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Michael Hantel

Abstract

A nonlinear, time-dependent, baroclinic model is developed for a zonally uniform, tropical, two-layer ocean on a north-south vertical section. The lower layer is infinitely deep, at rest, and at constant temperature. The dynamics of the well-mixed surface layer are described in terms of the components of horizontal mass transport, the specific mass, and the specific enthalpy. The forcing functions of the model are the zonal wind stress, the vertical entrainment of cold water from the lower layer into the surface layer, and the surface thermal energy input. The concept of entrainment forcing is based on the approach of Kraus and Turner for parameterizing the vertical motion of the seasonal thermocline.

Since zonal gradients of all quantities are neglected, the model applies only to the ocean's interior. This is rationalized by oceanographical observations. In particular, the cast-west pressure gradient term is one order of magnitude smaller than the wind stress; it may be considered as an additional forcing function and, as such, absorbed in the zonal wind stress. Scale analysis reveals two time scales inherent in the model: a short scale of 0.2 day governing the mass transport equations, and a long scale of several years governing the conservation equations for mass and enthalpy. Short-term climatic fluctuations may be controlled by the latter scale.

Solutions for the steady state with Rossby number zero are presented. For wind stress and thermal energy input, simple analytic functions similar in shape to observed patterns are used. For the entrainment function three different possible distributions are investigated, all of which have an equatorial maximum attributed to strong vertical mixing in the equatorial undercurrent region. The principle responses of the model are: 1) a meridional pattern of zonal mass transport exhibiting the main observed features, particularly an equatorial countercurrent; 2) a thickness of the mixed layer similar to the observations; and 3) a surface temperature profile with an equatorial minimum. The tendency of this model to develop an equatorial countercurrent is caused by the entrainment forcing. It is shown that entrainment and energy balance are not entirely independent of one another.

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