It is something of a misnomer to speak of CSF “circulation,” particularly in the spinal canal, as there is no continuous loop circulation of CSF as there is in the cardiovascular system.
For quite some time, it has been known that CSF movement results from the formation of new CSF and motion of cilia on the surface of the choroid plexus and ependyma lining the ventricles. - Fluids and Barriers of the CNS
The "circulation" of the CSF, as already mentioned, is something of a misnomer. CSF is not known to "circulate" in the manner of blood. It does get agitated by pressure differentials, and it is 'circulated' in terms of being reabsorbed and replaced every 6-7 hours. Other than that, no circulation occurs.
Blood circulation is not generated only by the heart. Pressure differentials throughout the body affect the circulation of blood as well. One that is easily demonstrated (first documented in 1733) is the effect of intrathoracic (chest) pressure on circulation. The blood pressure of healthy people falls during spontaneous inspiration. When someone takes a deep breath, the blood return to the heart via the vena cava decreases, and pressure is exerted on the right atrium. Both cause decreased filling, which will drop blood pressure. Although this is best demonstrated with a blood pressure cuff, it can be demonstrated without. An unrecommended method is exemplified in a childhood game of passing out. A Valsalva maneuver (deep breath and glottal closure) decreases blood flow to the heart. Squeezing the chest further decreases return, resulting in fainting.
The same pressure differentials agitate the CSF. Additionally, smaller movements were seen with pressure differentials caused by the beating of the heart.
By employing this respiration-induced spin labeling bSSFP cine method, we were able to visualize CSF movement induced by respiratory excursions. CSF moved cephalad (16.4 ± 7.7 mm) during deep inhalation and caudad (11.6 ± 3.0 mm) during deep exhalation in the prepontine cisternal area. Small but rapid cephalad (3.0 ± 0.4 mm) and caudad (3.0 ± 0.5 mm) movement was observed in the same region during breath holding and is thought to reflect cardiac pulsations.
This image from Wikipedia shows "circulation" that normally occurs with heartbeat.
There are other factors that cause movement of CSF, but they are intermittent and variable.
Influence of respiration on cerebrospinal fluid movement using magnetic resonance spin labeling, Yamada et. al., Fluids and Barriers of the CNS 2013, 10:36
MRI showing pulsation of CSF