Surface waves vs longitudinal waves

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in fluid only longitudinal waves propagate but in Ocean water both transverse and longitudinal waves propagate. Does that mean Ocean water is not a fluid? I am confused. Can anyone explain please.(Longitudinal wave is the evidence for Earth core is liquid)
 
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It is my understanding that transverse waves on the ocean are a surface phenomenon, occurring near the boundary of the fluid. They involve rotational trajectories of the fluid molecules with gravity/pressure providing the restoring force. They don't propagate through the bulk of the fluid because shear forces are non existent (or too small to matter).

Some nice animations of the various types of waves can be found here.
 
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Thank you so much for your attempt. I am sorry, I am not convinced though...