  The writhe polynomial is a fundamental invariant of an oriented virtual knot.
We introduce a kind of local moves for oriented virtual knots called shell
moves. The first aim of this paper is to prove that two oriented virtual knots
have the same writhe polynomial if and only if they are related by a finite
sequence of shell moves. The second aim of this paper is to classify oriented
$2$-component virtual links up to shell moves by using several invariants of
virtual links.
