 days, related to the passage of atmospheric pressure cells. Particulate matter concentrations recorded during the experiment do not show a clear seasonal variability, except outside the canyon, where significant peaks of particulate matter concentrations were recorded only during the winter-fall deployment. In addition, the temporal evolution of suspended particulate matter concentration is not linked to changes in the cross-slope or along-slope current components and did not show a clear relationship with river avenues or wave storm events. This suggests that suspended particulate matter exported from the shelf is dispersed on the slope by advective processes, which attenuate the signal of the shelf-slope sediment transfer. Mean particulate matter concentrations differed among sampling sites, but the magnitude of the mean horizontal suspended particle flux reflects a quite similar value in the whole study area, ranging from 2.53 to 4.05 mg m⁻² s⁻¹. These horizontal suspended particle fluxes are 27 (canyon head) to 360 (open slope) times higher than the settling particle fluxes measured at the same sampling sites, indicating that the suspended particulate transport on the Barcelona continental slope dominates over the settling particle fluxes, even inside the Foix submarine canyon.