Not sure about what you want to know, in turbulence regime there is a wide range of frequencies not a single one as happens in laminar vortex shedding. However, one can consider the averaging to determine the main frequency.

If you consider a single vortex shedding frequency, the lift and the drag are clearly both subject to the shedding but while the lift force is acted by one event in a full period, the drag is involved twice in a period.

https://www.sciencedirect.com/search?qs=Vortex%20shedding%20frequency&show=25&sortBy=relevance

Thank you Md. Washim Akram

Could you provide a simple explanation, please?

Not sure about what you want to know, in turbulence regime there is a wide range of frequencies not a single one as happens in laminar vortex shedding. However, one can consider the averaging to determine the main frequency.

If you consider a single vortex shedding frequency, the lift and the drag are clearly both subject to the shedding but while the lift force is acted by one event in a full period, the drag is involved twice in a period.

if I have a pendulum hanging in water fluid or building with wind flowing, the building experiences lateral and longitudinal frequency.

I read that the lateral frequency is half the longitudinal one?

Is it right and why?

Thanks Filippo Maria Denaro

Vortex shedding from a symmetric bluff body involves alternate shedding of vortices from the top and bottom sides. See, for instance, the red and blue blobs of vorticity in the top figure at:

Thesis On the planar flow development and structural loading of cyl...

The vorticity contained in these blobs originates from the separated shear layers that roll up on either side. Because the shear layers on the top and bottom sides contain opposite signs of vorticity, you see them as red and blue, respectively, in this figure. You can imagine that the shedding of red and blue blobs would induce opposite lift forced on the body; hence, a single cycle in the time history of the vertical (i.e., lateral in your terms) corresponds to the shedding of one red and one blue blob. On the other hand, the longitudinal force due to each vortex (red or blue, i.e., shed from top or bottom) is the same. Thus, the shedding of each single blob (red or blue) gives rise to a longitudinal force impulse, and hence, the cycle is only half as long.

I invite you to see:

https://vtechworks.lib.vt.edu/bitstream/handle/10919/32236/01e_Exploring_and_Envisioning_Periodic_Laminar_Flow.pdf?sequence=1&isAllowed=y

(pages 88 to 94) where we analyzed the periodic laminar flow, and specifically the contributions of pressure and viscous forces over the drag and lift on a cylinder divided in four arcs.

In a simply way, laminar flow (same concept I consider must be applied for turbulent flow) around an object, must reach the other side of the object with maximum velocities that alternates in two opposite preferent sides around this object. There are also two alternative vortices in the rear space of the object which contributes symetrically twice in a complete lift cycle to the drag effect. Frontal and rear sections shows contributions that tends to cancel values but frontal are around 42% greater than rear contributions to the drag force, all with the twice frequency, so the final result is an attenuated wave with an almost constant drag value.

Hope this help.

thank you Miguel Dario Ortega