It is said that the ocarina is a closed-pipe instrument. I remember my high school physics teacher told me that a good example of a closed-pipe instrument was an ocarina. However, as I study about it more, the categorization seems more difficult.
The physical definition of an closed-pipe instrument is this: "an wind instrument of which one end is a fixed-end the other is a free-end, thus generating only odd-number harmonic over tones. (Please refer this page, only Japanese). The clarinet is a typical example of a closed-pipe instrument based on this definition. But it is not convincing to tell people that the clarinet and the ocarina are in same category. It seems to me that one calls the ocarina an closed-pipe judging from the appearance only. According to a music dictionary of mine published from Ongaku-no-Tomo, the ocarina is not categorized as an wind instrument in the first place. It is a kind of vessel flutes where the sound is created by cavity resonation. It appears that the term 'closed' is confusingly used. Kenji Ogawa's website explains how the size and placement of the fingering holes of the flute and ocarina affects the instruments' pitch / notes.
Below is the categorization of wind instruments and the position of the ocarina as I understand it.
I. Categorization by sound origin
A wind instrument generates the sound by the vibration of air cylinder in the pipe. The ocarina is not a wind instrument by this definition because the inside of the ocarina is not pipe-shaped. There is a group of musical instruments called vessel flutes which make the sound by resonation in cavity. Ocarina is categorized as a vessel flute. The ocarina is similar to the recorder in the point that there is a sound hole connected to the air way which opened to the end of the pipe.
II. Categorization by physical definitions
The conclusion here is this: the term 'closed' which categorizes the clarinet as a closed-pipe and the term 'close' which categorizes the ocarina as a closed-pipe are based on different definitions.