The vertical structure of the surface wave radiation stress for circulation over a sloping bottom as given by thickness-weighted-mean theory

Previous attempts to derive the depth-dependent expression of the radiation stress have led to a debate concerning (i) the applicability of the Mellor approach to a sloping bottom, (ii) the introduction of the delta function at the mean sea surface in the later papers by Mellor, and (iii) a wave-induced pressure term derived in several recent studies. The authors use an equation system in vertically Lagrangian and horizontally Eulerian (VL) coordinates suitable for a concise treatment of the surface boundary and obtain an expression for the depth-dependent radiation stress that is consistent with the vertically integrated expression given by Longuet-Higgins and Stewart. Concerning (i)-(iii) above, the difficulty of handling a sloping bottom disappears when wave-averaged momentum equations in the VL coordinates are written for the development of (not the Lagrangian mean velocity but) the Eulerian mean velocity. There is also no delta function at the sea surface in the expression for the depth-dependent radiation stress. The connection between the wave-induced pressure term in the recent studies and the depth-dependent radiation stress term is easily shown by rewriting the pressure-based form stress term in the thickness-weighted-mean momentum equations as a velocity-based term that contains the time derivative of the pseudomomentum in the VL framework

Energetics of the global ocean: The role of mesoscale eddies

This article reviews the energy cycle of the global ocean circulation, focusing on the role of baroclinic mesoscale eddies. Two of the important effects of mesoscale eddies are: (i) the flattening of the slope of large-scale isopycnal surfaces by the eddy-induced overturning circulation, the basis for the Gent–McWilliams parametrization; and (ii) the vertical redistribution of the momentum of basic geostrophic currents by the eddy-induced form stress (the residual effect of pressure perturbations), the basis for the Greatbatch–Lamb parametrization. While only point (i) can be explained using the classical Lorenz energy diagram, both (i) and (ii) can be explained using the modified energy diagram of Bleck as in the following energy cycle. Wind forcing provides an input to the mean KE, which is then transferred to the available potential energy (APE) of the large-scale field by the wind-induced Ekman flow. Subsequently, the APE is extracted by the eddy-induced overturning circulation to feed the mean KE, indicating the enhancement of the vertical shear of the basic current. Meanwhile, the vertical shear of the basic current is relaxed by the eddy-induced form stress, taking the mean KE to endow the eddy field with an energy cascade. The above energy cycle is useful for understanding the dynamics of the Antarctic Circumpolar Current. On the other hand, while the source of the eddy field energy has become clearer, identifying the sink and flux of the eddy field energy in both physical and spectral space remains major challenges of present-day oceanography. A recent study using a combination of models, satellite altimetry, and climatological hydrographic data shows that the western boundary acts as a “graveyard” for the westward-propagating eddies

A model for the inertial recirculation of a gyre

This paper considers the time-mean circulation of wind-driven ocean gyres in the limit referred to as inertial or almost-free. In this limit, potential vorticity is conserved following the flow with sources and sinks of potential vorticity balancing in an integral sense around the gyre. Approximate analytic solutions are obtained for a continuously stratified quasi-geostrophic ocean by neglecting the relative vorticity in the gyre interiors. The solutions have features similar to those found in the western part of ocean basins both in eddy-resolving numerical models and in observations. In particular, a deep westward recirculation, such as proposed by Worthington (1976) for the Gulf Stream system, arises naturally from the analysis as an enhanced barotropic flow inside the region where the bowl containing the circulation has intersected the ocean floor. This flow, which is driven by eddies and dissipated by bottom friction, leads to a sudden increase in westward velocity similar to that found between 35N and 36N in the long-term current records along 55W discussed by Schmitz (1977, 1978, 1980)

Effect of the Kinematic Lower Boundary Condition on the Spectral and Autocorrelation Structure of Annular Variability in the Troposphere

The dynamical origin of the spectral and autocorrelation structure of annular variability in the troposphere is investigated by a deductive approach. Specifically, the structure of the power spectrum and autocorrelation function of the zonal-mean geopotential is analyzed for the case of a quasigeostrophic spherical atmosphere subject to a white noise mechanical forcing applied in a single Hough mode and concentrated at a particular level in the vertical, with vertically uniform Newtonian cooling and Rayleigh drag concentrated at a rigid lower boundary. Analytic expressions for the power spectrum are presented together with expressions for an approximate red noise (i.e., a Lorentzian-shaped) power spectrum. It is found that for an infinitely deep atmosphere the power spectrum can be well approximated by a red noise process for the first few Hough modes (associated with large Rossby heights), provided the distance from the forcing is not larger than about one Rossby height. When a frictional rigid lower boundary is included, however, the approximation is generally bad. The high-frequency part of the power spectrum exhibits near-exponential behavior and the autocorrelation function shows a transition from a rapid decay at short lags to a much slower decay at longer lags, if the thermal and mechanical damping time scales are sufficiently well separated. Since observed annular variability exhibits the same characteristics, the above results lead to the hypothesis that these characteristics may, to some extent, be intrinsic to the linear zonal-mean response problem—although the need for an additional contribution from eddy feedbacks is also implied by the results

The vertical structure of the surface wave radiation stress for circulation over a sloping bottom as given by thickness-weighted-mean theory

Previous attempts to derive the depth-dependent expression of the radiation stress have lead to a debate concerning (i) the applicability of Mellor’s approach to a sloping bottom, (ii) the introduction of the delta function at the mean sea surface in the later papers by Mellor, and (iii) a wave-induced pressure term derived in several recent studies. The authors use an equation system in vertically Lagrangian and horizontally Eulerian (VL) coordinates suitable for a concise treatment of the surface boundary, and obtain an expression for the depth-dependent radiation stress that is consistent with the vertically-integrated expression given by Longuet-Higgins and Stewart. Concerning (i)-(iii) in the above, the difficulty of handling a sloping bottom disappears when wave-averaged momentum equations in the VL coordinates are written for the development of (not the Lagrangian mean velocity but) the Eulerian mean velocity. There is also no delta function at the sea surface in the expression for the depth-dependent radiation stress. The connection between the wave-induced pressure term in the recent studies and the depth-dependent radiation stress term is easily shown by rewriting the pressure-based form stress term in the thickness-weighted-mean (TWM) momentum equations as a velocity-based term which contains the time derivative of the pseudomomentum in the TWM framework

The relationship between northern hemisphere winter blocking and tropical modes of variability

In the present study, the influence of some major tropical modes of variability on northern hemisphere regional blocking frequency variability during boreal winter is investigated. Reanalysis data and an ensemble experiment with the ECMWF model using relaxation towards the ERA-Interim reanalysis data inside the tropics are used. The tropical modes under investigation are El Niño Southern Oscillation (ENSO), the Madden-Julian Oscillation (MJO) and the upper tropospheric equatorial zonal-mean zonal wind . An early (late) MJO phase refers to the part of the MJO cycle when enhanced (suppressed) precipitation occurs over the western Indian Ocean and suppressed (enhanced) precipitation occurs over the Maritime Continent and the western tropical Pacific. Over the North Pacific sector, it is found that enhanced (suppressed) high latitude blocking occurs in association with El Niño (La Niña) events, late (early) MJO phases and westerly (easterly) . Over central to southern Europe and the east Atlantic, it is found that late MJO phases, as well as a suppressed MJO are leading to enhanced blocking frequency. Furthermore, early (late) MJO phases are followed by blocking anomalies over the western North Atlantic region, similar to those associated with a positive (negative) North Atlantic Oscillation. Over northern Europe, the easterly (westerly) phase of is associated with enhanced (suppressed) blocking. These results are largely confirmed by both the reanalysis and the model experiment

Effect of the Kinematic Lower Boundary Condition on the Spectral and Auto-correlation Structure of Annular Variability in the Troposphere

The dynamical origin of the spectral and auto-correlation structure of annular variability in the troposphere is investigated by a deductive approach. Specifically, the structure of the power spectrum and auto-correlation function of the zonal mean geopotential is analysed, for the case of a quasi-geostrophic spherical atmosphere subject to a white noise mechanical forcing applied in a single Hough mode and concentrated at a particular level in the vertical, with vertically uniform Newtonian cooling and Rayleigh drag concentrated at a rigid lower boundary. Analytic expressions for the power spectrum are presented together with expressions for an approximate red noise, i.e. a Lorentzian shaped power spectrum. It is found that for an infinitely deep atmosphere the power spectrum can be well approximated by a red noise process for the first few Hough modes (associated with large Rossby heights), provided the distance from the forcing is not larger than about one Rossby height. When a frictional rigid lower boundary is included, however, the approximation is generally bad. The high-frequency part of the power spectrum exhibits near exponential behaviour and the auto-correlation function shows a transition from a rapid decay at short lags to a much slower decay at longer lags. Since observed Northern Annular Mode variability exhibits the same characteristics, the above results lead to the hypothesis that these characteristics may be intrinsic to the linear zonal mean response problem—and may neither need to be explained by slow external forcings, nor by more advanced concepts like deterministic low-order chaos, as suggested in the literature

Barotropic variability in the presence of an ocean gyre

We describe results from some idealized numerical calculations in which we examine the influence of a barotropically stable mean flow on wind-driven variability in a flat-bottomed barotropic vorticity equation model. The mean flow has features in common with the vertically integrated time-mean circulation found in eddy-resolving models with a Sverdrup interior, western boundary current and inertial recirculation region. We integrate the equations of motion linearized about this flow and driven by oscillating wind forcing and compare the results with those obtained when the mean state is one of rest. We find that the presence of a mean flow leads to significant distortion of the model response particularly near the western boundary and in the inertial recirculation region. This distortion is characterized by downstream amplification and phase lag compared to the rest mean state cases. It is related, on the one hand, to the distortion of the mean potential vorticity contours from lines of latitude and, on the other, to advection by the mean flow. Possible applications of these results are discussed to explain features of observed variability in the Gulf Stream system and also the anomalous southward intrusion of the Oyashio Current along the coast of Japan

On the relationship between Atlantic Niño variability and ocean dynamics

The Atlantic Niño is the dominant mode of interannual sea surface temperature (SST) variability in the eastern equatorial Atlantic. Current coupled global climate models struggle to reproduce its variability. This is thought to be partly related to an equatorial SST bias that inhibits summer cold tongue growth. Here, we address the question whether the equatorial SST bias affects the ability of a coupled global climate model to produce realistic dynamical SST variability. We assess this by decomposing SST variability into dynamical and stochastic components. To compare our model results with observations, we employ empirical linear models of dynamical SST that, based on the Bjerknes feedback, use the two predictors sea surface height and zonal surface wind. We find that observed dynamical SST variance shows a pronounced seasonal cycle. It peaks during the active phase of the Atlantic Niño and is then roughly 4–7 times larger than stochastic SST variance. This indicates that the Atlantic Niño is a dynamical phenomenon that is related to the Bjerknes feedback. In the coupled model, the SST bias suppresses the summer peak in dynamical SST variance. Bias reduction, however, improves the representation of the seasonal cold tongue and enhances dynamical SST variability by supplying a background state that allows key feedbacks of the tropical ocean–atmosphere system to operate in the model. Due to the small zonal extent of the equatorial Atlantic, the observed Bjerknes feedback acts quasi-instantaneously during the dynamically active periods of boreal summer and early boreal winter. Then, all elements of the observed Bjerknes feedback operate simultaneously. The model cannot reproduce this, although it hints at a better performance when using bias reduction

An exploratory model study of sediment transport sources and deposits in the Bohai Sea, Yellow Sea, and East China Sea

A regional ocean circulation model (ROMS) is used to simulate the Chinese land-derived sediment transport in the Bohai Sea, Yellow Sea, and East China Sea (BYECS). The model includes the effect of currents, tides, and waves on the sediment transport and is used to study the pathway and dynamic mechanisms of the fine-grain sediment transport from the Huanghe River (Yellow River), the Old Huanghe Delta, and the Changjiang River (Yangtze River) in the BYECS. The seasonal variability of the sediment transport in the BYECS and the sources of the Yellow Sea Trough mud patch, the mud patch southwest of Cheju Island, the mud patch offshore from the Zhejiang and Fujian provinces and the Okinawa Trough mud patch are discussed. The results show that the Huanghe River sediment can be transported to the Yellow Sea Trough, but little makes it to the outer shelf while the Old Huanghe Delta sediment is mainly transported to the Yellow Sea Trough. Most of the sediment from the Changjiang River mouth is carried to the mud patch off the coast of the Zhejiang and Fujian provinces but with part of this sediment also transported to the Yellow Sea Trough. The model shows that it is difficult to transport land-derived sediment to the Okinawa Trough mud patch under normal conditions. The model also has difficulty accounting for the deposition of sediment in the region to the southwest of Cheju Island and offshore from the Zhejiang and Fujian provinces, an issue requiring further study