## 1 Introduction
Using the popular lattice Boltzmann LBGK-D2Q9 model, [PERSON] and [PERSON] [15] studied the flow inside lid driven square and triangular cavities. Three different motion conditions and Reynolds numbers between 100 and 10,000 were considered. Code validation was accomplished via comparing their simulations with previous researchers ones. 2D numerical studies of flow inside right-angled isosceles triangular cavities with five cross-sectional aspect ratios \(\Gamma\), was reported by [PERSON] and [PERSON] [16]. When studding shallow cavities with \(0.1\leq\Gamma\leq 0.43\) the instabilities were elliptic in nature. Three different types of instabilities were observed, two of them were oscillatory. The two instabilities for \(\Gamma>0.43\) were identified as centrifugal instabilities. Via employing a spectral collocation method, [PERSON] et al. [17] studied the viscous incompressible flow characteristics inside a lid-driven right-angled isosceles triangular cavity. Three Reynolds numbers, 100, 500, and 1000, were considered. They employed the Chebyshev-Gauss-Lobatto grid and observed that a third-order Adams Bashforth/backward differentiation method was providing good numerical stability, allowing to employ larger time steps. A multigrid algorithm for solving the finite element Navier-Stokes equations at low Reynolds numbers was employed by [PERSON] et al. [18] to study the flow in triangular cavities. The efficiency of the multigrid algorithm was proved, yet, due to grid anisotropy a slight deterioration of the convergence factor was observed. Some of the initial studies focused on flow performance inside trapezoidal lid driven cavities are [19; 20; 21]. [PERSON] and [PERSON] [19] discretized the Navier-Stokes equations using the finite-difference method and studied for the first time the flow structure in a trapezoidal cavity. Two cases with different driven conditions were reported, in the first case, the top-line was driven and on the second case, the top and base lines were driven in the same direction. Steady viscous flow in a trapezoidal cavity was studied by [PERSON] et al. [20]. The vortical structures generated were observed to be highly dependent on the geometry employed. Lid-driven flow in trapezoidal cavities at Reynolds numbers ranging from 100 to 15,000 and using the original 9-bit lattice Boltzmann method, were investigated by [PERSON] et al. [21]. The top angles were varied from 50 to 90 degrees. For a given Reynolds number and as the top angles increased to a value of around 60 degrees, they reported that the vortex near the bottom wall broke up into two smaller vortices. Regarding the latest investigations on trapezoidal cavity flow [22; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33; 34; 35], which is the main focus of the present research, it is noticed that nearly all of the recent work is related to the mixed convection [22; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33; 34; 35]. Air was employed as working fluid in [22; 29; 34; 35], nanofluids applications are introduced in [23; 24; 25; 27; 28; 30; 31; 32], ferrofluids were considered in [26], and non-Newtonian power-law fluids were considered in [33]. Hybrid nanofluid flow with an obstacle inside the domain was as well investigated in [36]. It is observed that, regarding the trapezoidal geometry, there is no research on the vortical structures, topology evolution, transitions, and Hopf bifurcation reported as similar as what has been performed in the present study. The authors believe that this is for the first time to reveal the vortical structures and transitional characteristics of the trapezoidal enclosures. It should be noticed as well that in authors' previous investigations [37; 38; 39; 40], the transitional characteristics of the flow inside a right-angled isosceles triangular lid-driven cavity [37] and two-sided wall-driven square cavity [38] were presented. The critical Reynolds numbers for Hopf and Neimark-Sacker bifurcations were presented for each driving condition, as well as the corresponding Reynold numbers for the appearance of chaos.