  In this paper we derive a new energy identity for the three-dimensional
incompressible Navier-Stokes equations by a special structure of helicity. The
new energy functional is critical with respect to the natural scalings of the
Navier-Stokes equations. Moreover, it is conditionally coercive. As an
application we construct a family of finite energy smooth solutions to the
Navier-Stokes equations whose critical norms can be arbitrarily large.
