The derivation of a Lagrangian invariant so-called spirality is reviewed through the Lagrangian coordinates. The value of the spirality is fixed up to a gauge transformation. The helicity conservation follows directly from this invariant. Among all ideal flows with zero helicity in a domain of flow frozen into the fluid motion, a special class is introduced. This special topological class has the possibility to transform its spirality to be identically zero everywhere in the domain. For those simply connected domains of motion, a necessary and a sufficient condition is presented for these zero spirality flows.
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