# Why an inertial gyro has a frequency and a geostrophic gyro does not?

Inertial flow is given by the balance between Coriolis and centrifugal forces. A geostrophic flow is given by a balance between Coriolis and the gradients of pressure. The frequency of the inertial flow is the Coriolis frequency (at 43.5N, the Coriolis frequency is $$10^{−4}$$ $$s^{−1}$$, which is equivalent to an inertial period of 17.4h). To me this is just the time that a particle takes to perform a full rotation around its center of rotation. Why does this peak shows up in plot like this? Is it because is carrying around a flow field at a certain smaller scale? In a perfect Inertial gyro, since it is at steady state, if you sample in one point you get always the same velocity, right? A perfect geostrophic balance does not have rotation, and I understand that in that case we would have frequency=0. But a little departure from that could give rise to large scale geostrophic gyro (like low pressure systems in the athmosphere). Would not that gyro be associated with a frequency, in the same way the inertial gyro has a frequency? Why it is common to say the geostrophic flows do not have a frequency? For a geostrophic gyro it still takes a certain time to rotate around a center of rotation.

• In inertial flows the only frequency is associated with the Coriolis effect. Meanwhile, in geostrophic balance, the Coriolis is balanced by the pressure gradient. What is the frequency of the pressure gradient? That is the issue. – arkaia Mar 30 at 2:43
• @arkaia Should we edit the question so that it says Coriolis effect and not force :) – gansub Mar 30 at 2:45
• I fell bad being such a pain about it. No need. It just leads to misconceptions. – arkaia Mar 30 at 14:54
• @arkaia No issue. It is not obvious from the question why the geostrophic balance does not lead to a frequency. Can you explain that in a probable answer ? – gansub Mar 31 at 2:03