# Upper-Bound General Circulation of the Ocean: A Theoretical Exposition

## Abstract

**:**

## 1. Introduction

## 2. Model Configuration

^{3}He age distribution [21]. In comparison, the Sverdrup velocity only reaches several millimeters per second to yield a basin transit time of several decades, so eddy-mixing should dominate the laminar regimes.

## 3. Upper-Bound GOC

#### 3.1. Interior

#### 3.2. Frontal Jet

#### 3.3. EUC

#### 3.4. MBC

#### 3.5. Recirculation

#### 3.6. MOC

## 4. Sverdrup Perspective

## 5. Conclusions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

EBC | Eastern boundary current |

EUC | Equatorial undercurrent |

GAC | General atmosphere circulation |

GOC | General ocean circulation |

GS | Gulf Stream |

GSE | Gulf Stream extension |

MBC | Meridional boundary current |

MEP | Maximum entropy production |

MOC | Meridional overturning circulation |

NEC | North equatorial current |

NSCC | Northern subsurface countercurrent |

NT | Nonequilibrium thermodynamics |

PV | Potential vorticity |

B | Bernoulli function |

$g\u2019$ | Reduced gravity $\left(=1.3\times {10}^{-2}\mathrm{m}{\mathrm{s}}^{-2}\right)$ |

h | Thermocline depth |

$\overline{h}$ | Mean thermocline depth (=.5 km) |

$\left[h\right]$ | Thermocline depth scale (=2$\overline{h}$ =1 km) |

l | Warm-layer extent (=4000 km) |

M | GS momentum flux at separation |

P | Columnar PV |

$\left[P\right]$ | PV scale ($=\beta l/\left[h\right])$ |

Q | GS mass transport at separation |

${r}_{C}$ | Deformation radius $(={\left({g}^{\prime}\left[h\right]\right)}^{1/2}{\left(\beta l\right)}^{-1}$ = 40 km) |

u | Zonal current |

$\left[u\right]$ | Velocity scale (=${\left({g}^{\prime}\left[h\right]\right)}^{1/2}=3.6\mathrm{m}{\mathrm{s}}^{-1})$ |

v | Meridional current |

y | Latitudinal distance |

$\left[y\right]$ | Distance scale ($=l=4000\mathrm{km})$ |

$\beta $ | Gradient of Coriolis parameter ($=2\times {10}^{-11}{\mathrm{m}}^{-1}{\mathrm{s}}^{-1})$ |

$\epsilon $ | $\equiv {r}_{C}/l=0.01$ |

$\left[\psi \right]$ | Transport scale ($=\left[h\right]\left[u\right]{r}_{c}=144\mathrm{S}\mathrm{v}$) |

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**Figure 1.**The model configuration of a moving warm layer (striped) separated from the motionless cold water by an outcropped thermocline. The prior constraints (boxed parameters) are the latitudinal extent (l), the reduced gravity (${g}^{\prime}$) and the mean depth ($\overline{h}$) of the warm layer. The GOC consists of an interior flow (a), the frontal jet (b), the EUC (c), the MBC (d), the recirculation (e) and the MOC (f), which are considered in separate subsections.

**Figure 2.**Meridional profiles of the warm-layer PV from the coarse-grain (thick dashed) and fine-grain (solid) numerical calculations (adapted from [5]), the thin dashed lines mark the outcrops. The eddy mixing has reduced the PV range to 20% of its laminar range.

**Figure 3.**The model solution plotted against the latitude. Solid and dashed lines are solutions outside the meridional boundary layers and along the meridional boundaries, respectively. The boundary layers along the subtropical front and equator (shaded) have been magnified 21 and 5 times, respectively.

**Figure 4.**A schematic of the EUC when overlain by a tropical layer (polka-dotted). The tropical layer depresses the main thermocline to weaken the EUC via the Bernoulli law. In addition, the tropical layer encroaches on the NEC to reduce the subtropical supply of the EUC, which is also syphoned by the NSCC, resulting in a much-reduced EUC transport.

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Ou, H.-W.
Upper-Bound General Circulation of the Ocean: A Theoretical Exposition. *J. Mar. Sci. Eng.* **2021**, *9*, 1090.
https://doi.org/10.3390/jmse9101090

**AMA Style**

Ou H-W.
Upper-Bound General Circulation of the Ocean: A Theoretical Exposition. *Journal of Marine Science and Engineering*. 2021; 9(10):1090.
https://doi.org/10.3390/jmse9101090

**Chicago/Turabian Style**

Ou, Hsien-Wang.
2021. "Upper-Bound General Circulation of the Ocean: A Theoretical Exposition" *Journal of Marine Science and Engineering* 9, no. 10: 1090.
https://doi.org/10.3390/jmse9101090