Hidenori Aiki

Intraseasonal variability in sea surface height over the South China Sea

Intraseasonal sea surface height (SSH) variability and associated eddy energy in the South China Sea is studied using satellite observations and an eddy-resolving, global ocean general circulation model. In both the model hindcast and satellite observations, a conspicuous minimum of intraseasonal SSH variance is found along the continental break between the shallow shelf and deep basin. Specifically strong intraseasonal variability (ISV) exists in the following regions: on the northern continental shelf, in the Gulf of Thailand, and along two bands in the deep basin with the northern band located west of Luzon Strait and the southern one southeast of Vietnam. SSH ISV exhibits clear seasonality. During active seasons, ISV in the deep water, high-variance bands displays robust propagations in the direction of mean flow. Low correlation between observations and model hindcast suggests the importance dynamical instabilities for ISV in the deep basin, in agreement with an energetics analysis. An exception is along the Vietnam offshore jet during summer, where ISV is forced by wind curls created by Annam Cordillera. In shallow waters, especially in the Gulf of Thailand, SSH ISV is dominated by barotropic response to intraseasonal wind stress forcing. The agreement between altimetry and the model simulation in the Gulf of Thailand demonstrates the ability of satellite altimeters to observe SSH variability in shallow shelves of weak tides.

Energetics of the Global Ocean: The Role of Layer-Thickness Form Drag

Abstract Understanding the role of mesoscale eddies in the global ocean is fundamental to gaining insight into the factors that control the strength of the circulation. This paper presents results of an analysis of a high-resolution numerical simulation. In particular, the authors perform an analysis of energetics in density space. Such an approach clearly demonstrates the role of layer-thickness form drag (residual effects of hydrostatic pressure perturbations), which is hidden in the classical analysis of the energetics of flows. For the first time in oceanic studies, the global distribution of layer-thickness form drag is determined. This study provides direct evidence to verify some basic characteristics of layer-thickness form drag that have often been assumed or speculated about in previous theoretical studies. The results justify most of the previous assumptions and speculations, including those associated with (i) the presence of an oceanic energy cycle explaining the relationship between layer-th...

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.

Thickness-Weighted Mean Theory for the Effect of Surface Gravity Waves on Mean Flows in the Upper Ocean

The residual effect of surface gravity waves on mean flows in the upper ocean is investigated using thicknessweighted mean (TWM) theory applied in a vertically Lagrangian and horizontally Eulerian coordinate system. Depth-dependent equations for the conservation of volume, momentum, and energy are derived. These equationsallowfor(i)finiteamplitudefluidmotions,(ii)thehorizontaldivergenceofcurrents,and(iii)aconcise treatment of both kinematic and viscous boundary conditions at the sea surface. Under the assumptions of steadyandmonochromaticwaves anda uniformturbulentviscosity,theTWMmomentum equationsare used to illustrate the pressure- and viscosity-induced momentum fluxes through the surface, which are implicit in previousstudiesofthewave-inducedmodification oftheclassicalEkmanspiralproblem. TheTWMapproach clarifies,inparticular,thesurfacemomentumfluxassociatedwiththeso-calledvirtualwavestressofLonguetHiggins.Overall,theTWMframeworkcanberegardedasanalternativetothethree-dimensionalLagrangian mean framework of Pierson. Moreover, the TWM framework can be used to include the residual effect of surface waves in large-scale circulation models. In specific models that carry the TWM velocity appropriate for advecting tracers as their velocity variable, the turbulent viscosity term should be modified so that the viscosity acts only on the Eulerian mean velocity.

Modeling and energetics of tidally generated wave trains in the Lombok Strait: Impact of the Indonesian Throughflow

[1] This study investigates the possible impact of the Indonesian Throughflow (ITF) on tidally generated internal waves in Lombok Strait and examines the energetics of these disturbances. Using a two‐dimensional nonhydrostatic numerical model which takes into account the variable width of the strait region, two main experiments have been performed, one without and one with an idealized ITF component in the upper layer flowing southward toward the Indian Ocean. These correspond to conditions in boreal winter and summer, respectively. Both experiments show trains of internal solitary‐like gravity waves (ISWs). Overall, ISWs are more numerous on the north side of the sill where the narrower channel in effect amplifies the disturbances. In both experiments about 3.9 GW of energy is injected into barotropic and baroclinic tidal currents, of which about 2.6 GW is radiated away by internal gravity waves. The ITF regulates the way that the radiated energy is partitioned between the two sides of the sill. Without the ITF (boreal winter), the northward radiated energy flux is greater in magnitude than that radiated to the south. However, when the ITF is present (boreal summer), the northward radiated energy flux is smaller in magnitude than that radiated to the south. This result is obtained by diagnosing the flux of the Montgomery potential which can take into account the effect of finite amplitude waves and also offers a simple and robust energy diagnosis in the presence of time mean flows.

An Exact Energy for TRM Theory

Abstract A time residual mean (TRM) energy is obtained by averaging a transformation of the energy of the Boussinesq hydrostatic incompressible equations of motion. The transformation is the fundamental TRM transformation between level Cartesian coordinates and coordinates that are the mean positions of density surfaces. The TRM energy consists of a sum of mean kinetic, mean potential, wave kinetic, and wave potential energies. It is shown that the interaction between the mean kinetic energy and mean potential energy can be expressed entirely in terms of mean fields. The wave forcing of the mean TRM momentum equations is expressed as a divergence. An explicit and exact form of the TRM equations, with the transformed pressure term expressed in terms of the mean and wave fields, is also noted. It is suggested that the mean domain for the TRM equations and the Cartesian domain may not be the same, which would have consequences for the TRM boundary conditions.

A numerical study on the successive formation of Meddy-like lenses

[1] We present a process study on the sustaining mechanism of lens formation using a series of numerical experiments of a density current over a sloping bottom. With a cape along the coastline, water parcels in the bottom density current are shed into the offshore region, leading to periodic formation of anticyclonic lenses as part of baroclinic dipolar vortices. The cyclonic partner is more prominent at the surface, and the coupled vortices are carried by the mean current established in the offshore region. Parameter dependence of dipole generation is examined, which suggests that the background current is necessary for the detached eddies to be coherent in the downstream direction and for shedding events to repeat [Nof and Pichevin, 1996]. It is also shown that the density mixing of the bottom current provides criteria for cyclogenesis at the sea surface. A detailed analysis is given by a five-layer model forced by a water mass source/sink, which reproduces the baroclinic dipolar vortices similar to those observed in the preceding z-coordinate model. We find that the dipole generation is due to the finite amplitude divergence/convergence of the baroclinic current passing the cape [Stern and Chassignet, 2000]. The overall analyses suggest three necessary conditions for successive eddy formation: (1) a localized variation in the coastline causing the finite amplitude disturbance, (2) mixing of Mediterranean Water with the surrounding fluids leading to anticyclonic rotation of Meddies as well as cyclogenesis at the surface, and (3) background currents that advect the detached vortices out of the source region. INDEX TERMS: 4255 Oceanography: General: Numerical modeling; 4219 Oceanography: General: Continental shelf processes; 4520 Oceanography: Physical: Eddies and mesoscale processes; 4528 Oceanography: Physical: Fronts and jets; KEYWORDS: eddy shedding, dense water plume, numerical simulation

A New Expression for the Form Stress Term in the Vertically Lagrangian Mean Framework for the Effect of Surface Waves on the Upper-Ocean Circulation

There is an ongoing discussion in the community concerning the wave-averaged momentum equations in the hybrid vertically Lagrangian and horizontally Eulerian (VL) framework and, in particular, the form stress term (representing the residual effect of pressure perturbations) which is thought to restrict the handling of higher order waves in terms of a perturbation expansion. The present study shows that the traditional pressure-based form stress term can be transformed into a set of terms that do not contain any pressure quantities but do contain the time derivative of a wave-induced velocity. This wave-induced velocity is referred to as the pseudomomentum in the VL framework, as it is analogous to the generalized pseudomomentum in Andrews and McIntyre. This enables the second expression for the wave-averaged momentum equations in the VL framework (this time for the development of the total transport velocity minus the VL pseudomomentum) to be derived together with the vortex force. The velocity-based expression of the form stress term also contains the residual effect of the turbulent viscosity, which is useful for understanding the dissipation of wave energy leading to transfer of momentum from waves to circulation. It is found that the concept of the virtual wave stress of Longuet-Higgins is applicable to quite general situations: it does not matter whether there is wind forcing or not, the waves can have slow variations, and the viscosity coefficient can vary in the vertical. These results provide a basis for revisiting the surface boundary condition used in numerical circulation models.

Successive formation of planetary lenses in an intermediate layer

Abstract We study the formation of lenses of the oceans intermediate water using a 2.5-layerβ-plane primitive equation model with localized injection of water mass. For the injecting rate of 1.0 Sv, we have observed that strong vortices are shed regularly. These vortices propagate westward much faster than the second baroclinic long Rossby wave. They are totally isolated from each other and show strong baroclinicity as well. Moreover, they remain stable over a sufficiently long period of time. Regular formation of such strong vortices in the intermediate layer has not been reported previously. The translation speed is explained using the Eulers momentum integral theorem for the nonlinear baroclinic vortex on the β-plane. We have demonstrated that coupling between the primary motion in the intermediate layer and the secondary motion in the upper layer with a meridional shift is crucial to the fast westward translation of the intense vortices. A simple dispersion formula relating the zonal translation speed with the vortex radius is also derived under the assumption of quasi-geostrophy. It has turned out that the analytical relation explains the numerical results surprisingly well despite the limitation of its derivation.

Comments on “A Combined Derivation of the Integrated and Vertically Resolved, Coupled Wave–Current Equations”

AbstractSeveral equivalent equations for the evolution of the wave-averaged current momentum have been proposed, implemented, and used. In contrast, the equation for the total momentum, which is the sum of the current and wave momenta, has not been widely used because it requires a less practical wave forcing. In an update on previous derivations, Mellor proposed a new formulation of the wave forcing for the total momentum equation. Here, the authors show that this derivation misses a leading-order term that has a zero depth-integrated value. Corrected for this omission, the wave forcing is equivalent to that in the first paper by Mellor. When this wave forcing effect on the currents is approximated it leads to an inconsistency. This study finally repeats and clarifies that the vertical integration of several various forms of the current-only momentum equations are consistent with the known depth-integrated equations for the mean flow momentum obtained by subtracting the wave momentum equation from the to...