Characterizing elastic turbulence in the three-dimensional von Kármán swirling flow using the Oldroyd-B model

We present the full three-dimensional numerical investigation of von Karman swirling flow between two parallel plates using Oldroyd-B model and characterize onset development elastic turbulence. quantify state with secondary-flow strength, a measure average strength velocity fluctuations, then define an order parameter as time strength. The displays subcritical transition from laminar to bistable that switches weakly chaotic occurs at critical Weissenberg number $\mathrm{Wi_c}=12$. Above $\mathrm{Wi_c}$, in turbulent state, we observe strong increase fluctuations resistance, which total work performed on fluid. Upon starting simulations subsequently lowering $\mathrm{Wi}$ below its value, hysteretic behavior is common feature transition. Hysteresis has also been found experiments. Additionally, find power-law scaling spatial temporal power spectra characteristic for maximum values exponents our are $\alpha_t= 3.41$ exponent $\alpha_s= 3.17$ exponent, remarkably close obtained