Major mergers are considered to be a significant source of turbulence in clusters. We performed a numerical simulation of a major merger event using nested-grid initial conditions, adaptive mesh refinement, radiative cooling of primordial gas, and a homogeneous ultraviolet background. By calculating the microscopic viscosity on the basis of various theoretical assumptions and estimating the Kolmogorov length from the turbulent dissipation rate computed with a subgrid-scale model, we are able to demonstrate that most of the warm-hot intergalactic medium can sustain a fully turbulent state only if the magnetic suppression of the viscosity is considerable. Accepting this as premise, it turns out that ratios of turbulent and thermal quantities change only little in the course of the merger. This confirms the tight correlations between the mean thermal and non-thermal energy content for large samples of clusters in earlier studies, which can be interpreted as second self-similarity on top of the self-similarity for different halo masses. Another long-standing question is how and to which extent turbulence contributes to the support of the gas against gravity. From a global perspective, the ratio of turbulent and thermal pressures is significant for the clusters in our simulation. On the other hand, a local measure is provided by the compression rate, i.e. the growth rate of the divergence of the flow. Particularly for the intracluster medium, we find that the dominant contribution against gravity comes from thermal pressure, while compressible turbulence effectively counteracts the support. For this reason it appears to be too simplistic to consider turbulence merely as an effective enhancement of thermal energy.