We used a computational grid consisting of hexagonal element

We used a computational grid consisting of hexagonal elements: about 5·105 gw501516 belonged to the fluid region and 2·105 cells to each of the horizontal walls. The grid was clustered to the walls and to the interface surfaces (the vertical cell dimension near the interface amounted to about 1.5·10–4H). The distribution of the cells in various cross-sections is shown in Fig. 1b,c. The time step was of the order of one thousandth of the characteristic convection time of the problem, defined as
Computational results As noted above, the scale quantities were chosen so as to ensure the effective Rayleigh number close to 106. In order to maintain continuity with the previous study [27], the reference value of the Rayleigh number, selected for solving the non-conjugate problem, was 9.64·105. In solving the conjugate problem, the scale Rayleigh numbers providing Ra= 9.64·105 were selected for three variants with different values of the specified scale rotational parameter, namely, for K 0; 0.499 and 5.823. The selected values of the scale Rayleigh number were, respectively, 2.72·106, 2.66·106 and 1.28·106. The resulting values of the effective rotational parameter K amounted to 0, 0.834 and 6.706. Fig. 2 shows the convective flow structure, simulated in the conjugate setting with three different rotational intensities. At low values of the rotational parameter (K= 0 and 0.834) the flow can be generally characterized as a global convective cell (Fig. 2a, b) whose visual images were earlier presented in [21,23,27]. The flow structure changes with increasing rotation intensity: the convective cell disintegrates into a group of smaller structures (Fig. 2c). Similar changes in the flow structure with increasing rotational parameter were noted by the authors of Ref. [6], who performed the DNS computations with Pr= 0.7, and in Ref. [23] with Pr= 6.4. We should also note that the vertical velocity isosurfaces obtained for the same values of the governing parameters in the non-conjugate computations are similar to those shown in Fig. 2. Fig. 3 shows the pattern of the temporal changes in the dimensionless vertical velocity component, computed for different rotation rates of the container in the conjugate setting (the buoyancy rate =(HgβΔT)0.5 serves as the velocity scale). The time sample (which was also used for averaging) is much longer in the absence of rotation than for the variants with the rotating container. This is due to the fact that the above-mentioned global circulation cell oscillates in space from time to time. However, it can be seen fromFig. 3a that two relatively stable states are observed for this structure. Similar behavior of the numerical solution is also observed in simulations using the ANSYS Fluent 15.0 software package. We should also note that similar phenomena have been observed in the experiments described in Ref. [9], where Elongation factors were explained by the high sensitivity of the global convection cell to small defects of the experimental setup and by non-ideal isothermality of the horizontal walls. With applied rotation of the container, the oscillation of the global convection cell ceases to be random in character. The action of the Coriolis force under moderate rotation leads to a precession of the convection cell with a constant angular velocity; this can be clearly observed in Fig. 3b, which shows the periodic alternation of the sections corresponding to the positive and negative values of the vertical velocity. Strong rotation results not only in the disintegration of the global convection cell into several structures, but also in a sharp decrease in the fluctuation amplitude of the vertical velocity component (see Fig. 3c), which indicates the general suppression of convection. Fig. 4 shows the dependences of the dimensionless RMS (Root Mean Square) fluctuations of the velocity and temperature components on the dimensionless vertical coordinate (measured from the lower interface, along the axis of the container) for different variants of computing the convection in a rotating cavity. Here u, v, w are the fluctuations of the velocity components , respectively. The profiles of the mean dimensionless temperature are also shown. We should stress that in solving the conjugate problem the temperature was counted from the averaged value of the temperature of the lower interface and transformed into a dimensionless quantity by dividing this value by the difference ΔT between the averaged temperatures of the lower and upper interfaces. It can be seen from the data shown in Fig. 4a–c that in case of moderate rotation (K= 0.834), the computations in the conjugate setting predict slightly higher fluctuation intensities for the velocity and the temperature than those obtained for the non-conjugate problem: the differences in the vicinity of the central horizontal cross-section are about 10%. Strong rotation (K= 6.706) leads to a sharp decrease in the fluctuation level, and the difference in the profiles of the RMS values obtained for the conjugate and the non-conjugate settings practically disappears. Fig. 4d shows that the transition to the conjugate setting has no pronounced effect on the behavior of the mean temperature profile in the region occupied by the fluid both under moderate and relatively strong rotation. In the latter case, the mean temperature profile becomes linear, pointing to the prevalence of diffusive heat transfer over the convective one for the entire fluid region.