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On the nonlinear three-dimensional models in equatorial ocean flows

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  • The paper focusses on some of the recent breakthroughs in the development of models for nonlinear, three-dimensional Equatorial oceanic flows by Constantin and Johnson. The unique character of the formulations is in the systematic approach followed, while making approximations as required, and consequently assessing the implications. These Constantin-Johnson type of models are general enough, as effects such as that of Earth's rotation, Coriolis term, stratification, thermocline, pycnocline, density variations and vertical velocities can be accounted for. Exact solutions based on the use of singular perturbation theory have been obtained for several different cases and situations. The novelty in the models lies in the introduction of a quasi-stream-function which facilitates the derivation of the solutions. Analytical results are supplemented with some numerical illustrations to provide a flavour of the complex flow structures involved. Insights are provided into the velocity field and flow paths, indicating the presence of cellular structures, upwelling/downwelling and subsurface ocean 'bridges'.

    Mathematics Subject Classification: Primary: 35Q31, 35Q35; Secondary: 76B70.


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  • Figure 1.  (A) The rotating frame of reference for the Earth with the North pole, South pole and the Equator indicated (as well as the rotation direction around the polar axis). (B) The spherical coordinate system

    Figure 2.  (A) Horizontal velocity, $ v $. (B) Vertical velocity, $ w $ (see [2])

    Figure 3.  Streamlines in the $ y $-$ \zeta $ plane at $ x = 0.5 $ for $ \omega = 0.3 $ (see [2])

    Figure 4.  Evolution of in-plane velocity amplitude maps in the $ y $-$ \zeta $ plane along the azimuthal $ x $ axis for $ \omega = 0.3 $ (see [2])

    Figure 5.  3D flow paths for quadratic-quartic EUC profile with paths initiating from points (A) near surface (B) at intermediate depth (see [1])

    Figure 6.  (A) Contour plot of the meridional (nondimensional) velocity component (B) Plots of two examples of upwelling (red - on the left) and downwelling (green - on the right) (see [17])

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