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The answer here What is the rotating gold object on the outside of ISS? describes in detail what the rotating dish is, and what the package is used for. However, it is not clearly explained why specifically the dish needs to rotate.
Why does the dish need to rotate? Why do the instruments mounted on the dish need to rotate?
The unobstructed 360 degree spin gives it a very wide scanning range, approximately 1000km wide, it allows the instrument to scan both fore and aft per scan - around a 1000km in front and 350km aft - this allows more accurate observations in terms of wind direction retrieval (because wind direction from the ocean is periodic, adding a second observation increases accuracy) and also observations of a 3D storm structure, useful for tropical cyclone monitoring showing tilted eye walls which are an indicator of upper level sheer.
This document is from when COWVR was projected to be mounted on a satellite (before it became an ISS payload):
https://trs.jpl.nasa.gov/bitstream/handle/2014/49850/CL%2318-2716.pdf
Ref: COWVR_2014_AMS_extended_abstract.pdf
Additional links, including WindSat refs:
Although not COWVR, its predecessor is WindSat the older, larger, heavier design on a sun-synchronous orbit.
https://apps.dtic.mil/sti/pdfs/ADA464841.pdf
https://www.eoportal.org/satellite-missions/ors-6#cowvr-mission
https://www.eoportal.org/satellite-missions/iss-stp-h8#cowvr-compact-ocean-wind-vector-radiometer
https://www.star.nesdis.noaa.gov/mirs/windsat.php
https://www.remss.com/missions/windsat/
https://www.ospo.noaa.gov/Products/land/smops/sensors_WindSat.html
http://apdrc.soest.hawaii.edu/datadoc/windsat_day.php
https://www.remss.com/missions/windsat/
https://images.remss.com/windsat/windsat_data_daily.html
https://www.esmats.eu/amspapers/pastpapers/pdfs/2006/koss.pdf
The dish is a reflector (like a radar antennae). It spins for the same reason as a radar dish: it is scanning.
The electronics don't want to spin (can you imagine the tangled mess of wires?) so they remain stationary. The reflector spins and reflects the signal to its spin axis where a non-spinning waveguide (labeled "feed horn" in the diagram) conducts the signal to the electronics.
