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“…We solved the velocity field once as it is independent from the species using spectral/hp elements method with 4008 quadrilateral elements and polynomial order 5. For more details on the spectral element method see for example [34][35][36] . We then solve the species transport equations and f-OTD equations in the rectangular domain shown by dashed lines in Figure 6.…”

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“…We solved the velocity field once as it is independent from the species using spectral/hp elements method with 4008 quadrilateral elements and polynomial order 5. For more details on the spectral element method see for example [34][35][36] . We then solve the species transport equations and f-OTD equations in the rectangular domain shown by dashed lines in Figure 6.…”

“…These methods can be computationally prohibitive since a large number of samples are required to obtain a sufficient degree of accuracy. Another class of technique called the polynomial chaos expansion (PCE) is based on the Galerkin projection of the response onto a PCE [8][9][10][11][12][13][14][15][16][17][18]. The efficiency of PCE has been demonstrated for solving elliptic and low Reynolds number fluids problems [19][20][21][22][23][24][25][26][27].…”

“…Uncertainty in modeling procedure and also inaccuracy of the measured data are two main factors in arising epistemic uncertainty. The uncertainty in modeling could be the result of a variety of possibilities including the effects of geometry [30][31][32][33][34] , constitutive laws [35][36][37][38][39][40][41][42][43][44][45][46][47][48] , rheological models [49][50][51] , low-fidelity and reduced-order modeling [52][53][54][55][56][57][58][59][60][61][62][63][64] , and random forcing sources in addition to the random field boundary/initial conditions [65][66][67][68][69][70][71] . In the current work, we seek to fill a gap in the rich literature of investigating flow instabilities inside rotating flow systems by emphasizing on the stochastic modeling of the fluid dynamics and later focusing on the anomalies in the anomalous transport features of such system through statistical and scaling analysis of the response.…”