Why do we do only a half circle around the Śiva-liṅga?

tradition says not to cross the channel (somasūtra) through which the abhiṣeka water flows, so you go round and come back the same way.

The water poured on the liṅga flows out through a spout and channel called the somasūtra or praṇāla, usually on the north side. This water is considered charged with Śiva’s energy and is treated with great respect, so stepping over it is avoided.

The usual method: begin on the left, walk clockwise up to the channel, turn back without crossing it, and walk anticlockwise to the other side of the channel, then return. Together this forms a crescent shape, which is why it is called the candrākāra or ardha pradakṣiṇā. Many temples guide this with railings or markings.

Practices vary by region and temple; in some, the channel is covered and devotees walk all the way round. Follow what the temple priests indicate. At home, simply turning around in place three times is enough.

Source: Śaiva Āgama and temple tradition · Also called candrākāra pradakṣiṇā

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