Statistics of kinetic and thermal energy dissipation rates in two-dimensional thermal vibrational convection

We investigate the statistical properties of kinetic & varepsilon;(u) and thermal & varepsilon;(theta )energy dissipation rates in two-dimensional (2D) thermal vibrational convection (TVC). Direct numerical simulations were conducted in a unit aspect ratio box across a dimensionless angular frequency range of 10(3) <= omega <= 10(7) for amplitudes 0.001 <= a <= 0.1, with a fixed Prandtl number of 4.38. Our findings indicate & varepsilon;(u) is primarily associated with the characteristics of the vibration force, while & varepsilon;(theta) is more related to the large-scale columnar structures. Both energy dissipation rates exhibit a power-law relationship with the oscillational Reynolds number Re-os. & varepsilon;(u) exhibits a scaling relation as <& varepsilon;(u)>(V , t) similar to a(- 1) Re-os (0.93 +/- 0.01), while & varepsilon;(theta) exhibits two distinct scaling behaviors, i.e., < & varepsilon;(theta) >(V , t )similar to a(- 1 )Re(os)(1.97 +/- 0.04) for Re-os < Re-os, cr and < & varepsilon;(theta) >(V ,t) similar to a(- 1) Re-os (1.31 +/- 0.02) for Re-os> Re-os, cr, where the fitted critical oscillational Reynolds number is approximately Re-os, cr approximate to 80. The different scaling of < & varepsilon;(theta) > V , t is determined by the competition between the thermal boundary layer and the oscillating boundary layer. Moreover, the probability density functions (PDFs) of both dissipation rates deviate significantly from the lognormal distribution and exhibit a bimodal shape. By partitioning the contributions from the boundary layer and bulk regions, it is shown that the bulk contributes to the small and moderate dissipation rates, whereas the high dissipation rates are predominantly contributed by the boundary layer. As Re-os increases, the heavy tail of the PDFs becomes more pronounced, revealing an enhanced level of small-scale intermittency. This small-scale intermittency is mainly caused by the influence of BL due to vibration. Our study provides insight into the small-scale characteristics of 2D TVC, highlighting the non-trivial scaling laws and intermittent behavior of energy dissipation rates with respect to vibration intensity.