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Rui Xin Huang

Abstract

A one-and-one-half layer, reduced gravity model has been studied numerically in parallel to previous analytical studies by Huang and Flierl. The main emphasis is on a strong nonlinearity associated with the layer depth, especially when the lower layer outcrops.

The numerical results show some highly asymmetric circulation patterns in a subtropical/subpolar basin, even when the wind forcing is symmetric with respect to the zero-wind-curl line. When the lower layer outcrops in the subarctic gyre, there is a closed loop of boundary currents, including an isolated northern boundary current, an isolated western boundary current, and an interior boundary current. All these currents have structures consistent with the theoretical analysis by Huang and Flierl.

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Rui Xin Huang

Abstract

The parameter sensitivity of a continuously stratified model of the ideal-fluid thermocline in the subtropical gyre interior is studied. A one-dimensional advection–diffusion model is used to set up a background stratification that can provide both the potential vorticity function for the unventilated thermocline and the mixed layer depth used in the ideal-fluid thermocline model. The wind-driven circulation is treated as a perturbation to this background stratification. Although the perturbation solution excludes mixing/diffusion, the dynamic effect of diapycnal mixing is included in the unperturbed solution; therefore, the ideal-fluid solution should correspond to a nonzero diffusion solution for the wind-driven and thermohaline circulation in the ocean.

It is shown that the model can reproduce the thermocline structure, which corresponds to either finite or infinitely weak mixing. Under the extreme weak diffusion limit, the model produces a thermocline that looks like a step function in the stratification, which separates the wind-driven gyre above it and the stagnant abyssal water underneath it.

It is shown that the subduction rate and production of mode water with low-potential vorticity are closely related to the stratification (or the potential vorticity) of the unventilated thermocline, the geometry of the mixed layer, the Ekman pumping rate, and the orientation of the intergyre boundary. Changes in the structure of the thermocline in response to different upper boundary conditions are explored. It is found that cooling and southward migration of the jet stream induce the production of low potential vorticity mode water, while changes in the vertical density profile have an appearance like the second baroclinic mode.

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Rui Xin Huang

Abstract

Climate variability in the subtropical gyre interior induced by anomalous surface thermal forcing, Ekman pumping, mixed layer depth variability, and anomalous subpolar water formation is examined, using a continuously stratified model of the ideal-fluid thermocline. Cooling (heating) induces a negative (positive) potential vorticity perturbation in the ventilated thermocline, and the associated density perturbations propagate downstream in the form of second and higher baroclinic modes. The second baroclinic mode resembles the traditional second baroclinic mode because it has a thermal structure with cooling (warming) in the upper thermocline and warming (cooling) in the lower thermocline.

Anomalous Ekman pumping can also induce density perturbations that propagate westward in the form of the first baroclinic mode. In addition, if the outcrop lines are nonzonal, there are density perturbations that propagate downstream in the form of the second or third baroclinic modes. Perturbations in the sea surface elevation are mostly confined to the region of anomalous forcing. On the other hand, when the low potential vorticity anomaly in the subpolar mode water spreads into the subtropical basin, both the unventilated and ventilated thermocline move downward. Consequently, temperature at a given depth seems to increase.

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Rui Xin Huang

Abstract

An exact analytical solution for the ideal-fluid thermocline is discussed. The solution is calculated from the specified functional relations: for the ventilated thermocline it is a linear functional relation between the potential thickness and the Bernoulli function, and for the unventilated thermocline the potential thickness is a constant. The solution satisfies the most important dynamic constraints—the Sverdrup relation and other boundary conditions. For any given Ekman pumping field, the surface density that satisfies the a priori specified potential thickness function is calculated as part of the solution. Climate variability induced by surface cooling/heating is inferred from the construction of the Green function. It is shown that for the model based on the special functional form discussed in this paper, the cooling-induced anomaly is in the form of the second dynamic thermocline mode that has a zero-crossing in the middle of the thermocline, resembling the second baroclinic mode defined in the classic stability analysis.

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Rui Xin Huang

Abstract

A two-layered ventilated thermocline model is matched with inertial western boundary currents in the southern part of the western boundary region. For general cases the western boundary currents break down much earlier than expected from general physical considerations. In fact, the boundary layer solutions appear in the form of two disconnected branches, i.e., the northern/southern or upper/lower branches. When the external parameters of the midocean thermocline are altered the distance between these two branches of the solution also changes. It is shown that for special values of parameters these two branches join smoothly and form a solution extending continuously to high latitude. Thus, in terms of the climatological mean circulation the midocean thermocline seems to have self-adjusted so as to avoid discontinuity in the western boundary region. In other words, the external parameters for the midocean thermocline have to satisfy some intrinsic constraints imposed by western boundary currents.

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Rui Xin Huang

Abstract

Recent developments of ideal-fluid thermocline models are briefly reviewed. Using density coordinates, boundary value problems are formulated for the ideal-fluid thermocline with continuous stratification. Ekman pumping and surface density are specified as the upper boundary conditions. No flow is permitted through the ocean's eastern boundary nor its bottom. Each water column is divided into three parts, i.e., the stagnant abyssal water with specified stratification the unventilated thermocline with its potential vorticity specified, and the ventilated thermocline with its potential vorticity determined by a global dynamic balance. The unventilated thermocline is further divided into the shallow and deep parts, potential vorticity is specified a priori for the latter, however, for the former, potential vorticity has to be chosen in the process of calculating the solution so as to make the solution self-consistent.

Numerical integration of the ideal-fluid thermocline equations is reduced to repeatedly integrating a second-order ordinary differential equation at each station. This integration process reveals the nonlinear interaction between the ventilated and unventilated thermocline and sheds light on the long-pursued question of how the potential vorticity field is determined in the ventilated thermocline of a continuously stratified ocean. A numerical example shows the three-dimensional circulation pattern of a wind-driven ocean interior with continuous stratification, including a subtropical gyre and a subpolar gyre.

The novel contributions in this study are formulating the suitable boundary value problem of the continuously stratified thermocline equations and solving these problems numerically.

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Rui Xin Huang

Abstract

From an examination of possible ways to satisfy the essential upper boundary conditions, a general way to solve the ideal fluid thermocline is proposed. Through specifying the functional relation between the potential vorticity, the density, the Bernoulli functional [fρz = F(ρ, B)], and the sea surface pressure on the western/eastern walls, the problem is reduced to one of repeatedly integrating two first-order ordinary differential equations.

The present model is essentially a diagnostic model. With appropriate choice of F, this model produces three-dimensional thermocline and current structures in a continuously stratified wind-driven ocean that are quite realistic. It also emphasizes the importance of diffusion and upwelling/downwelling in the western/eastern boundary currents and diffusion in the abyssal ocean. The model confirms the conjecture that to solve the ideal fluid thermocline problem, information is needed wherever fluid moves into (or out of) the domain.

The calculated results are very similar to the observed thermocline and current structures in subtropical/subpolar basins.

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Rui Xin Huang

Abstract

A three-layer model is formulated and run numerically in order to understand the highly nonlinear structure of the wind-driven circulation in a basin including both a subtropical and a subpolar gyre. The third layer is assumed to be infinitely deep and motionless. We emphasize the strong nonlinearity associated with large layer thickness change. A broad range of parameters has been tested to explore possible flow patterns.

For cases of weak wind forcing and large amounts of water in the upper layer, the upper layer covers the whole basin. The second layer is stagnant, except near the western boundary. For stronger forcing, closed potential vorticity isolines appear within the second layer and there is a strong nonlinear coupling between the first and second layers.

The numerical results show some flow patterns highly asymmetric with respect to the zero wind-curl line. The potential vorticity distribution in the second layer shows a strong competition between potential vorticity advection, interfacial friction, and along-isopycnal mixing. With only two moving layers, the model produces some structures which are very similar to the results from the primitive equation model developed at the Geophysical Fluid Dynamics Laboratory and to observations.

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Rui Xin Huang

Abstract

A three-layer model, in which both the second and third layers are allowed to outcrop for strong wind forcing, is studied numerically. A broad range of parameters has been tested to explore possible flow patterns.

There are two possible states with outcropping, depending mainly on a nondimensional forcing parameter. For a moderate the second layer outcrops in the subpolar basin, this is called a supercritical state. For a large the third layer outcrops, the hypercritical state.

Including an active second layer provides a very simple model which reproduces many interesting features including one or two fronts in the upper ocean. For certain parameter settings the model reproduces a loop of boundary currents around the edge of an outcropping zone which resembles the current system in the North Atlantic (i.e., the Gulf Stream, the North Atlantic Current, the Greenland Current, and the Labrador Current). Unlike the quasi-geostrophic models which produce symmetric patterns, the present model always produces highly asymmetric circulation patterns in a subtropical–subpolar basin. Within a certain range of the parameter space, the model reproduces a Gulf Stream-like interior boundary current which branches in the middle of the basin. The southern branch moves southward and forms a C-shape structure when the interfacial friction is very weak. For very strong wind forcing the upper layers separate from the eastern wall and form a warm water pool in the southwestern corner of the basin.

The potential vorticity maps in the second layer clearly show zones of different dynamic balance between potential vorticity advection, interfacial friction, air–sea interaction, and isopycnal mixing.

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Rui Xin Huang

Abstract

Using an idealized tube model and scaling analysis, the physics supporting the oceanic thermohaline circulation is examined. Thermal circulation in the tube model can be classified into two categories. When the cooling source is at a level higher than that of the heating source, the thermal circulation is friction-controlled; thus, mixing is not important in determining the circulation rate. When the cooling source is at a level lower than that of the heating source, the circulation is mixing controlled; thus, weak (strong) mixing will lead to weak (strong) thermal circulation.

Within realistic parameter regimes the thermohaline circulation requires external sources of mechanical energy to support mixing in order to maintain the basic stratification. Thus, the oceanic circulation is only a heat conveyor belt, not a heat engine. Simple scaling shows that the meridional mass and heat fluxes are linearly proportional to the energy supplied to mixing.

The rate of tidal dissipation in the open oceans (excluding the shallow marginal seas) is about 0.9–1.3 (×1012 W); the rate of potential energy generated by geothermal heating is estimated to be 0.5 × 1012 W. Accordingly, the global-mean rate of mixing inferred from oceanic climatological data is about 0.22 × 10−4 m2 s−1.

Using a primitive equation model, numerical experiments based on a fixed energy source for mixing have been carried out in order to test the scaling law. In comparison with models under fixed rate of mixing, a model under a fixed energy for mixing is less sensitive to changes in the forcing conditions due to climatic changes. Under a surface relaxation condition for temperature and standard parameters, the model is well within the region of Hopf bifurcation, so decadal variability is expected.

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