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Sea level across the wide warm northeastward current off California is calculated from hydrographic data along 35N using the hydrostatic balance and the assumption that the warm mixed layer water floats on the colder stratified water underneath. It is found that the sea level is higher above the warm water by a maximum of 7 cm in the middle of the flow. However, the mean east/west slope of the sea surface is deduced to be too small to balance the Coriolis force on the northward current. Therefore, geostrophy, as it is usually understood, is not operating strictly within the surface layer itself.

Off the coast of California, a wide (4000 km) warm surface current flows north [

What is not known at the present time is a complete understanding of the internal dynamics of this current. How are the physical forces kept in balance to allow such a large-scale flow to be permanently in a steady state? Where does geostrophy fit in to the picture?

Since it is important to eventually examine all aspects of the enormous physical phenomenon at hand, one characteristic in particular is selected for study below: the sea level elevation across the top of the warm water. Below the surface the warm water forms a lens, convex side down, a mixed layer with temperatures nearly uniform vertically. Sea level is estimated by using the published sea water density values [

Above the warm water lens it might be anticipated that there would exist a large-scale dome in the sea level height with the maximum height of the dome being located over the deepest mixed layer depths in the middle of the current. In general that is what is found below, and the greatest sea level height is computed to be 7 cm. At the moment, there is apparently no way to compare this value with any outside independent information, but there is an internal consistency in the hydrographic data set as explained below.

Consider that the lens of warm surface water is floating on the colder water underneath it and apply the hydrostatic balance in the vertical direction.

ρ 1 g h 1 = ρ 2 g h 2 (1)

where ρ 1 is the density of the cold water at the base of the mixed layer with height h 1 , and ρ 2 is the density of the nearly uniform water of the mixed layer of thickness h 2 . Acceleration of gravity is g.

By definition sigma-t, σ t , is [

σ t = ( ρ − 1 ) × 10 3 (2)

where the density, ρ , is given in units of grams per cubic centimeter. From (1) and (2) comes the difference in sea level, ∇ h , over the warm mixed layer

∇ h = h 2 − h 1 ≈ h 1 ( σ t 1 − σ t 2 ) × 10 − 3 (3)

where σ t 1 is related to ρ 1 and σ t 2 to ρ 2 . In (3) the approximation made is

[ 10 − 3 σ t 2 ] 2 ≪ 1

To make

Station 45 is just outside the western edge of the warm current, and all the sea level height differences in

Sea level over the warm surface water is relatively high as

On each station an STD instrument was used, giving an independent temperature trace continuously as a function of depth, but these data were also read only at the standard depths for publication in the data report [

Besides a sea level variation there is another way a geostrophic balance can take place, and that involves

a horizontal velocity shear in the current that has a magnitude exactly equal to the Coriolis parameter [

Consequently, in conclusion, there appears to be no horizontal balance of forces entirely inside the warm surface flow. Return flows of colder water to the south on either or both sides and below the northward flow must somehow be involved. For example, opposing Coriolis forces might largely cancel each other out. And for conservation of mass, return flows must exist.

If the above method were to be applied to the hydrographic section at 28S in the South Pacific, similar results are expected. That is a possible project for the future.

The largest permanent surface current in the North Pacific is not in geostrophic balance in isolation. This prediction is based on computing the sea level height across the wide warm northward flow off California using closely spaced hydrographic data along 35N. Mean slopes of the sea level obtained are too small to balance the Coriolis force of the estimated north moving current inside the warm mixed layer at the surface. Other ways that the Coriolis force could be balanced are mentioned.

The author declares no conflicts of interest regarding the publication of this paper.