  We study the spin polarization generated by the hydrodynamic gradients. In
addition to the widely studied thermal vorticity effects, we identify an
undiscovered contribution from the fluid shear. This shear-induced polarization
(SIP) can be viewed as the fluid analog of strain-induced polarization observed
in elastic and nematic materials. We obtain the explicit expression for SIP
using the quantum kinetic equation and linear response theory. Based on a
realistic hydrodynamic model, we compute the differential spin polarization
along both the beam direction $\hat{z}$ and the out-plane direction $\hat{y}$
in non-central heavy-ion collisions at $\sqrt{s_{NN}}=200$ GeV, including both
SIP and thermal vorticity effects. We find that SIP contribution always shows
the same azimuthal angle dependence as experimental data and competes with
thermal vorticity effects. In the scenario that $\Lambda$ inherits and
memorizes the spin polarization of strange quark, SIP wins the competition, and
the resulting azimuthal angle dependent spin polarization $P_y$ and $P_z$
agrees qualitatively with the experimental data.
