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.     

Quasigeostrophic planetary waves in a two-layer ocean with one-dimensional periodic bottom topography

Although the study of topographic effects on the Rossby waves in a stratified ocean has a long history, the wave property over a periodic bottom topography whose lateral scale is comparable to the wavelength is still not clear. The present paper treats this problem in a two-layer ocean with one-dimensional periodic bottom topography by a simple numerical method, in which no restriction on the wavelength and/or the horizontal scale of the topography is required. The dispersion diagram is obtained for a wavenumber range of [?π/L _b , π/L _b ], where L _b is the periodic length of the topography. When the topographic?β?is not negligible compared to the planetary β, the Rossby wave solutions around the wavenumbers which satisfy the resonant condition among the waves and topography disappear and separate into an infinite number of discrete modes. For convenience, each mode is numbered in order of frequency. As topographic height is increased, the high frequency barotropic Rossby wave (mode 1) becomes a topographic mode which can exist even on the f plane, and the highfrequency baroclinic mode (mode 2) becomes a surface intensified mode. Behaviors of low frequency modes are somewhat complicated. When the topographic amplitude is small, the low frequency baroclinic modes tend to be bottom trapped and the low frequency barotropic modes tend to be surface intensified. As topographic amplitude further increases, the relation between the mode number and vertical structure changes. This change can be attributed to the increase of the frequency of the topographic mode with the topographic amplitude.     

On steady and travelling waves over bottom topography in the model of homogeneous flow in a beta-plane channel

Abstract

A spectral low-order model is proposed in order to investigate some effects of bottom corrugation on the dynamics of forced and free Rossby waves. The analysis of the interaction between the waves and the topographic modes in the linear version of the model shows that the natural frequencies lie between the corresponding Rossby wave frequencies for a flat bottom and those applying in the “topographic limit” when the beta-effect is zero. There is a possibility of standing or eastward-travelling free waves when the integrated topograhic effect exceeds the planetary beta-effect.

The nonlinear interactions between forced waves in the presence of topography and the beta-effect give rise to a steady dynamical mode correlated to the topographic mode. The periodic solution that includes this steady wave is stable when the forcing field moves to the West with relatively large phase speed. The energy of this solution may be transferred to the steady zonal shear flow if the spatial scale of this zonal mode exceeds the scale of the directly forced large-scale dynamical mode.     

Linear theory of the response of a two layer ocean to a moving hurricane‡

Abstract

This paper describes the linear response of an inviscid two‐layer model of a deep ocean on an f‐plane to a hurricane translating across the surface at constant speed. The forcing is a localized, radially‐symmetric pattern of positive wind stress curl and negative pressure anomaly. Only the steady state response is considered. The principal result is the identification of an internal wake in the lee of the storm, present when the translation speed of the storm exceeds the baroclinic long wave speed. The amplitude of the wake depends on the length of time over which the stress is experienced at a given point. The angle of the wedge filled by the wake is small, an effect due to the fact that the scale of a hurricane is typically larger than the baroclinic radius of deformation. After the wake disperses, a geostrophically balanced baroclinic ridge remains along the storm track.     

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.     

Can a minimalist model of wind forced baroclinic Rossby waves produce reasonable results?

The linear theory predicts that Rossby waves are the large scale mechanism of adjustment to perturbations of the geophysical fluid. Satellite measurements of sea level anomaly (SLA) provided sturdy evidence of the existence of these waves. Recent studies suggest that the variability in the altimeter records is mostly due to mesoscale nonlinear eddies and challenges the original interpretation of westward propagating features as Rossby waves. The objective of this work is to test whether a classic linear dynamic model is a reasonable explanation for the observed SLA. A linear-reduced gravity non-dispersive Rossby wave model is used to estimate the SLA forced by direct and remote wind stress. Correlations between model results and observations are up to 0.88. The best agreement is in the tropical region of all ocean basins. These correlations decrease towards insignificance in mid-latitudes. The relative contributions of eastern boundary (remote) forcing and local wind forcing in the generation of Rossby waves are also estimated and suggest that the main wave forming mechanism is the remote forcing. Results suggest that linear long baroclinic Rossby wave dynamics explain a significant part of the SLA annual variability at least in the tropical oceans.     

Wave-induced topographic formstress in baroclinic channel flow

Large-scale zonal flow driven across submarine topography establishes standing Rossby waves. In the presence of stratification, the wave pattern can be represented by barotropic and baroclinic Rossby waves of mixed planetary topographic nature, which are locked to the topography. In the balance of momentum, the wave pattern manifests itself as topographic formstress. This wave-induced formstress has the net effect of braking the flow and reducing the zonal transport. Locally, it may lead to acceleration, and the parts induced by the barotropic and baroclinic waves may have opposing effects. This flow regime occurs in the circumpolar flow around Antarctica. The different roles that the wave-induced formstress plays in homogeneous and stratified flows through a zonal channel are analyzed with the BARBI (BARotropic-Baroclinic-Interaction ocean model, Olbers and Eden, J Phys Oceanogr 33:2719–2737, 2003) model. It is used in complete form and in a low-order version to clarify the different regimes. It is shown that the barotropic formstress arises by topographic locking due to viscous friction and the baroclinic one due to eddy-induced density advection. For the sinusoidal topography used in this study, the transport obeys a law in which friction and wave-induced formstress act as additive resistances, and windstress, the effect of Ekman pumping on the density stratification, and the buoyancy forcing (diapycnal mixing of the stratified water column) of the potential energy stored in the stratification act as additive forcing functions. The dependence of the resistance on the system parameters (lateral viscosity ε, lateral diffusivity κ of eddy density advection, Rossby radius λ, and topography height δ) as well as the dependence of transport on the forcing functions are determined. While the current intensity in a channel with homogeneous density decreases from the viscous flat bottom case in an inverse quadratic law ~δ ^–2 with increasing topography height and always depends on ε, a stratified system runs into a saturated state in which the transport becomes independent of δ and ε and is determined by the density diffusivity κ rather than the viscosity: κ/λ ² acts as a vertical eddy viscosity, and the transport is λ ²/κ times the applied forcing. Critical values for the topographic heights in these regimes are identified.     

On the generation of baroclinic rossby waves in the presence of a semi-circular boundary

Abstract

An analytical model is constructed for the generation of baroclinic Rossby waves by a vorticity source in the presence of a semi-circular boundary. The vorticity source is used to represent the effect of the Agulhas retroflection to the south of Southern Africa. The displacement of the interface between the two layers of the model ocean consists of quantized waves near the coast and a train of Rossby waves drifting westward further offshore.     

北太平洋海表面高度的年际变化及其机制

利用15年（1993～2007年）月平均的海表面高度（SSH）异常资料,分析了北太平洋海表面高度的年际变化的时空结构,并研究了热通量和风应力两个因子对其的强迫作用.结果表明,北太平洋年际时间尺度SSH变化的大值区在黑潮延伸区和西太平洋暖池区.EOF分解第一模态的空间结构沿纬向呈带状分布,第二模态为沿经向呈带状分布.热通量强迫作用在中纬度的东北太平洋可以解释SSH年际变化40%以上.风应力对SSH的作用包括正压和斜压两个方面.正压Sverdrup平衡模型模拟的SSH年际变化较弱,仅能解释高纬度副极地环流西部的20%~40%.由大尺度风应力强迫的第一阶斜压Rossby波模型可以解释热带地区的20%~60%,中纬度中部的20%~40%,以及阿拉斯加环流东部和副极地环流西部的20%~60%.风应力强迫的一阶斜压Rossby波模型对SSH的强迫机理又可分为局地风应力强迫和西传Rossby波作用.其中,风应力的局地强迫作用（Ekman抽吸）在东北太平洋、白令海以及热带中部有显著的预报技巧,可以解释SSH年际变异的40%以上.Rossby波的传播作用在中纬度海域的副热带环流中西部和夏威夷岛以东起着重要作用,可解释20%~60%.     

Assessing the importance of tropical cyclones on continental margin sedimentation in the Mississippi delta region

Recent research on the Mississippi margin indicates notable seasonal variation in seabed dynamics. During years with minimal tropical-system activity, sediments initially deposited from late spring to early fall are remobilized by wind-driven currents and wave energy during extra-tropical weather systems in the winter. This research reveals the profound significance of tropical cyclones on Louisiana Shelf sedimentation. The amount of material delivered to and advected across the shelf by recent tropical cyclones is considerably larger than that related to winter storm systems. In Fall 2004, the river-dominated shelf of Louisiana was impacted by three tropical systems in less than a month, including Hurricane Ivan. Ivan, with maximum sustained winds in excess of 74 m s⁻¹ (144 knots) and a minimum measured central pressure of 910 mbar, was the eighth most intense Atlantic hurricane on record at the time. In order to assess the impact these tropical systems had on the continental margin west of the Mississippi delta, seabed samples were collected from box cores in October 2004 and analyzed for particle-reactive radionuclides ²³⁴Th, ⁷Be, and ²¹⁰Pb. Radiochemical data and observations from X-radiographs indicate event-driven sediment deposits ranged from 4 to 30 cm on the shelf and 2–6 cm in the Mississippi Canyon. These deposits exhibit distinct radiochemical signatures and differ visually and texturally from the underlying sediment. The well-developed physical stratification and graded nature of the deposits observed in core X-radiographs suggests that the sediment could have been deposited from sediment-gravity flows. Inventories of ⁷Be and ⁷Be/²³⁴Th_xs ratios reveal this series of cyclones transported considerably more material to the outer shelf and slope than periods of minimal tropical-system activity. When compared to seasonal depositional rates created by winter storms, tropical-cyclone-related event deposits on the middle and outer shelf are up to an order of magnitude greater in thickness. The number and thickness of these event deposits decrease with distance from the delta and suggest that only the most severe tropical systems are likely capable of redistributing significant quantities of sediment to more distal portions of the shelf and slope. These severe-event-driven deposits may account for as much as 75% of the sediment burial budget on decadal time scales within Mississippi Canyon. Higher than average tropical cyclone activity, predicted by the National Hurricane Center over the next decade, may be the major mechanism controlling sediment transport and deposition on the Mississippi River continental shelf and in Mississippi Canyon.     

Traveling planetary waves in the stratosphere

This paper reviews the theory and observations of some traveling planetary waves in the stratosphere. Two categories of waves which appear prominently in the literature are discussed: westward propagating waves of periods in the range 3–7 days (the 5-day wave) and in the range 10–20 days (the 16-day wave). Although the observations seem to indicate that these waves are waves of the Rossby type (planetary waves), the evidence is less clear regarding (1) the question of whether these waves are forced internal waves or free (resonant) external waves, and (2) the identification of the observed waves with specific theoretical waves of the Rossby type. When recent observations are compared with theory, the evidence seems to favor the notion that the 5-day and 16-day waves of longitudinal wave number 1 may be identified, respectively, with the gravest and next gravest symmetric free Rossby modes. However, the observational evidence seems to be less clear regarding the nature of the 16-day wave than the 5-day wave.     

Connection of sea level variability between the tropical western Pacific and the southern Indian Ocean during recent two decades

Based on the merged satellite altimeter data and in-situ observations,as well as a diagnosis of linear baroclinic Rossby wave solutions,this study analyzed the rapidly rise of sea level/sea surface height(SSH)in the tropical Pacific and Indian Oceans during recent two decades.Results show that the sea level rise signals in the tropical west Pacific and the southeast Indian Ocean are closely linked to each other through the pathways of oceanic waveguide within the Indonesian Seas in the form of thermocline adjustment.The sea level changes in the southeast Indian Ocean are strongly influenced by the low-frequency westward-propagating waves originated in the tropical Pacific,whereas those in the southwest Indian Ocean respond mainly to the local wind forcing.Analyses of the lead-lag correlation further reveal the different origins of interannual and interdecadal variabilities in the tropical Pacific.The interannual wave signals are dominated by the wind variability along the equatorial Pacific,which is associated with the El Ni?o-Southern Oscillation;whereas the interdecadal signals are driven mainly by the wind curl off the equatorial Pacific,which is closely related to the Pacific Decadal Oscillation.     

On isallobaric effect in a quasi-geostrophic topographic-drag problem

Abstract

Isallobaric effect of a slowly varying quasi-geostrophic flow represented by propagating waves may give rise to a mean steady topographic drag component which turns out to be the principal one when viscous effects are negligibly small. This drag component decreases, in contrast to the quasi-geostrophic component, when statistical properties of the topography become isotropic. When the phase velocity of the incident wave is much larger (smaller) than the phase speed of Rossby waves, the isallobaric drag becomes independent (dependent) on the sign of that velocity.     

Barotropic and baroclinic processes in the transport variability of the Antarctic Circumpolar Current

Synoptic scale variability of the Southern Ocean wind field in the high-frequency range of barotropic Rossby waves results in transport variations of the Antarctic Circumpolar Current (ACC), which are highly coherent with the bottom pressure field all around the Antarctic continent. The coherence pattern, in contrast to the steady state ACC, is steered by the geostrophic f/h contours passing through Drake Passage and circling closely around the continent. At lower frequencies, with interannual and decadal periods, the correlation with the bottom pressure continues, but baroclinic processes gain importance. For periods exceeding a few years, variations of the ACC transport are in geostrophic balance with the pressure field associated with the baroclinic potential energy stored in the stratification, whereas bottom pressure plays a minor role. The low-frequency variability of the ACC transport is correlated with the baroclinic state variable in the entire Southern Ocean, mediated by baroclinic topographic–planetary Rossby waves that are not bound to f/h contours. To clarify the processes of wave dynamics and pattern correlation, we apply a circulation model with simplified physics (the barotropic–baroclinic-interaction model BARBI) and use two types of wind forcing: the National Centers for Environmental Prediction (NCEP) wind field with integrations spanning three decades and an artificial wind field constructed from the first three empirical orthogonal functions of NCEP combined with a temporal variability according to an autoregressive process. Experiments with this Southern Annular Mode type forcing have been performed for 1,800 years. We analyze the spin-up, trends, and variability of the model runs. Particular emphasis is placed on coherence and correlation patterns between the ACC transport, the wind forcing, the bottom pressure field and the pressure associated with the baroclinic potential energy. A stochastic dynamical model is developed that describes the dominant barotropic and baroclinic processes and represents the spectral properties for a wide range of frequencies, from monthly periods to hundreds of years.     

Resonance induced by Rossby Lee waves

Abstract

The mutual interaction of fields induced by spatially separated potential vorticity sources in a quasi-geostrophic barotropic flow is investigated using the weakly nonlinear approach. It is found that a powerful nonlinear response can be triggered by Rossby lee waves. This resonance phenomenon which dominates all other nonlinear corrections depends on certain global resonance conditions and on the change in the phase of the Rossby lee wave across the distance separating the sources. The response is particularly strong for topographic forcing possessing δ-function characterisitics.     

Instability of planetary waves in a high vertical resolution model

Abstract

A high vertical resolution model is used to examine the instability of a baroclinic zonal flow and a finite amplitude topographically forced wave. Two families of unstable modes are found, consisting of zonally propagating most unstable modes, and stationary unstable modes. The former have time scale and spatial structure similar to baroclinic synoptic disturbances, but are localized in space due to interaction with the zonally asymmetric forcing. These modes transport heat efficiently in both the zonal and meridional directions. The second family of stationary unstable modes has characteristics of modes of low frequency variability of the atmosphere. They have time scales of 10 days and longer, and are of planetary scale with an equivalent barotropic vertical structure. The horizontal structure resembles blocking flows. They are maintained by available potential energy of the basic wave, and have large zonal heat fluxes. The results for both families of modes are interpreted in terms of an interaction between forcing and baroclinic instability to create favoured regions for eddy development. Applications to baroclinic planetary waves are also considered.     

Boundary layer dissipation and the nonlinear interaction of equatorial baroclinic and barotropic rossby waves

Two-layer equatorial primitive equations for the free troposphere in the presence of a thin atmospheric boundary layer and thermal dissipation are developed here. An asymptotic theory for the resonant nonlinear interaction of long equatorial baroclinic and barotropic Rossby waves is derived in the presence of such dissipation. In this model, a self-consistent asymptotic derivation establishes that boundary layer flows are generated by meridional pressure gradients in the lower troposphere and give rise to degenerate equatorial Ekman friction. That is to say, the asymptotic model has the property that the dissipation matrix has one eigenvalue which is nearly zero: therefore the dynamics rapidly dissipates flows with pressure at the base of the troposphere and creates barotropic/baroclinic spin up/spin down. The simplified asymptotic equations for the amplitudes of the dissipative equatorial barotropic and baroclinic waves are studied by linear theory and integrated numerically. The results indicate that although the dissipation slightly weakens the tropics to midlatitude connection, strong localized wave packets are nonetheless able to exchange energy between barotropic and baroclinic waves on intraseasonal timescales in the presence of baroclinic mean shear. Interesting dissipation balanced wave-mean flow states are discovered through numerical simulations. In general, the boundary layer dissipation is very efficient for flows in which the barotropic and baroclinic components are of the same sign at the base of the free troposphere whereas the boundary layer dissipation is less efficient for flows whose barotropic and baroclinic components are of opposite sign at the base of the free troposphere.     

Numerical experiments on the generation of long ocean waves in coastal waters of the Buenos Aires province,Argentina

A numerical model (two horizontal dimensions, vertically integrated) is used to investigate the generation of long ocean waves, ranging from 20 min to almost 2 h, at Buenos Aires continental shelf. The domain includes the Río de la Plata estuary and the continental shelf together and extends from 33.5° to 40.5°S latitude, and from 51° to 63°W longitude. Sea-level oscillations are modeled by forcing with passage of atmospheric cold fronts and atmospheric gravity waves. Both forcing mechanisms, which have been present during high activity lapses of long ocean waves, are mathematically implemented. After several numerical simulations, it is concluded that the pressure and wind fields associated to cold fronts do not generate long ocean waves in the area, though they do produce disturbances with periods longer than the tidal ones. On the other hand, it is so concluded that atmospheric gravity waves are an effective mechanism to force long ocean waves. Results obtained show that generation of long ocean waves is highly sensitive depending on the propagation direction and the phase speed of the atmospheric gravity waves. The long ocean wave event detected during the large-amplitude gravity-wave event of 13 October 1985 is successfully simulated. Finally, all our results suggest that atmospheric gravity waves are a highly effective mechanism forcing for the generation of long ocean waves in Buenos Aires coastal waters.     

Simulation of irregular waves in an offshore wind farm with a spectral wave model

A numerical study of irregular waves in the Norwegian continental shelf wind farm (HAVSUL-II) was conducted using 3rd generation spectral wave models. The study was composed of two parts: the study of the effect of a single windmill monopile in the local incoming wave field using an empirical JONSWAP spectrum, and a wave hindcast study in the wind farm area using realistic incoming wave spectra obtained from large scale simulations for the 1991-1992 winter period. In the single windmill monopile study the SWAN wave model was used, while the hindcast study was conducted by successively nesting from a coarse grid using the WAM model up to a high-resolution (56 m) grid covering 26.2 km² of the HAVSUL-II windmill farm using the SWAN model. The effect of a single monopile on incident waves with realistic spectra was also studied. In the single windmill study the monopile was represented as a closed circular obstacle and in the hindcast study it was represented as a dry grid point. The results showed that the single windmill monopile creates a shadow zone in the down wave region with lower significant wave height (H_s) values and a slight increase of H_s in the up wave region. The effects of the windmill monopile on the wave field were found to be dependent on the directional distribution of the incoming wave spectrum and also on the wave diffraction and reflection. The hindcast study showed that the group of windmill monopiles may contribute to the reduction of the wave energy inside the offshore wind farm and that once the waves enter into the offshore wind farm they experience modifications due to the presence of the windmill monopiles, which cause a blocking of the wave energy propagation resulting in an altered distribution of the H_s field.