  A series of new flow observables mixed harmonic multi-particle cumulants
(MHC), which allow for the first time to quantify the correlations strength
between different order of flow coefficients with various moments, was
investigated using hydrodynamic model. These new observables are constructed
based on multi-particle cumulants, and thus by design will be less sensitive to
the non-flow contaminations. In addition to the previous study of correlation
involving two flow coefficients with their second moments, both correlations of
three flow coefficients and the correlations of higher order moments of $v_2$
and $v_3$ are systematically investigated using iEBE-VISHNU hybrid model with
two different initial conditions, AMPT and TRENTo, respectively. These
systematic studies using hydrodynamic models will significantly improve the
understanding on the correlations between different orders (and moments) of
flow coefficients. The hydrodynamic predictions shown in this paper and the
future comparisons to experimental measurements will provide more constraints
on theoretical models and extract more information about the transport
properties of the quark-gluon plasma created in heavy-ion collisions.
