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.     

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.     

On the theory of internal waves under ice cover

A theoretical model is contrived that describes the propagation of internal waves under ice cover. According to the results obtained in the study, the flexures of the ice surface with a frequency close to but smaller than the Brunt-Väisälä frequency can gain amplitudes sufficient for recording internal waves. A comparison of the theory with observations showed a satisfactory agreement.     

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.     

海浪双峰方向分布的一种物理解释

用 １８个波高计组成的直径为 ４０ｃｍ的圆形阵列在大型风浪槽内系统地测量了风浪和涌浪方向谱。用两种分辨力较高的方向谱估计方法最大似然法（ＭＬＭ）和贝叶斯方法（ＢＤＭ）分析的结果表明：风浪高频域出现的依赖于估计方法的双峰方向分布是一种物理假象;在较成长的涌浪低频域,得到跟传播方向对称、两峰间隔大约６０°－９０°非常规则的双峰方向分布,它跟频率和涌浪的成长状态有关,而跟估计方法无关,这种现象可以用非线性波－波相互作用过弱,在不同方向之间不能有效传递能量来解释。     

Transmission and reflection of the Rossby waves in a stratified ocean with bottom topography

Transmission and reflection coefficients are calculated for Rossby waves incident on a bottom topography with constant slope in a continuously stratified ocean. The characteristics of the coefficients are interpreted in terms of the quasigeostrophic waves on the slope. In the parameter range where only the barotropic Rossby waves can propagate in the region outside the slope, the bottom trapped wave plays the same role as the topographic Rossby wave in a homogeneous ocean, and hence the transmission is weak unless phase matching takes place. When both of the barotropic and baroclinic Rossby waves can propagate outside the slope, the total transmission can be strong. The bottom trapped wave affects the transmission and reflection, and it leads to the possibility that the Rossby wave is transmitted as a mode different from the incident mode. When the number of the wavy modes on the slope is smaller than that of the Rossby wave modes outside the slope, strong reflection occurs.The results for an ocean with linear distribution of the squared Brunt-Väisälä frequency are compared to those in a uniformly stratified ocean. The weakening of the stratification near the bottom is almost equivalent to reducing the effect of the slope.     

双曲余弦海脊上海啸俘获波的解析与数值研究

海啸能被大洋海脊引导以俘获波的形式沿其传播上万千米,且因其特殊的运动方式,携带巨大能量影响远场地区的港口,严重威胁海岸安全。本文首先基于线性浅水方程,推导了双曲余弦平方海脊上俘获波的波面解,其为μ阶ν次的连带勒让德函数的第一类解和第二类解的组合。进一步推导出其对应的频散关系,其中对于确定的频率ω,存在无穷多个波数k_y与之对应。采用MIKE21-BW模型,模拟了产生于海脊脊顶处的海啸在理想双曲余弦平方海脊上的传播变形过程。结果表明,小部分能量以自由先驱波进行传播,海啸波的波能大部分被海脊俘获。海脊俘获波沿着海脊方向为行进波,随着海啸波传播时间的增加,波浪在沿着海脊方向的延展范围也逐渐增大,波高逐渐减小、波的个数逐渐增加。俘获波能量主要由不同频率以相同速度传播的具有孤立波特性的波浪成分和能量主要集中在特定频率范围内的波浪成分组成。     

Study on the negative bias temperature instability effect under dynamic stress

This paper studies negative bias temperature instability (NBTI) under alternant and alternating current (AC) stress. Under alternant stress, the degradation smaller than that of single negative stress is obtained. The smaller degradation is resulted from the recovery of positive stress. There are two reasons for the recovery. One is the passivation of H dangling bonds, and another is the detrapping of charges trapped in the oxide. Under different frequencies of AC stress, the parameters all show regular degradation, and also smaller than that of the direct current stress. The higher the frequency is, the smaller the degradation becomes. As the negative stress time is too small under higher frequency, the deeper defects are hard to be filled in. Therefore, the detrapping of oxide charges is easy to occur under positive bias and the degradation is smaller with higher frequency.     

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.     

Topographically trapped waves over the continental shelf and slope

General characteristics of topographically trapped subinertia waves are discussed from the viewpoint of an eigenvalue problem and ray theory. Special attention is paid to the slope parameterS(x) (=(dh/dx)/h, wherex denotes the coordinate perpendicular to the shoreline, increasing seaward, andh(x) is the depth) which is a measure of the strength of the restoring force of the waves. Three cases for theS distribution are considered, in whichS is assumed to be positive at the coast and to tend to zero far from the coast. The first is whereS(x) decreases monotonically towards the open ocean. It is found in this case that waves are trapped near the coast. The second is whereS(x) does not decrease monotonically, but has a maximum. It is concluded that this case may contain two types of waves, i.e., those trapped near the coast and those trapped near the maximum, and the dispersion curves corresponding to different types may nearly intersect, namely, result in “kissing”. The third is whereS(x) has a negative region (corresponding to the presence of a trench). It is found in this case that an infinite sequence of waves is trapped in the negativeS region which propagate with the coast to their left (right) in the northern (southern) hemisphere besides the waves trapped near the coast. The topography in the second case corresponds to a typical continental shelf and a typical continental slope. It is shown by model calculation that trapped waves are present over the continental slope as well as over the continental shelf. Almost the same results are obtained for superinertia waves ifS is replaced by 1/h which is a measure of the restoring force of superinertia waves.     

Effects of rotation on self-resonant internal gravity waves in the ocean

The Resonant Triad Model (RTM) developed in (Ibragimov, 2007), is used to study the Thorpe’s problem (Thorpe, 1997) on the existence of self-resonant internal waves, i.e., the waves for which a resonant interaction occurs at second order between the incident and reflected internal waves off slopes. The RTM represents the extension of the McComas and Bretherton’s three wave hydrostatic model (McComas and Bretherton, 1977) which ignores the effects of the earth’s rotation to the case of the non-hydrostatic analytical model involving arbitrarily large number of rotating internal waves with frequencies spanning the range of possible frequencies, i.e., between the maximum of the buoyancy frequency (vertical motion) and a minimum of the inertial frequency (horizontal motion). The present analysis is based on classification of resonant interactions into the sum, middle and difference interaction classes. It is shown in this paper that there exists a certain value of latitude, which is classified as the singular latitude, at which the coalescence of the middle and difference interaction classes occurs. Such coalescence, which apparently had passed unnoticed before, can be used to study the Thorpe’s problem on the existence of self-resonant waves. In particular, it is shown that the value of the bottom slope at which the second-order frequency and wavenumber components of the incident and reflected waves satisfy the internal wave dispersion relation can be approximated by two latitude-dependent parameters in the limiting case when latitude approaches its singular value. Since the existence of a such singular latitude is generic for resonant triad interactions, a question on application of the RTM to the modeling of enhanced mixing in the vicinity of ridges in the ocean arises.     

Detection of nonlinear waves and their contribution to ocean wave spectra Part I: Theoretical consideration

This is a Part I of a paper of nonlinearities of wind waves in the deep open ocean. First, considerations are given in order to verify the theoretical expression for bound waves from observed data. We compare the contribution of bound waves and double Bragg scattering to the second-order scattering, and we show that the contribution of bound waves is larger, and that bound waves can be detected by measuring the Doppler spectra of HF (high-frequency) radio wave scattering from the sea surface. Moreover, if the theory of the HF radio wave scattering from the sea surface is verified, so is the second-order perturbation theory for bound waves. Then, the contributions of bound waves to ocean wave spectra are investigated on the basis of the nonlinear theory. The bound waves are shown to modify frequency spectra and wave directional distributions at higher frequencies, and it is shown that although the modifications of frequency spectra are smaller for a two-dimensional field case than for a one-dimensional field case, they are not negligible at higher frequencies. On the other hand, the modifications of wave directional distributions are shown to be significant at higher frequencies. These discussions become significant only when bound wave predictions are verified in the open ocean. Consequently, it is shown that nonlinearities of water waves are important in considering both radio wave scattering from the sea surface and the detailed structures of ocean wave spectra at high frequencies.     

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.     

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.     

Evaluation of methods to remove inertial force from measured model wave impact force signals

The subject of wave impact on offshore structures and their components is important to vessel designers and operators for many reasons. They are often required to quantify these impact loads. Standard methods for wave load prediction will underestimate the forces on these structures due to intermittent loading. This necessitates the use of physical model tests to establish wave impact loads. The model measurement systems are designed to have high stiffness. This ensures that the natural frequency of the structure is above the wave frequency. However, it is widely believed that impacting waves contain high-frequency energy components that cause the structure to vibrate at its modal frequencies. This impact-induced vibration is recorded by the measuring system as a force (inertial force), and corrupts the actual applied force measurement. Before scaling can occur, the inertial force must be removed from the measured signal.A number of techniques for removing inertial force from measured signals are described in the published literature. Three methods are discussed, implemented and compared in this paper. The algorithms and procedures are presented. Each technique contains inherent and unique problems, while some are common to all methods.Neither of the techniques produced results that are fully satisfactory. The main problem is unwanted high-frequency content after the application of the methods. While neither method offers the perfect solution, the use of digital filtering techniques is recommended based on their relative performance and ease of implementation.     

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.     

Inertial oscillations as deep ocean response to hurricanes

We discuss the deep ocean response to passing hurricanes (aka typhoons), which are considered as generators of near-inertial, internal waves. The analysis of data collected in the northwestern parts of the Pacific and Atlantic oceans in the hurricane season permit us to assess the deep ocean response to such a strong atmospheric forcing. A large number of moorings (more than 100) in the northwestern Pacific have allowed us to characterize the spatial features of the oceanic response to typhoons and the variable downward velocity of near-inertial wave propagation. The velocity of their downward propagation varies in the range 1–10 m/hour. It is higher in the regions of low stratification and high anticyclonic vorticity. The inertial oscillations generated by a hurricane last for 10–12 days. The mean anticyclonic vorticity in the region increases the effective frequency of inertial oscillations by 0.001–0.004 cyc/hour.     

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.     

The effect of horizontal Coriolis force on internal wave-mean flow interaction

-In this paper, an improvement and revision of the theory of Miiller (1974, 1976), has been made under two conditions: (1) the horizontal component of the Coriolis force has been taken into account in the equations of motion for the internal wave field; and (2) the role of internal waves with frequencies close to the inertial frequency has been considered. The values of the viscosity coefficients and the diffusivity coefficients obtained in this paper are: Theappearance of the cross-diffusion (vc) of momentum is a natural result from the effect of the horizontal Coriolis force. Therefore the role of the horizontal shear of the mean flow cannot be absolutely separated from that of the vertical shear. So far in testing Muller's theory, the approximation of effective wave stress obtained by Ruddick and Joyce (1979) was extensively used, but it has to be revised under the conditions of this paper. The revised approximation shows that the internal waves with low frequencies close to the inertial frequency pl     

Observation of ocean current response to 1998 Hurricane Georges in the Gulf of Mexico

1 Introduction Hurricane is an extremely high wind event, which injects momentum into the oceanic mixed layer along its passage for a very short duration. If our interest is not at the surface, but in a depth away from the imme-diate surface wave influenc…