<p>I believe it makes sense to factor in sea level height. If we assume a northward flow in geostrophic balance (see <a href="https://en.wikipedia.org/wiki/Geostrophic_wind" rel="nofollow noreferrer">geostrophic wind</a>) we have
<span class="math-container">\begin{equation}
fv = \frac{1}{\rho}\frac{\partial p}{\partial x}.
\end{equation}</span></p>
<p>Using the <a href="https://en.wikipedia.org/wiki/Hydrostatic_equilibrium" rel="nofollow noreferrer">hydrostatic relation</a> we can replace the term on the right hand side and find</p>
<p><span class="math-container">\begin{equation}
fv = g\frac{\partial h}{\partial x},
\end{equation}</span>
(I assumed constant density <span class="math-container">$\rho$</span>) or equivalently
<span class="math-container">\begin{equation}
\frac{\partial h}{\partial x} = \frac{fv}{g}.
\end{equation}</span></p>
<p>We can conclude that in order to maintain the geostrophic balance the sea level must rise the further we move east.</p>

CC BY-SA 4.0
2023-05-20T12:19:29.863Z
2023-05-20T12:24:58.420Z
2023-05-20T12:24:58.420Z
Joscha Fregin
<p>A geostrophic current in the northern hemisphere features a pressure gradient force directed towards the left of the current (west if the current heads straight north) and Coriolis force directed to the right. For the pressure gradient to be maintained, I can only conclude that the water on the right side of this current must be denser but instead looking at actual data (for example currents between Catalonia and Balearic Islands) it seems to be the opposite. Is my reasoning correct here or are there other circumstances that affect density distribution along currents?</p>

<oceanography><ocean-currents><mediterranean>
Density of sea water on the side of currents
Redirectk
# Density of sea water on the side of currents

(Asked by: username_0 on 2023-05-19)

A geostrophic current in the northern hemisphere features a pressure gradient force directed towards the left of the current (west if the current heads straight north) and Coriolis force directed to the right. For the pressure gradient to be maintained, I can only conclude that the water on the right side of this current must be denser but instead looking at actual data (for example currents between Catalonia and Balearic Islands) it seems to be the opposite. Is my reasoning correct here or are there other circumstances that affect density distribution along currents?

**Tags:** oceanography, ocean-currents, mediterranean


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## 1 answers

### Answer by username_1 on 2023-05-20. Score: 3 | Accepted answer

I believe it makes sense to factor in sea level height. If we assume a northward flow in geostrophic balance (see [geostrophic wind](https://en.wikipedia.org/wiki/Geostrophic_wind)) we have
\begin{equation}
fv = \frac{1}{\rho}\frac{\partial p}{\partial x}.
\end{equation}

Using the [hydrostatic relation](https://en.wikipedia.org/wiki/Hydrostatic_equilibrium) we can replace the term on the right hand side and find

\begin{equation}
fv = g\frac{\partial h}{\partial x},
\end{equation}
(I assumed constant density $\rho$) or equivalently
\begin{equation}
\frac{\partial h}{\partial x} = \frac{fv}{g}.
\end{equation}

We can conclude that in order to maintain the geostrophic balance the sea level must rise the further we move east.


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