Search Results

You are looking at 1 - 10 of 59 items for

  • Author or Editor: Rui Xin Huang x
  • Refine by Access: All Content x
Clear All Modify Search
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.

Full access
Rui Xin Huang

Abstract

Using an ideal-fluid model, the main thermocline in the North Atlantic is reconstructed. The new feature in the model is the use of a nonlinear background stratification calculated from the hydrographic measurements collected on the Discovery cruise along 46–49°N. The basic stratification is assumed to be set up by an external thermohaline circulation and modified by a wind-driven circulation superimposed upon it. The numerical results of the model distinctly show the three-dimensional structure of the main thermocline in the ocean. In addition, the wind-driven gyre reaches a great depth (≈4.5 km), thus topographic effects on the gyre-scale circulation must be considered in further models. The model confirms the classical notion that the basic structure of the main thermocline and the three-dimensional density and velocity fields in the upper ocean can be simulated very well without explicitly including friction in the model.

Full access
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.

Full access
Rui Xin Huang

Abstract

The classic theory of deep circulation by Stommel and Arons is extended to a two-level model. Instead of specifying the interfacial upwelling a priori, it is calculated as part of the solution. The model shows strong upwelling along the southern and eastern boundaries, while the upwelling in the interior ocean is much weaker. With a medium rate of Ekman pumping, the basin is separated into western and eastern regions by critical characteristics. It is shown that across the boundary between the different regions temperature and velocity are continuous, but vorticity (or some higher-order quantity) is discontinuous.

Full access
Rui Xin Huang

Abstract

Recent progress in thermocline theory is linked and demonstrated by a wind-driven three-layer numerical model. The dynamic balances of the circulation of the model are studied through examination of potential vorticity budgets. Potential vorticity balances of two cases of the subcritical state have been calculated over the entire basin and along trajectories. Vorticity budget analysis clearly shows several zones of different dynamics in the gyre scale circulation. High potential vorticity water masses in the subtropical western boundary region are shown to be created by strong lateral momentum mixing and bottom friction implemented in the model. These water masses move into the subtropical gyre interior in the form of high potential vorticity tongues. Within the gyre interior the potential vorticity of the water parcels can be either quasi-conservative (within a regime of weak forcing/diffusion) or slowly modified by local forcing/diffusion. The potential vorticity dynamics in the subpolar gyre shows a similar feature but generally with different sign for the source/sink terms. Along-trajectory analysis of a case of the supercritical state shows clearly four zones of different potential vorticity dynamics, i.e., the frontal zone, the outcropping zone, the subduction zone, and the western boundary zone. These concrete numerical examples illustrate the dynamics of the fundamental regimes in the gyre-scale circulation as discussed in the recently proposed theories of the thermocline.

Full access
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.

Full access
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.

Full access
Rui Xin Huang

Abstract

A two-layer model for the recirculation is studied Initially, a narrow jet of the upper layer moves eastward with the lower layer remaining stagnant. Att = 0 cold air flows over the narrow front region, all the moving water in the upper layer sinks to the lower layer with the momentum vertically well mixed within the lower layer. Thus, cooling creates an unbalanced eastward jet in the second layer and an unbalanced pressure field at a vertical density front. After the geostrophic adjustment a high pressure center south of the front and a low pressure center north of the front are established. These pressure centers drive a much stronger barotropic eastward current slightly north of the pressure center and slow westward return flow in the far field both south and north of the front. Thus, cooling over a narrow stream can intensify an eastward jet and create recirculation gyres both north and south of the stream.

Full access
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.

Full access
Rui Xin Huang

Abstract

Freshwater flux used as a natural boundary condition for the salinity balance is applied to a primitive equation model of the oceanic general circulation. Instead of the relaxation condition or the virtual salt flux boundary conditions used in many existing models, the real freshwater flux across the upper surface is specified as the vertical velocity boundary condition for the continuity equation, and the salinity flux is set to identically zero at the sea surface. Numerical experiments show that a model with the natural boundary conditions runs smoothly.

Much important physics involving the freshwater flux emerge from the new model. The barotropic Goldsbrough–Stommel gyres driven by the precipitation and evaporation, which were excluded in the previous numerical models, are reproduced. In addition, the model's results reveal extremely complex structure of the three-dimensional circulation driven by the freshwater flux. In fact, a relatively small amount of freshwater flux drives very strong meridional and zonal cells and baroclinic gyres, which are 100 times stronger than the driving freshwater flux. Most importantly, the model provides an accurate description of the meridional salt fluxes and their roles in setting up the thermohaline circulation. It is suggested that, with or without the rigid-lid approximation, the real freshwater flux can be used as the upper boundary condition in oceanic general circulation models, including the mixed-layer models, the ice–ocean coupling models, and atmosphere–ocean coupling models.

Full access