  We study the dynamics and indications of the flows with all the eigenvalues
of the velocity gradients being real, thus `lone', \textit{i.e.}, without
forming the complex conjugate pairs associated to the swirls. A generic
prototype is the `lone Schur flow (LSF)' whose velocity gradient tensor is
uniformly of Schur form but free of complex eigenvalues. A (partial)
integral-differential equation governing such LSF is established, and a
semi-analytical algorithm is accordingly designed for computation. Simulated
evolutions of example LSFs in 2- and 3-spaces show rich dynamics and vortical
structures, but no obvious swirls (nor even the homoclinic loops in whatever
distorted forms) could be found. We discovered the flux loop scenario and the
anisotropic analogy of the incompressible turbulence at or close to the
critical dimension $D_c =4/3$ decimated from 2-space.
