<p>The geostrophic equilibrium is indeed without any time evolution, and even the quasi-geostrophic version only introduces a weak time dependence in the momentum equation (but in <span class="math-container">$O(Rossby)$</span>). Geostrophic equilibrium is then purely diagnostic, but not prognostic. Density gradient can only be neutralized by adding some dissipation (either through mixing or friction).</p>
<p>As a quite rough first guess, adding a dissipation coefficient <span class="math-container">$K$</span> and having geostrophic density gradient scaling with the Rossby deformation radius <span class="math-container">$R_d$</span>, I would dimensionnally answer that the typical timescale would be <span class="math-container">$ \tau \sim R_d^2/K$</span></p>
<p>However numerical application with ocean value of horizontal mixing <span class="math-container">$K \approx 1 \,m^2/s$</span> and <span class="math-container">$R_d \approx 50 \,km$</span> leads to decay in decades (lol).</p>
<p>Some mesoscale eddies can last for as much as 4-5 years, but it probably means that in the real ocean other forcings (atmospheric in particular) can destroy geostrophic structure over shorter timescales.</p>

CC BY-SA 4.0
2022-03-01T13:55:51.753Z
2022-03-01T13:55:51.753Z
Scylla
<p>My professor posed this question, without any relevant material. I suppose the currents last until the density gradient is neutralized, but I can't find any literature nor articles on this, regarding the time scale. Any suggestions? Thanks!</p>

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2021-08-27T13:29:30.397Z
Are you talking about the theoretical/lecture perspective without friction etc.  or a real application? In the case where only the pressure gradient balances the coriolis force, those flows can last indefinetly, because the flow is circular and therefore induces no mass-transport that would eliminate pressure gradients.
AtmosphericPrisonEscape
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2021-08-27T14:20:43.437Z
Thanks for the reply! The question is, as far as I know, applied to real situations. I kept digging around and found that, for the Coriolis force to take non-neglectable effect, the spatial scale should be at least 100 km, then, using the space-time scale in oceanography and combining with average wind speeds, the duration of an average geostrophic currents is somewhere from a week to several months. Is this an acceptable estimate?
a Ljeonjko
<geophysics><oceanography>
How long do geostrophic currents last?
a Ljeonjko
# How long do geostrophic currents last?

(Asked by: username_0 on 2021-08-27)

My professor posed this question, without any relevant material. I suppose the currents last until the density gradient is neutralized, but I can't find any literature nor articles on this, regarding the time scale. Any suggestions? Thanks!

**Tags:** geophysics, oceanography

> **Comments:**
> **username_1**: Are you talking about the theoretical/lecture perspective without friction etc.  or a real application? In the case where only the pressure gradient balances the coriolis force, those flows can last indefinetly, because the flow is circular and therefore induces no mass-transport that would eliminate pressure gradients.  
> **username_0**: Thanks for the reply! The question is, as far as I know, applied to real situations. I kept digging around and found that, for the Coriolis force to take non-neglectable effect, the spatial scale should be at least 100 km, then, using the space-time scale in oceanography and combining with average wind speeds, the duration of an average geostrophic currents is somewhere from a week to several months. Is this an acceptable estimate?  

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## 1 answers

### Answer by username_2 on 2022-03-01. Score: 2

The geostrophic equilibrium is indeed without any time evolution, and even the quasi-geostrophic version only introduces a weak time dependence in the momentum equation (but in $O(Rossby)$). Geostrophic equilibrium is then purely diagnostic, but not prognostic. Density gradient can only be neutralized by adding some dissipation (either through mixing or friction).

As a quite rough first guess, adding a dissipation coefficient $K$ and having geostrophic density gradient scaling with the Rossby deformation radius $R\_d$, I would dimensionnally answer that the typical timescale would be $ \tau \sim R\_d^2/K$

However numerical application with ocean value of horizontal mixing $K \approx 1 \,m^2/s$ and $R\_d \approx 50 \,km$ leads to decay in decades (lol).

Some mesoscale eddies can last for as much as 4-5 years, but it probably means that in the real ocean other forcings (atmospheric in particular) can destroy geostrophic structure over shorter timescales.


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