Open-ocean response and normal mode excitation in an eddy-resolving general circulation model

Abstract

Analysis of a two-layer, flat-bottom, steady-wind driven, eddy-resolving general circulation model reveals a distinct separation in frequency of baroclinic and barotropic motion in the region distant from the model Gulf Stream. The far-field motions at periods less (greater) than about 100 days are predominantly barotropic (baroclinic), unlike the near-field, eddy-generating, free-jet region which contains barotropic and baroclinic energy throughout the modei frequency range. The far-field barotropic energy produces a peak in the model sea-level spectra between 25 and 50 days with a magnitude comparable to energy levels observed in spectra of sea level from oceanic island tide gauges. The far-field barotropic motion is clearly composed of large-scale, resonant, barotropic normal modes drive by mesoscale activity of the turbulent, free-jet region. Oceanic mesoscale turbulence may therefore provide for planetary normal modes an excitation mechanism distinct from atmospheric forcing. The open-ocean, barotropic, model response is very similar to that of a fluctuating-wind driven model, which suggests that atmospheric and intrinsic forcing of mid-ocean eddies may be of comparable importance.     

Non-hydrostatic and non-linear contributions to the internal wave energy flux in sill regions

A three-dimensional non-linear, non-hydrostatic model in cross-sectional form is used to determine the factors influencing the relative importance of the linear, non-hydrostatic and non-linear contributions to the internal wave energy flux in sill regions due to tidal forcing. The importance of the free surface elevation term is also considered. Idealised topography representing the sill at the entrance to Loch Etive, the site of a recent measurement programme, is used. Calculations show that the non-linear terms in the energy flux become increasingly important as the sill Froude Number (F _s) increases and the sill aspect ratio is increased. The vertical profile of the stratification, in particular its value close to the sill crest where internal waves are generated, has a significant influence on unsteady lee wave and mixed tidal–lee wave generation and the non-linear contribution to the energy flux. Calculations show that as F _s increases, the energy flux due to the non-linear and non-hydrostatic terms increases more rapidly than the linear term. The importance of the non-linear terms in the energy flux also increases as the sill aspect ratio is increased. Increasing the buoyancy frequency reduces the contribution of the non-hydrostatic and non-linear terms to the total energy flux. Also, as the buoyancy frequency is increased, this reduces unsteady lee wave and mixed tidal–lee wave generation. In essence, these calculations show that the energy flux due to the non-hydrostatic and non-linear terms is appreciable in sill regions.     

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.     

Tidal-induced buoyancy flux and mean transverse circulation

A weakly nonlinear model is used to examine the mean transverse circulation (cross-isobath) driven by tidal-induced buoyancy flux. The mean Eulerian flows driven by both the barotropic and baroclinic tide are presented for a semi-infinite wedge. The mean flow driven by the barotropic tide is significant only near the apex where the thickness of the frictional boundary layer is comparable to the water depth. The mean flow there is characterized by a single-cell circulation with offshore flow near the bottom, and its magnitude can reach a few percentage or a significant fraction of the tidal velocity in oceanic applications. The mean flow driven by the baroclinic tide, on the other hand, is characterized by pairs of half-open (on the seaward side) counter-rotating cells, the number of which equals the vertical mode number. For a baroclinic tide propagating onshore, the mean flow near the top and bottom surfaces is always directed offshore and its magnitude can reach a large fraction of the tidal velocity. Taken together, the model thus predicts a mean offshore flow near the bottom while higher up in the water column the mean flow direction is less definite due to the contribution from different tidal components. The model results are consistent with some current measurements over the Georges Bank.     

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.     

Sill dynamics and energy transformation in a jet fjord

A detailed set of observations are presented of the tidal forcing and basin response of Loch Etive, a jet-type fjordic system on the west coast of Scotland. The characteristics of the tidal jet observed during a spring tide are discussed in detail, and with reference to laboratory studies of Baines and Hoinka (1985). Although the system is categorized as a jet basin during spring tides (when the mode-1 densimetric Froude number exceeds 1) and a wave basin during neap tides (when the Froude number remains below 1), a mode-1 baroclinic wave response is observed throughout the spring/neap cycle. Of the total incident tidal energy, 16% is lost from the barotropic tide. The ratio between loss to bottom friction, barotropic form drag and baroclinic wave drag is estimated to be 1:4:1 (1:4:3.3) at springs (neaps). Despite this, during a spring tide, a 20-m amplitude baroclinic mode-1 wave is observed to propagate along the full length of the basin at a speed of 0.2 m s^–1, somewhat slower than the predicted linear mode-1 phase speed. A hydrographic section supports the implication of the dissipation of the baroclinic wave towards the loch head. The stratification of the upper layers is observed to decrease rapidly landward of the 40-m isobath, a possible signature of enhanced diapycnal mixing in the shallower reaches towards the loch head.Responsible Editor: Jens Kappenberg     

Tidal mixing in sill regions: influence of sill depth and aspect ratio

A non-hydrostatic model in cross-sectional form with an idealized sill is used to examine the influence of sill depth (h _s) and aspect ratio upon internal motion. The model is forced with a barotropic tide and internal waves and mixing occurs at the sill. Calculations using a wide sill and quantifying the response using power spectra show that for a given tidal forcing namely Froude number F _r as the sill depth (h _s) increases the lee wave response and vertical mixing decrease. This is because of a reduction in across sill velocity U _s due to increased depth. Calculations show that the sill Froude number F _s based on sill depth and across sill velocity is one parameter that controls the response at the sill. At low F _s (namely F _s ≪ 1) in the wide sill case, there is little lee wave production, and the response is in terms of internal tides. At high F _s, calculations with a narrow sill show that for a given F _s value, the lee wave response and internal mixing increase with increasing aspect ratio. Calculations using a narrow sill with constant U _s show that for small values of h _s, a near surface mixed layer can occur on the downstream side of the sill. For large values of h _s, a thick well-mixed bottom boundary layer occurs due to turbulence produced by the lee waves at the seabed. For intermediate values of h _s, “internal mixing” dominates the solution and controls across thermocline mixing.     

Generation of baroclinic topographic waves by a tropical cyclone impacting a low-latitude continental shelf

Numerical model experiments have been performed to analyze the low-latitude baroclinic continental shelf response to a tropical cyclone. The theory of coastally trapped waves suggests that, provided appropriate slope, latitude, stratification and wind stress, bottom-intensified topographic Rossby waves can be generated by the storm. Based on a scale analysis, the Nicaragua Shelf is chosen to study propagating topographic waves excited by a storm, and a model domain is configured with simplified but similar geometry. The model is forced with wind stress representative of a hurricane translating slowly over the region at 6 km h⁻¹. Scale analysis leads to the assumption that baroclinic Kelvin wave modes have minimal effect on the low-frequency wave motions along the slope, and coastal-trapped waves are restricted to topographic Rossby waves. Analysis of the simulated motions suggests that the shallow part of the continental slope is under the influence of barotropic topographic wave motions and at the deeper part of the slope baroclinic topographic Rossby waves dominate the low-frequency motions. Numerical solutions are in a good agreement with theoretical scale analysis. Characteristics of the simulated baroclinic waves are calculated based on linear theory of bottom-intensified topographic Rossby waves. Simulated waves have periods ranging from 153 to 203 h. The length scale of the waves is from 59 to 87 km. Analysis of energy fluxes for a fixed volume on the slope reveals predominantly along-isobath energy propagation in the direction of the group velocity of a topographic Rossby wave. Another model experiment forced with a faster translating hurricane demonstrates that fast moving tropical cyclones do not excite energetic baroclinic topographic Rossby waves. Instead, robust inertial oscillations are identified over the slope.     

Energy distributions of the large-scale horizontal currents caused by wind in the baroclinic ocean

Wind is the main energy source for the generation of the internal waves and the ocean mixing. Wunsch[1] estimated that about 1 TW (1 TW = 1012 W) energy was transported into the ocean from the winds by us-ing the altimeter data. Watanabe et al.[2] numerically calculated that the mixing processes obtained 0.7 TW energy from the global wind, which afforded most of the energy needed by the maintenance of the Merid-ional Overturning Circulation (MOC). During the past 50 years, in the Norther…     

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.     

Influence of bottom frictional effects in sill regions upon lee wave generation and implications for internal mixing

A cross-sectional nonhydrostatic model using idealized sill topography is used to examine the influence of bottom friction upon unsteady lee wave generation and flow in the region of a sill. The implications of changes in shear and lee wave intensity in terms of local mixing are also considered. Motion is induced by a barotropic tidal flow which produces a hydraulic transition, associated with which are convective overturning cells, wave breaking, and unsteady lee waves that give rise to mixing on the lee side of the sill. Calculations show that, as bottom friction is increased, current profiles on the shallow sill crest develop a highly sheared bottom boundary layer. This enhanced current shear changes the downwelling of isotherms downstream of the sill with an associated increase in the hydraulic transition, wave breaking, and convective mixing in the upper part of the water column. Both short and longer time calculations with wide and narrow sills for a number of sill depths and buoyancy frequencies confirm that increasing bottom friction modifies the flow and unsteady lee wave distribution on the downstream side of a sill. Associated with this increase in bottom friction coefficient, there is increased mixing in the upper part of the water column with an associated decrease in the vertical temperature gradient. However, this increase in mixing and decrease in temperature gradient in the upper part of the water column is very different from the conventional change in near-bed temperature gradient produced by increased bottom mixing that occurs in shallow sea regions as the bottom drag coefficient is increased.     

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.     

A two time-scale model of stratified shelf currents

Stratification is incorporated into an unsteady model of shelf currents by splitting the dynamic response of the flow into two parts, each with its own time scale. The barotropic part of the response is independent of depth and varies rapidly on a short time scale, whereas the baroclinic part depends on depth and changes slowly with time on a long time scale.The three-dimensional model has a continental shelf sloping down from an eastern boundary to the deep ocean. The equations for the barotropic component of the pressure field contain forcing by the wind stress and feedback from the baroclinic field. An integral of the heat equation over the long time scale determines the slow changes in the temperature field and hence in the baroclinic component of the velocity distribution.The temperature field is specified at the start of the numerical calculation. Its subsequent development is controlled by the numerical procedure. It is found that significant changes in the temperature field require a long period of upwelling favourable winds, whereas the longshore currents react more quickly to changes in the wind stress.     

Variability in infragravity wave processes during estuary artificial entrance openings

Intermittently open/closed estuaries (IOCE) are wave-dominated estuaries with entrances that temporarily close to the ocean. Wave–current interactions play a major role in estuary entrance morphodynamics and influence the degree of energy transfer from the ocean into the lagoon. This study utilizes artificial entrance openings of multiple ICOE in Victoria, Australia, to capture continuous hydrodynamic and geomorphic data throughout the opening cycle. We illustrate that water level oscillations in the infragravity (IG) band) are present in the basin during open entrance conditions. IG waves were observed to propagate up to 1.8 km upstream of the mouth while the entrance was open. Our work identifies that changes in cross-sectional area, bed depth at the berm position, and offshore wave height control the magnitude of IG waves within the estuary basin. IG wave magnitude is also tidally modulated and increases with high tides when the nearshore water level is higher. Late during the drainage phase, waves were observed to track the margins of the channel, away from the thalweg, and reach the basin. IG wave energy was highest immediately after the basin had ceased draining and while channel dimensions at the mouth were within 10% of their maximum value. As the entrance aggrades, IG wave magnitude decreases in the absence of energetic offshore wave conditions. We relate the changes in IG wave magnitude and frequency to a six-stage conceptual model of the opening–closure sequence. Within the basin, IG wave energy, height and frequency were also consistently highest closer to the mouth and decreased with distance upstream. Our findings indicate that water level oscillations in the IG band are a persistent feature in IOCE and may be the norm rather than the exception in these systems. As IG waves were captured serendipitously as part of a larger field campaign, future work will focus on instrumenting IOCE to gain high-resolution data to quantify IG wave processes during entrance openings. © 2020 John Wiley & Sons, Ltd.     

Maintenance of the mean kinetic energy in the global ocean by the barotropic and baroclinic energy routes: the roles of JEBAR and Ekman dynamics

In order to determine the maintenance mechanisms of the currents of the global ocean, this study investigates the budget of the annual mean kinetic energy (KE) in a high-resolution (0.1° × 0.1°) semi-global ocean simulation. The analysis is based on a separation of the mean KE using the barotropic (i.e., depth-averaged) and baroclinic (the residual) components of velocity. The barotropic and baroclinic KEs dominate in higher and lower latitudes, respectively, with their global average being comparable to each other. The working rates of wind forcing on the barotropic and baroclinic circulations in the global ocean are 243 and 747 gigawatts, respectively. This study presents at least three new results for the budget of the barotropic KE. Firstly, an energy diagram is rederived to show that the work of the barotropic component of the horizontal pressure gradient (HPG) is connected to the work related to the joint effect of baroclinicity and bottom relief (JEBAR), and then to the budget of potential energy (PE). Secondly, the model analysis shows that the globally averaged work of the barotropic HPG (which is connected to the work related to JEBAR and then to the budget of the PE) is nearly zero. This indicates that the wind- and buoyancy-induced barotropic circulations in the global ocean are of the same strength with opposite sign. Thirdly, it is found that the work of the wind forcing on the barotropic component of the simulated Antarctic Circumpolar Current (ACC) is canceled by the combined effect, in equal measure, of the work of the barotropic HPG and the work of dissipative processes for mean KE. This result makes a significant contribution to the discussion on the depth-integrated momentum balance of the ACC. The barotropic KE is dissipated by the effects of bottom frictional stress, lateral frictional stress, and the Reynolds stress, of which more than half is attributed to an unexpectedly large contribution from biharmonic horizontal friction. Future studies should pay more attention to the role of biharmonic friction used in high-resolution numerical models.     

The scattering of Rossby waves from finite abrupt topography

The scattering of first mode linear baroclinic Rossby waves by a top-hat ridge in a continuously stratified ocean, with Brunt-Väisälä frequency that decays exponentially with depth below a surface mixed layer, is the subject of this study. A numerical mode matching technique is used to calculate the transmission coefficients for the propagating modes over the ridge. It is found that the scattered field depends crucially upon the stratification. For example, when the majority of the density variation is confined to a thin thermocline, corresponding to a small e-folding scale, gamma ^?1, for the Brunt-Väisälä frequency, a large amount of the incident wave energy is reflected by a small amplitude ridge. Appreciable energy conversion between the propagating barotropic and baroclinic modes takes place in this case. An asymptotic analysis for a small amplitude ridge is presented that confirms these numerical results. In the limit gamma ^?1→ 0, it is demonstrated that the scattered field in the continuously stratified ocean model differs markedly from the two-layer solution. The latter does not exhibit appreciable reflection of the incident wave energy for a small amplitude ridge. In conclusion, the application of a two-layer ocean model to describe Rossby wave scattering by ridges in place of a continuously stratified model cannot be recommended.     

The effects of vertical shear and stratification on stationary rossby waves

Abstract

The generation of stationary Rossby waves by sources of potential vorticity in a westerly flow is examined here in the context of a two-layer, quasi-geostrophic, β-plane model. The response in each layer consists of a combination of a barotropic Rossby wave disturbance that extends far downstream of the source, and a baroclinic disturbance which is evanescent or wave-like in character, depending on the shear and degree of stratification. Contributions from each of these modes in each layer are strongly dependent on the basic flows in each layer; the degree of stratification; and the depths of the two layers. The lower layer response is dominated by an evanescent baroclinic mode when the upper layer westerlies are much larger than those in the lower layer. In this case, weak stationary Rossby waves of large wavelengths are confined to the upper layer and the disturbance in the lower layer is confined to the source region.

Increasing the upper layer flow (with the lower layer flow fixed) increases the Rossby wavelength and decreases the amplitude. Decreasing the lower layer flow (with the upper layer flow fixed) decreases the wavelength and increases the amplitude. Stratification increases the contribution from the barotropic wave-like mode and causes the response to be confined to the lower layer.

The finite amplitude response to westerly flow over two sources of potential vorticity is also considered. In this case stationary Rossby waves induced by both sources interact to reinforce or diminish the downstream wave pattern depending on the separation distance of the sources relative to the Rossby wavelength. For fixed separation distance, enhancement of the downstreatm Rossby waves will only occur for a narrow range of flow variables and stratification.     

西沙群岛西北深水海域的内潮特征分析

基于海南岛至西沙群岛之间深水海域一长达5年的锚定潜标测流资料,采用谱分析、调和分析和动力模态分解等方法主要分析了局部海域内潮的基本特征.结果表明:研究海域的正压和斜压潮均以全日振荡为主,500~900m的海洋中层全日等密度线垂向振幅可达40m;全日内潮主要沿垂直于陆坡方向传播,与天文潮锁相的全日内潮可占全日内潮总能量的41%;海洋上层,O1内潮垂向平均振幅与局地海面高度呈显著正相关关系,K1内潮则表现为夏、冬季增强的半年循环特征;超过70%的O1分潮能量集中于第一、二斜压模态上,K1分潮在第三斜压模态上亦有相当能量.     

基于混合波场地震动输入技术的近海场地地震反应分析方法

基于人工边界子结构模型,提出一种利用混合波场实现近海场地中地震P波和SV波垂直输入的方法.该方法中用于波动输入的混合波场由计算模型两侧截断边界的自由波场和底面边界的入射波场构成,避免了不规则近海场地的自由波场求解.同时采用基于声流体单元的流固耦合算法模拟场地-海水动力相互作用,利用流体介质人工边界和黏弹性人工边界单元模...