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.     

Planetary Boundary Layer Flows in the Atmosphere and the Ocean at the Equator

—The boundary layer flows created by the frictional dissipation of the wind speed at the surface in the atmosphere and by surface wind stress in the ocean at the equator and in the equatorial region, are obtained by taking the influence of the surface friction on the zonal velocity as being balanced by vertical transport for the long-term mean flow and by a corresponding time variation for time-dependent flow fields. Solutions are expressed in terms of the velocities in zonal and vertical directions and the divergence of the horizontal current in the two media. It is found that under the ever present easterly flow in the lower atmosphere, the boundary layer flow in the atmosphere is convergence and ascending motion in the lower troposphere, and divergence at the surface and uplift in ocean, and in reverse directions for the westerly flow. Similar results are obtained for time-dependent wind fields and they give way to the steady asymptotic solutions when the period of the variation exceeds 10 months.     

Influence of open boundary conditions and sill height upon seiche motion in a gulf

A cross-sectional model of an idealised constant depth gulf with a sill at its entrance, connected to a deep ocean, is used to examine the barotropic and baroclinic response of the region to wind forcing. The role of the oceanic boundary condition is also considered. Calculations show that in the case of a tall sill, where the pycnocline intersects the sill, the baroclinic response of the gulf is similar to that of a lake, and internal waves cannot radiate energy out of the gulf. The barotropic response shows free surface oscillations, with nodes located close to the centre of the oceanic basin and entrance to the gulf, with associated barotropic resonant periods. As the sill height is reduced, baroclinic wave energy is radiated from the gulf into the ocean, and the form of the baroclinic response changes from a standing wave (tall sill) as in a lake to a progressive wave (no sill). The location of sea surface elevation nodes and resonant periods changes as the sill height is reduced. Calculations of the barotropic resonant periods with and without stratification could not determine if they were influenced by the presence of stratification, although published analytical theory suggests that they should be able to when energy is lost from the gulf by internal wave radiation. This inability to detect changes in barotropic resonant period due to stratification effects is due to the small change in resonant frequency produced by baroclinic effects, as shown by analytical results, and the broad peak nature of the computed resonant frequency. In the case of a closed offshore boundary (an offshore island), there is a stronger and narrower energy peak at the resonant frequency than when a barotropic radiation condition is applied. However, the influence of stratification upon the resonant frequency could not be accurately determined. Although the offshore boundary was well removed from the gulf to such an extent that any baroclinic waves reflected from it could not reach the gulf within the integration period, it did, however, slightly influence the gulf baroclinic response due to its influence on the barotropic response.     

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.     

On the origin of jets in the ocean

We show a mechanism whereby the jets result during the development of β-plumes (i.e., low-frequency Rossby waves that establish gyre circulations) in a model of ocean-basin circulation. The energy originates in baroclinic meanders of circulation at the eastern boundary of the ocean. Eddies are intimately related and occur as a result of the instability of this process. This mechanism does not rely on the existence of the small-scale turbulence to establish zonal flows. Zonal jets can then be amplified by eddies arranged in certain order in the flow. The underlying dynamics include the propagation of linear and nonlinear basin scale Rossby waves. The related barotropic theory for these waves is developed here. We demonstrate the radiative development of jets and β-plumes in a laboratory experiment using a rotating fluid with a paraboloidal free surface. The dynamical fields are measured by the laboratory analog of the satellite altimetry.     

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.     

Long Wave Resonance in Tropical Oceans and Implications on Climate: the Atlantic Ocean

Based on the well established importance of long, non-dispersive baroclinic Kelvin and Rossby waves, a resonance of tropical planetary waves is demonstrated. Three main basin modes are highlighted through joint wavelet analyses of sea surface height (SSH) and surface current velocity (SCV), scale-averaged over relevant bands to address the co-variability of variables: (1) a 1-year period quasi-stationary wave (QSW) formed from gravest mode baroclinic planetary waves which consists of a northern, an equatorial and a southern antinode, and a major node off the South American coast that straddles the north equatorial current (NEC) and the north equatorial counter current (NECC), (2) a half-a-year period harmonic, (3) an 8-year sub-harmonic. Contrary to what is commonly accepted, the 1-year period QSW is not composed of wind-generated Kelvin and Rossby beams but results from the excitation of a tuned basin mode. Trade winds sustain a free tropical basin mode, the natural frequency of which is tuned to synchronize the excitation and the ridge of the QSWs. The functioning of the 1-year period basin mode is confirmed by solving the momentum equations, expanding in terms of Fourier series both the coefficients and the forcing terms. The terms of Fourier series have singularities, highlighting resonances and the relation between the resonance frequency and the wavenumbers. This ill-posed problem is regularized by considering Rayleigh friction. The waves are supposed to be semi-infinite, i.e. they do not reflect at the western and eastern boundaries of the basin, which would assume the waves vanish at these boundaries. At the western boundary the equatorial Rossby wave is deflected towards the northern antinode while forming the NECC that induces a positive Doppler-shifted wavenumber. At the eastern boundary, the Kelvin wave splits into coastal Kelvin waves that flow mainly southward to leave the Gulf of Guinea. In turn, off-tropical waves extend as an equatorially trapped Kelvin wave, being deflected off the western boundary. The succession of warm and cold waters transferred by baroclinic waves during a cycle leaves the tropical ocean by radiation and contributes to western boundary currents. The main manifestation of the basin modes concerns the variability of the NECC, of the branch of the South Equatorial Current (SEC) along the equator, of the western boundary currents as well as the formation of remote resonances, as will be presented in a future work. Remote resonances occur at midlatitudes, the role of which is suspected of being crucial in the functioning of subtropical gyres and in climate variability.     

Tidally generated internal waves in partially mixed estuaries

The generation of internal waves in the partially mixed estuaries is examined. The numerical experiments consider the barotropic tidal currents interacting with isolated obstacles in an open channel. The bottom boundary layer and longitudinal salinity gradient are included. Internal lee (arrested) waves are excited when the accelerating barotropic tidal current approaches the first-mode internal wave speed. The arrested waves are amplified, and are subsequently released when the decelerating tidal current falls below the first-mode internal wave speed. The power input from the barotropic tidal energy into internal wave energy is calculated. It is on the order of 10⁻² W/m², and is comparable to the estimated interior dissipation rate. This suggests that the tidally generated internal waves could be a significant energy source for mixing in the halocline.     

切变基本纬向流中非线性赤道Rossby长波

为了解决观测和理论研究中的一些问题以及更好地了解热带大气动力学 ,有必要进一步研究基本气流的变化对大气中赤道Rossby波动的影响 .本文研究分析基本气流对赤道Rossby长波的影响 ,利用一个简单赤道 β平面浅水模式和摄动法 ,研究纬向基本气流切变中非线性赤道Rossby波 ,推导出在切变基本纬向流中赤道Rossby长波振幅演变所满足的非线性KdV方程并得到其孤立波解 .分析表明 ,孤立波存在的必要条件是基本气流有切变 ,而且基流切变不能太强 ,否则将产生正压不稳定 .     

A simple numerical experiment concerning the general circulation in the lower stratosphere

Summary By means of highly truncated spherical harmonic expansions, an extended four-level quasi-geostrophic model with variable Coriolis parameter is transformed into a set of ordinary non-linear differential equations. Non-adiabatic effects, frictional dissipation, and boundary effects are approximately included in the equations. A numerical experiment made with the equations succeeds in producing many realistic statistical gross features, especially in the lower stratosphere, e. g., a poleward temperature incrase, the up-gradient horizontal transports of heat and momentum due to large-scale eddies, the upward energy flux of extra-long waves, and the trapping of the upward energy flux of tropospheric unstable waves near the tropopause. The mean energy flow in the lower stratosphere and in the troposphere are analyzed and compared with each other, indicating very clearly the baroclinical activness of the troposphere and the passiveness of the lower stratosphere. The dynamics in the lower stratosphere are discussed. the mean meridional circulation is also studied.     

Can zonally symmetric inertial waves drive an oscillating zonal mean flow?

In the present paper zonal mean flow excitation by inertial waves is studied in analogy to mean flow excitation by gravity waves that plays an important role for the quasi-biennial oscillation in the equatorial atmosphere. In geophysical flows that are stratified and rotating, pure gravity and inertial waves correspond to the two limiting cases: gravity waves neglect rotation, inertial waves neglect stratification. The former are more relevant for fluids like the atmosphere, where stratification is dominant, the latter for the deep oceans or planet cores, where rotation dominates. In the present study a hierarchy of simple analytical and numerical models of zonally symmetric inertial wave-mean flow interactions is considered and the results are compared with data from a laboratory experiment. The main findings can be summarised as follows: (i) when the waves are decoupled from the mean flow they just drive a retrograde (eastward) zonal mean flow, independent of the sign of the meridional phase speed; (ii) when coupling is present and the zonal mean flow is assumed to be steady, the waves can drive vertically alternating jets, but still, in contrast to the gravity wave case, the structure is independent of the sign of the meridional phase speed; (iii) when coupling is present and time-dependent zonal mean flows are considered the waves can drive vertically and temporarily oscillating mean flows. The comparison with laboratory data from a rotating annulus experiment shows a qualitative agreement. It appears that the experiment captures the basic elements of the inertial wave mean flow coupling. The results might be relevant to understand how the Equatorial Deep Jets can be maintained against dissipation, a process currently discussed controversially.     

从经向气流看亚澳季风的季节区域特征

利用1979～2003年的NCEP/NCAR再分析资料探讨了亚澳季风区经向气流的季节性分支和结构特征. 结果表明,亚澳季风区经向气流的垂直斜压结构由冬到夏发生季节性转向,即从冬季时的低层北风、高层南风转换为夏季时的低层南风、高层北风. 季节反向的经向气流主体偏向北半球,其区域差异性在对流层中低层更为显著. 以印度半岛和中南半岛为界,亚洲热带季风区中低层经向气流在冬夏季均呈现三通道特征,与此相应,亚澳季风区自西向东存在三支相对独立的经向环流分支,且冬夏季的差异均很显著,如冬季的中心高度自西向东递减、夏季的经向跨度自西向东递增等.     

Array measurements of the bottom boundary layer and the internal wave field on the continental slope

Abstract

An array of current meters was placed on the continental slope and rise for two months in the autumn of 1970. The bottom boundary layer was penetrated on the slope. On the smallest array scale, of the order of 1 kilometer, the array functioned as a directional internal wave antenna. Moving shoreward, the current spectra show strong suppression of the inertial peak and strong enhancement of the semidiurnal tide. The measured wave number spectra show that the tidal energy is almost completely baroclinic, and probably being generated in the region where the slope becomes “critical” for the tidal period. If this area is typical of worldwide conditions, a substantial fraction of the dissipation of surface tides takes place on the continental slopes by conversion to baroclinic waves. The bottom boundary layer has been modeled by an extension of the work of Ellison (1956) to a sloping boundary in a fluid of positive stability. An equivalent constant eddy coefficient has the value 3 cm²/sec as determined from the measurements.     

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.     

A reduced model for nonlinear dispersive waves in a rotating environment

Abstract

The simplest model for geophysical flows is one layer of a constant density fluid with a free surface, where the fluid motions occur on a scale in which the Coriolis force is significant. In the linear shallow water limit, there are non-dispersive Kelvin waves, localized near a boundary or near the equator, and a large family of dispersive waves. We study weakly nonlinear and finite depth corrections to these waves, and derive a reduced system of equations governing the flow. For this system we find approximate solitary Kelvin waves, both for waves traveling along a boundary and along the equator. These waves induce jets perpendicular to their direction of propagation, which may have a role in mixing. We also derive an equivalent reduced system for the evolution of perturbations to a mean geostrophic flow.     

An external–internal mode coupling for a 3D hydrodynamical model for applications at regional scale (MARS)

This paper presents a 3D model in sigma coordinates. Although the principles it is based on have been established for some time, some original aspects for this type of 3D mode splitting model are presented here. The model was designed to simulate flows in various coastal areas from the regional scale down to the inshore scale of small bays or estuaries where circulation is generally driven by a mix of processes. The processes to be modeled enable simplifications of the Navier–Stokes equations on the classic Boussinesq and hydrostatic hypotheses. These equations are transformed within a sigma framework to make free surface processing easier. The main point of our demonstration focuses on the original aspect of the coupling between barotropic and baroclinic modes especially designed for ADI. It explains how full consistency of the transport calculated within the 2D and 3D equation sets was obtained. Lastly, we describe the physical processes simulated on a realistic configuration at a regional scale in the Bay of Biscay.     

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.     

Changes in the dynamics/energetics of surface and internal tides in the White Sea on the coexistence of shore-fast and drifting ice covers

The results of modeling for _M2${\mathrm{M}}_2$ surface and internal tides in the White Sea are discussed. These results are obtained for the case when shore-fast and drifting ice covers are present concurrently. It is assumed that the interface between ice covers is of non-tidal origin (i.e., it is pre-assigned) and that ice rheology is viscous-elastic, representative of the low temperatures typical of winter conditions. Emphasis is placed on tidal energetics and, in particular, on the averaged (over a tidal cycle) values of the density and the dissipation rate of barotropic/baroclinic tidal energy. It is shown that in the White Sea, unlike in other marginal seas, the averaged (over a tidal cycle) and depth-integrated density of baroclinic tidal energy for the combined ice cover is much less than the same defined density of barotropic tidal energy. Similarly, the averaged and integrated (over the volume of the White Sea) rate of baroclinic tidal energy dissipation is much less than the same defined rate of barotropic tidal energy dissipation. The latter, in turn, is greater than for the shore-fast ice cover, but is smaller than for the drifting ice cover.     

Parametrization of momentum and energy depositions from gravity waves generated by tropospheric hydrodynamic sources

The mechanism of generation of internal gravity waves (IGW) by mesoscale turbulence in the troposphere is considered. The equations that describe the generation of waves by hydrodynamic sources of momentum, heat and mass are derived. Calculations of amplitudes, wave energy fluxes, turbulent viscosities, and accelerations of the mean flow caused by IGWs generated in the troposphere are made. A comparison of different mechanisms of turbulence production in the atmosphere by IGWs shows that the nonlinear destruction of a primary IGW into a spectrum of secondary waves may provide additional dissipation of nonsatu-rated stable waves. The mean wind increases both the effectiveness of generation and dissipation of IGWs propagating in the direction of the wind. Competition of both effects may lead to the dominance of IGWs propagating upstream at long distances from tropospheric wave sources, and to the formation of eastward wave accelerations in summer and westward accelerations in winter near the mesopause.