Update…

…the answer is, Leno!
It creates a different kind of wave pattern, but the essence is still there. At least with the Leno (warp twist) treatment, there is little chance of the wave shape collapsing.

Conclusion…

The final cloth contains every possible movement I could make with a wavy shuttle, so it is not straight, nor regular. It’s mostly experimental, so please ignore the (many) imperfections!

It would appear that plain weaving with a wavy shuttle does not produce much of a wave pattern. There is evidence of line shifting within the texture, but it is too subtle and not worth getting excited about!

However… my accidental shuttle work has produced waves that appear to work nicely on the loom.

Wave 1: 10 rows of plain weave, then alternated the placement of wavy shuttle and worked 10 rows of plain weave. The warps are exposed and unsupported.

Wave 2: 10 rows of plain weave, then 1 row of 1x1 Leno, then 10 rows of plain weave in alternate placement. The Leno braces the exposed warps, but it does bring down the first and last row of plain weave.

After Blocking…

The cloth was wet blocked in hot water, squeezed in a towel and hung to dry. The cloth held up well to being handled without affecting the pattern. After a few days I ironed it, giving it a few blasts of hot steam. Still looking good!

Generally, both Wave patterns are not as accentuated as they were on the loom, but have held up well without collapsing or losing their ‘prettiness’!

Working notes

Warp: Merino Worsted.
Weft: Airy Singles (fingering) (contains alpaca).
Weft application angle: 55º-65º (higher than the normal 45º).
Beat strength: Firm.