...I also thought that ideal fluid flow is laminar...Turbulent flow is not characteristic of an ideal fluid flow.
I am assuming that by ideal fluid you mean inviscid fluid. For a flow to be called turbulent, as distinct from a complicated laminar flow, it must possess a few characteristics (see A first course in turbulence by Tennekes and Lumley, chapter 1). Among others, it must contain a 3-dimensional distribution of vorticity, and it must be dissipative. In an ideal fluid, due to absence of viscosity, there is no vorticity generation at walls and other boundaries (because no-slip isn't obeyed). Therefore an ideal fluid of uniform density, which doesn't contain vorticity initially, will be free of vorticity for all subsequent times. Such a flow, no matter how complicated it might become due to inertial instabilities, cannot be called turbulent. If the ideal fluid had some distribution of vorticity to begin with, there is still no dissipation of mechanical energy of the flow due to absence of viscosity. Again as before, no matter how complicated the flow becomes, it can't be called turbulent.
Vorticity can be generated in an inviscid fluid by other means, for example due to unstable density differences. I am not aware of dissipative mechanisms other than due to viscosity. So perhaps absence of dissipation won't allow an ideal fluid flow to be called turbulent. But the ideal fluid flow may be as complicated as a turbulent flow.
I am not sure of @tpg2114 's claim that "...energy cascade and dissipation rate in turbulent flows is due to the viscosity." Dissipation I agree with, but energy cascade is due to inertial instabilities which (as far as I am aware) has no connection with viscosity. Viscosity dissipates mechanical energy of the flow, and sets the smallest scale at which turbulent fluctuations can occur. In a dissipative fluid, a continual supply of energy from outside is needed to maintain turbulence; in the absence of viscosity, such a continual supply isn't required (fluid's kinetic energy is conserved at all times), but energy cascade can still happen and the resulting flow may appear as complicated as a turbulent flow. However there isn't viscosity to set the smallest scale, so the velocity profile may develop singularities (since ideal fluids don't exist, it's all hypothetical anyway).
...an ideal fluid flow is approximated by real fluid flow with a high Reynolds number...The Reynolds number being very large corresponds to the shear stress being negligible.
That's correct. Viscous effects aren't negligible in certain portions of the flow (as @ChesterMiller pointed out), for example at rigid boundaries where a real fluid must obey no-slip condition. Away from such regions, the average flow may be approximated as that of an ideal fluid. Bernoulli equation is approximately valid for the average flow. (I presume you are familiar with Reynolds averaging of turbulent flows)