Internal waves and temperature fronts on slopes

Time series measurements from an array of temperature miniloggers in a line at constant depth along the sloping boundary of a lake are used to describe the ‘internal surf zone” where internal waves interact with the sloping boundary. More small positive temperature time derivatives are recorded than negative, but there are more large negative values than positive, giving the overall distribution of temperature time derivatives a small negative skewness. This is consistent with the internal wave dynamics; fronts form during the up-slope phase of the motion, bringing cold water up the slope, and the return flow may become unstable, leading to small advecting billows and weak warm fronts. The data are analysed to detect ‘events’, periods in which the temperature derivatives exceed a set threshold. The speed and distance travelled by ‘events’ are described. The motion along the slope may be a consequence of (a) instabilities advected by the flow (b) internal waves propagating along-slope or (c) internal waves approaching the slope from oblique directions. The propagation of several of the observed ‘events’ can only be explained by (c), evidence that the internal surf zone has some, but possibly not all, the characteristics of the conventional ‘surface wave’ surf zone, with waves steepening as they approach the slope at oblique angles.     

Reflection of equatorial Kelvin waves at eastern ocean boundaries Part I: hypothetical boundaries

A baroclinic shallow-water model is developed to investigate the effect of the orientation of the eastern ocean boundary on the behavior of equatorial Kelvin waves. The model is formulated in a spherical polar coordinate system and includes dissipation and non-linear terms, effects which have not been previously included in analytical approaches to the problem. Both equatorial and middle latitude response are considered given the large latitudinal extent used in the model. Baroclinic equatorial Kelvin waves of intraseasonal, seasonal and annual periods are introduced into the domain as pulses of finite width. Their subsequent reflection, transmission and dissipation are investigated. It is found that dissipation is very important for the transmission of wave energy along the boundary and for reflections from the boundary. The dissipation was found to be dependent not only on the presence of the coastal Kelvin waves in the domain, but also on the period of these coastal waves. In particular the dissipation increases with wave period. It is also shown that the equatorial β-plane approximation can allow an anomalous generation of Rossby waves at higher latitudes. Nonlinearities generally have a small effect on the solutions, within the confines of this model.     

Reflection of equatorial Kelvin waves at eastern ocean boundaries Part II: Pacific and Atlantic Oceans

The effect of viscosity, non linearities, incident wave period and realistic eastern coastline geometry on energy fluxes are investigated using a shallow water model with a spatial resolution of 1/4 degree in both meridional and zonal directions. Equatorial and mid-latitude responses are considered. It is found that (1) the influence of the coastline geometry and the incident wave period is more important for the westward energy flux than for the poleward flux, and (2) the effect of the inclination of the eastern ocean boundary on the poleward energy flux, for the Pacific and Atlantic Oceans, decline as the period of the incident wave increases. Furthermore, the model simulations suggest that the poleward energy fluxes from meridional boundaries give plausible results for motions of seasonal and annual periods. For comparatively shorter periods, a realistic coastline geometry has to be included for more accurate results. It is recommended that any numerical model involving the reflection of baroclinic Rossby waves (of intraseasonal, seasonal or annual periods) on the eastern Pacific or Atlantic Oceans, should consider the effect of the coastline geometry in order to improve the accuracy of the results.     

Internal waves,baroclinic energy fluxes and mixing at the European shelf edge

The energy flux in internal waves generated at the Celtic Sea shelf break was estimated by (i) applying perturbation theory to a week-long dataset from a mooring at 200 m depth, and (ii) using a 2D non-hydrostatic circulation model over the shelf break. The dataset consisted of high resolution time-series of currents and vertical stratification together with two 25-h sets of vertical profiles of the dissipation of turbulent kinetic energy. The observations indicated an average energy flux of 139 W m⁻¹, travelling along the shelf break towards the northwest. The average energy flux across the shelf break at the mooring was only 8 W m⁻¹. However, the waves propagating onshelf transported up to 200 W m⁻¹, but they were only present 51% of the time. A comparison between the divergence of the baroclinic energy flux and observed dissipation within the seasonal thermocline at the mooring showed that the dissipation was at least one order of magnitude larger. Results from a 2D model along a transect perpendicular to the shelf break showed a time-averaged onshelf energy flux of 153–425 W m⁻¹, depending on the magnitude of the barotropic forcing. A divergence zone of the energy flux was found a few kilometre offshore of the location of the observations in the model results, and fluxes on the order of several kW m⁻¹ were present in the deep waters further offshelf from the divergence zone. The modelled fluxes exhibited qualitative agreements with the phase and hourly onshelf magnitudes of the observed energy fluxes. Both the observations and the model results show an intermittent onshelf energy flux of 100–200 W m⁻¹, but these waves could only propagate ∼20–30 km onshore before dissipating. This conclusion was supported by a 25-h dataset sampled some 180 km onto the shelf, where a weak wave energy flux was found going towards the shelf break. We therefore conclude that shelf break generated internal waves are unlikely to be the main source of energy for mixing on the inner part of the shelf.     

High-frequency vertical current observations in stratified seas

Although large-scale tidal and inertial motions dominate the kinetic energy and vertical current shear in shelf seas and ocean, short-scale internal waves at higher frequencies close to the local buoyancy frequency are of some interest for studying internal wave breaking and associated diapycnal mixing. Such waves near the upper limit of the inertio-gravity wave band are thought to have relatively short O (10²–10³ m) horizontal scales and to show mainly up- and downward motions, which contrasts with generally low aspect ratio large-scale ocean currents. Here, short-term vertical current (w) observations using moored acoustic Doppler current profiler (ADCP) are presented from a shelf sea, above a continental slope and from the open ocean. The observed w, with amplitudes between 0.015 and 0.05 m s⁻¹, all span a considerable part of the water column, which is not a small vertical scale O(water depth) or O (100–500 m, the maximum range of observations), with either 0 or π phase change. This implies that they actually represent internal waves of low vertical modes 1 or 2. Maximum amplitudes are found in layers of largest stratification, some in the main pycnocline bordering the frictional bottom boundary layer, suggesting a tidal source. These ‘pycnocline-w’ compose a regular train of (solitary) internal waves and linearly decrease to small values near surface and bottom.     

Generation and evolution of internal solitary waves in the southern Taiwan Strait

ABSTRACT

The generation processes and potential energy sources of internal solitary waves (ISWs) in the southern Taiwan Strait are investigated by driving a high resolution non-hydrostatic numerical model with realistic background conditions. Two main types of ISWs are clarified according to their different energy sources. One is generated by the nonlinear disintegration of remote internal tides emanating from Luzon Strait, and the other type is generated by local tide-topography interaction at the continental slope. The basic properties and evolution processes differ between these two kinds of ISWs. The waves originated from the remote internal tides at Luzon Strait have amplitudes comparable to previous field observations. In contrast, the ISWs generated locally are much weaker than observed waves, even in the presence of a steady offshore background current, which intensifies the generation of onshore ISWs. The ISWs induced by remotely generated M₂ internal tides are stronger than those induced by K₁ internal tides, and the fraction of internal wave energy transmitted onto the shelf is not significantly influenced by the intensity of remotely generated internal tides.     

Characteristics of coastal trapped waves along the northern coast of the South China Sea during year?1990

The structures and evolution of the coastal-trapped waves (CTW) along the northern coast of the South China Sea (SCS) in the year?1990 are studied using observed hourly sea level records collected from four sites around the northern SCS and a three-dimensional numerical model with realistic bathymetry and wind forcing. Analysis of the yearlong records of the observed sea level data indicates that the sea level variations are highly correlated between the stations and the sea level variability propagates southwestward along the coast. The sea level signals traveling from northeast to southwest along the coast with a propagation speed of 5.5–17.9?m?s^?1 during both the typhoon season and the winter month show the characteristics of a CTW. The wave speed is faster between stations Shanwei and Zhapo than that between Xiamen and Shanwei. Sea level variations during both typhoon season and winter month are reasonably well represented by the numerical model. The model runs focused on the wave signals related to typhoons and winter storm show that the CTW propagating southwestward along the coast can be reinforced or decreased by the local wind forcing during its propagation and there are apparent differences in the propagation characteristics between the waves along the mainland and those traveling around Hainan Island. The abrupt change of the shelf width and coastline around Leizhou Peninsula and Hainan Island are responsible for strong scattering of CTWs from one mode into higher modes. The alongshore velocities across different transects associated with CTW are investigated to examine the vertical structures of the waves. The alongshore velocity structures at transects during different events are related to the combined effect of stratification and shelf profile, which can be estimated using the Burger number. The empirical orthogonal function analysis of alongshore velocity and nodal lines of the mode structure suggest mode two CTWs in transect S2 during typhoon season and mode 1 CTWs during winter. Sensitivity model experiments are also performed to demonstrate the effects of local wind and topography on the wave propagation.     

A three-dimensional model study of warm core ring interaction with continental shelf and slope

The interaction of warm core rings with a western wall and shelf/slope is examined with a three-dimensional primitive-equation model. The model ring is initialized with an axisymmetric Gaussian-type anticyclonic eddy placing far from the coastal boundary to allow the ring to freely propagate towards the wall and shelf/slope. The ring initially propagates steadily to the southwest at about 3 km/day under the combined planetary β and nonlinear effects. When colliding with a wall, the ring adjusts into a ‘D’ shape and moves poleward under primarily the image effect. When colliding with a shelf and slope, the ring however becomes stalled and bounces on and off the shelf/slope with little net movement. Small cyclones marked by strong upwelling are generated near the shelfbreak. Cyclones and anticyclones also are spawned at the periphery of the ring. Satellite SST images and concurrent ADCP transects are used to illustrate the strong interaction of a Gulf Stream warm ring (99B) with the Middle Atlantic Bight.     

The beneficial role of rubble mound coastal structures on seawater oxygenation

The beneficial role of rubble mound coastal structures on oxygenation under the effect of waves is discussed, based on analytical considerations and experimental data from laboratory experiments with permeable and impermeable structures. Significant oxygenation of the wave-protected area was observed as a result of horizontal transport through the permeable structure. A two-cell model describing the transport of dissolved oxygen (DO) near a rubble mound breakwater structure was developed and used for the determination of the oxygen transfer coefficients from the experimental data. Oxygen transfer through the air-water interface is considered a source term in the transport equation and the oxygen flux through the structure is taken into account. The mass transport equations for both sides of the structure are solved analytically in terms of time evolution of DO concentration. The behaviour of the solution is illustrated for three different characteristic cases of initial conditions. The oxygen transfer through the air-water interface in the wave-influenced area increases the DO content in the area; the resulting oxygen flux through the structure is discussed. The analytical results depend on the initial conditions, the oxygen transfer coefficient and the exchange flow rate through the structure. Experiments with impermeable structures show that air water oxygen transfer in the harbour area is negligible in the absence of waves. In addition the ratio of the horizontal DO flux to the vertical flux into the seaward side tends towards a constant value, independent of the initial conditions.     

地震海洋学方法在海洋混合参数提取中的研究与应用——以南海内波和地中海涡旋为例

混合是海洋中普遍存在的一种海水运动形式,对多个海洋学分支的研究具有重要的影响.随着物理海洋学的研究重心从大尺度向中小尺度现象过渡,近年来混合问题的研究重心也逐渐转向了中小尺度现象.内波与中尺度涡都是非常重要的中小尺度物理海洋学现象,对海洋能量在不同尺度中的级联发挥着重要的作用.本文基于地震海洋学研究了海洋混合参数的提取方法,并以南海内波和地中海涡旋为例进行了计算和分析.结果显示,南海内波在200~600 m深度范围内所引起的混合可达10-2.79 m2·s-1左右,比大洋的统计结果10-5 m2·s-1高出两个数量级以上.而地中海涡旋所引起的湍流混合率可达10-3.44m2·s-1左右,与大洋统计结果相比高出1.5个数量级左右,并且地中海涡旋下边界的混合要强于上边界,这一特征与前人的研究一致,另外涡旋上边界之上以及侧边界的外侧也具有非常高的混合率.     

Comparison of finite difference and element models of internal tides on the Malin–Hebrides shelf

A three-dimensional baroclinic finite element model with a coarse and fine (i.e. local refinement along the shelf edge) grid is used to examine the influence of shelf edge grid refinement upon the internal tide generation and propagation off the west coast of Scotland. Comparisons are made with observations in the region and with a published solution using a finite difference model. The calculations show that provided that the finite element grid is refined in the internal tide generation area and the adjacent region through which the internal tide propagates, then a numerically accurate solution is obtained. In the regions of strong internal tide generation with a local grid refinement, internal wave energy can accumulate at small scales and must be removed by a scale-selective filter.     

Interaction of surface waves at very close wavenumbers

We show that interaction of two monochromatic waves at the water surface enters a different dynamic regime if their wavenumbers become very close. The study is conducted by means of a fully nonlinear wave model. In the course of evolution of the two waves, downshifting of the initial wave energy and growth of the first mode occur depending on wave steepness and dk/k. Behaviour of these features changes if dk/k?<?0.0025: both downshifting and growth rate become independent of dk/k, accompanied by rapid transfer of wave energy to large scales.     

Crustal microdeformations and tides in the coastal zone of the Sea of Japan

Based on experimental data and numerical modeling, the possible mechanisms of the effect of internal gravitational waves within the range of periods from tidal values to a few tens of minutes on crustal microdeformations in the coastal zone of the Sea of Japan are examined. The spectral analysis of oscillations in the sea level and microdeformations recorded in various seasons reveals common maximums of energy at diumal and semidiurnal periods, but the coincidence of the maximums at shorter periods is random and varies with time. The phase shifts between the surface tide and crustal deformations are also unstable in time. To explain the observed interrelations between the processes at sea and in the Earth’s crust, we modeled numerically the generation of internal tides, bores, and packets of short internal waves in terms of a nonlinear model of shallow water. It is shown that the observed effects can be caused (1) by the resonance between the wavelength of the internal tide and the shelf width and (2) by the reflection of bores and internal wave packets from a steep bottom and rocky shores or by their collapse.     

Analysis of effects of active sources on observed phase velocity based on the thin layer method

In the wave field induced by active sources, the observed phase velocity of surface waves is influenced by both mode incompatibility (i.e. non-planar spread of surface waves is idealized as plane waves) and body waves. Effects of sources are usually investigated based on numerical simulations and physical models. Several methods have been proposed to mitigate the effects. In application, however, these methods may also have difficulties since the energy of the body waves depends on soil stratification and parameters. There are multiple modes of surface waves in layered media, among which the higher modes dominate the wave field for soils with the irregular shear velocity profiles. Considering the mode incompatibility and the higher modes, we derive analytical expressions for the effective phase velocity of the surface waves based on the thin layer stiffness method, and investigate the effects of the body waves on the observed phase velocity through the phase analysis of the vibrations of both the surface waves and the body waves. The results indicate that the effective phase velocity of the surface waves in layered media varies with the frequency and the spread distance, and is underestimated compared to that of the plane surface waves in the spread range less than about one wavelength. The oscillations that appeared in the observed phase velocity are due to the involvement of the body waves. The mode incompatibility can be ignored in the range beyond one wavelength, while the influence range of the body waves is far beyond one wavelength. The body waves have a significant influence on the observed phase velocity of the surface waves in soils with a soft layer trapped between the first and the second layers because of strong reflections.     

Modelling offshore sand wave evolution

We present a two-dimensional vertical (2DV) flow and morphological numerical model describing the behaviour of offshore sand waves. The model contains the 2DV shallow water equations, with a free water surface and a general bed load formula. The water movement is coupled to the sediment transport equation by a seabed evolution equation. Using this model, we investigate the evolution of sand waves in a marine environment. As a result, we find sand wave saturation for heights of 10–30% of the average water depth on a timescale of decades. The stabilization mechanism, causing sand waves to saturate, is found to be based on the balance between the shear stress at the seabed and the principle that sediment is transported more easily downhill than uphill. The migration rate of the sand waves decreases slightly during their evolution. For a unidirectional steady flow the sand waves become asymmetrical in the horizontal direction and for a unidirectional block current asymmetrical in the vertical. A sensitivity analysis showed the slope effect of the sediment transport plays an important role herein. Furthermore, the magnitude of the resistance at the seabed and the eddy viscosity influence both the timescale and height of sand waves. The order of magnitudes found of the time and spatial scales coincide with observations made in the southern bight of the North Sea, Japan and Spain.     

Nonlinear internal waves in ideal rotating basins

Abstract

Starting from Euler's equations of motion a nonlinear model for internal waves in fluids is developed by an appropriate scaling and a vertical integration over two layers of different but constant density. The model allows the barotropic and the first baroclinic mode to be calculated. In addition to the nonlinear advective terms dispersion and Coriolis force due to the Earth's rotation are taken into account. The model equations are solved numerically by an implicit finite difference scheme. In this paper we discuss the results for ideal basins: the effects of nonlinear terms, dispersion and Coriolis force, the mechanism of wind forcing, the evolution of Kelvin waves and the corresponding transport of particles and, finally, wave propagation over variable topography. First applications to Lake Constance are shown, but a detailed analysis is deferred to a second paper [Bauer et al. (1994)].     

Observations of semidiurnal internal tidal currents off central Chile (36.6°S)

Observations of semidiurnal internal tidal currents from three moorings deployed on the continental shelf off central Chile during summer and winter of 2005 are reported. The spectra of the baroclinic currents showed large peaks at the semidiurnal band with a dominant counterclockwise rotation, which was consistent with internal wave activity. The amplitude of the barotropic tidal currents varied according to the spring–neap cycle following the sea level fluctuations. In contrast, the amplitudes of the internal tide showed high spatial-temporal variability not directly related to the spring–neap modulation. Near the middle of the continental shelf and near the coast (San Vicente Bay) the variance of the semidiurnal baroclinic current is larger than the variance of its barotropic counterpart. The vertical structure of the baroclinic tidal current fluctuations was similar to the structure of the first baroclinic internal wave mode. In general, in the three study sites the variance of the baroclinic current was larger near the surface and bottom and tended to show a minimum value at mid depths. Kinetic energy related to semidiurnal internal waves was larger in winter when stratification of the water column was stronger. During summer, upwelling and the decrease of freshwater input from nearby rivers reduced the vertical density stratification. The amplitude of the semidiurnal internal tide showed a tendency to be enhanced with increasing stratification as observed in other upwelling areas. The continental shelf break and submarine canyons, which limit the continental shelf in the alongshore direction, represent near-critical slopes for the semidiurnal period and are suggested to be the main internal tide generation sites in the study region.     

High-resolution modelling of a large-scale river plume

Evolution of a large-scale river plume is studied numerically using the Massachusetts Institute of Technology general circulation model. The model parameters were set close to those observed in the area of the Columbia River mouth. The fine-resolution grid along with the non-hydrostatic dispersion included in the model allowed for the reproduction of detailed inner plume structure, as well as a system of internal waves radiated from the plume’s boundary. It was found that not only first-mode but also second- and third-mode internal waves are radiated from the plume at the latest stages of its relaxation when the velocity of the front propagation drops below an appropriate wave phase speed of internal baroclinic mode. The model output shows that the amplitude of these high-mode waves is of the same order as the leading first-mode waves, which in combination with the specific vertical structure (location of the maximum structure function beyond the pycnocline layer) creates favourable conditions for the generation of shear instabilities. High-resolution model output also reveals evidence of a fine internal structure of the plume characterized by the presence of secondary fronts inside the plume and secondary internal wave systems propagated radially from the lift-off area to the outer boundary. These structures intensify the mixing processes within the propagating plume with predominance of the entrainment mechanism developing on the lower boundary between the plume’s body and underlying waters. The scheme of horizontal circulation in the plume was reproduced by the methodology of Lagrange drifters released near the mouth at different depths.

     

Relative role of subinertial and superinertial modes in the coastal long wave response forced by the landfall of a tropical cyclone

A set of numerical experiments has been performed in order to analyze the long-wave response of the coastal ocean to a translating mesoscale atmospheric cyclone approaching the coastline at a normal angle. An idealized two-slope shelf topography is chosen. The model is forced by a radially symmetric atmospheric pressure perturbation with a corresponding gradient wind field. The cyclone's translation speed, radius, and the continental shelf width are considered as parameters whose impact on the long wave period, modal structure, and amplitude is studied. Subinertial continental shelf waves (CSW) dominate the response under typical forcing conditions and on the narrower shelves. They propagate in the downstream (in the sense of Kelvin wave propagation) direction. Superinertial edge wave modes have higher free surface amplitudes and faster phase speeds than the CSW modes. While potentially more dangerous, edge waves are not as common as subinertial shelf waves because their generation requires a wide, gently sloping shelf and a storm system translating at a relatively high (∼10 m s⁻¹ or faster) speed. A relatively smaller size of an atmospheric cyclone also favors edge wave generation. Edge waves with the highest amplitude (up to 60% of the forced storm surge) propagate upstream. They are produced by a storm system with an Eulerian time scale equal to the period of a zero-mode edge wave with the wavelength of the storm spatial scale. Large amplitude edge waves were generated during Hurricane Wilma's landfall (2005) on the West Florida shelf with particularly severe flooding occurring upstream of the landfall site.     

Internal waves over the shelf in the western Bay of Bengal: a case study

Generation and propagation of internal waves (IWs) in the coastal waters of the extended shelf of the western Bay of Bengal are investigated for late winter by using the Massachusetts Institute of Technology General Circulation Model (MITgcm). The model is forced with astronomical tides and daily winds. Monthly climatological temperature and salinity fields are used as initial conditions. The simulations are compared with time series observations of temperature and currents from acoustic Doppler current profiler (ADCP) and conductivity-temperature-depth (CTD) moored at three locations south of Gopalpur: two at a local depth of 100 m and another at 400-m depth during 19–21 February 2012. The comparison of the spectral estimates for the time series of temperature from the model and observations are in reasonable agreement for the near-tidal frequency waves. The peak of temperature spectra is always found near the shelf break region which steadily lost its intensity over the continental shelf. The calculation of Richardson number reflected the presence of local mixing due to density overturning in the shelf region. To understand further the generation and propagation of internal tides in the region, energy flux and conversion of barotropic-to-baroclinic M₂ tidal energy are examined. The model simulations suggest that the internal tide is generated all along the shelf slope. The energy flux analysis shows that the internal tides propagate to either side of the generation sites.