  The interplay between viscoelasticity and inertia in dilute polymer solutions
at high deformation rates can result in inertio-elastic instabilities. The
nonlinear evolution of these instabilities generates a state of turbulence with
significantly different spatio-temporal features compared to Newtonian
turbulence, termed elasto-inertial turbulence (EIT). We explore EIT by studying
the dynamics of a submerged planar jet of a dilute aqueous polymer solution
injected into a quiescent tank of water using a combination of schlieren
imaging and laser Doppler velocimetry (LDV). We show how fluid elasticity has a
nonmonotonic effect on the jet stability depending on its magnitude, creating
two distinct regimes in which elastic effects can either destabilize or
stabilize the jet. In agreement with linear stability analyses of viscoelastic
jets, an inertio-elastic shear-layer instability emerges near the edge of the
jet for small levels of elasticity, independent of bulk undulations in the
fluid column. The growth of this disturbance mode destabilizes the flow,
resulting in a turbulence transition at lower Reynolds numbers and closer to
the nozzle compared to the conditions required for the transition to turbulence
in a Newtonian jet. Increasing the fluid elasticity merges the shear-layer
instability into a bulk instability of the jet column. In this regime, elastic
tensile stresses generated in the shear layer act as an "elastic membrane" that
partially stabilizes the flow, retarding the transition to turbulence to higher
levels of inertia and greater distances from the nozzle. In the fully turbulent
state far from the nozzle, planar viscoelastic jets exhibit unique
spatio-temporal features associated with EIT. The time-averaged angle of jet
spreading, an Eulerian measure of the degree of entrainment, and the centerline
velocity of the jets both evolve self-similarly with distance from the nozzle.
The autocovariance of the schlieren images in the fully turbulent region of the
jets shows coherent structures that are elongated in the streamwise direction,
consistent with the suppression of streamwise vortices by elastic stresses.
These coherent structures give a higher spectral energy to small frequency
modes in EIT characterized by LDV measurements of the velocity fluctuations at
the jet centerline. Finally, our LDV measurements reveal a frequency spectrum
characterized by a $-3$ power-law exponent, different from the well-known
$-5/3$ power-law exponent characteristic of Newtonian turbulence.
