  Comprehensive knowledge of local flame displacement speed, $S_d$, in
turbulent premixed flames is crucial towards the design and development of
hydrogen fuelled next-generation engines. Premixed hydrogen-air flames are
characterized by significantly higher laminar flame speed compared to other
conventional fuels. Furthermore, in the presence of turbulence, $S_d$ is
enhanced much beyond its corresponding unstretched, planar laminar value $S_L$.
In this study, the effect of high Karlovitz number ($Ka$) turbulence on
density-weighted flame displacement speed, $\widetilde{S_d}$, in a H$_2$-air
flame is investigated. Recently, it has been identified that flame-flame
interactions in regions of large negative curvature govern large deviations of
$\widetilde{S_d}$ from $S_L$, for moderately turbulent flames. An interaction
model for the same has also been proposed. In this work, we seek to test the
interaction model's applicability to intensely turbulent flames characterized
by large $Ka$. To that end, we investigate the local flame structures: thermal,
chemical structure, the effect of curvature, along the direction that is normal
to the chosen isothermal surfaces. Furthermore, relative contributions of the
transport and chemistry terms to $\widetilde{S_d}$ are also analyzed. It is
found that, unlike the moderately turbulent premixed flames, where enhanced
$\widetilde{S_d}$ is driven by interactions among complete flame structures,
$\widetilde{S_d}$ enhancement in high $Re_t$ and high $Ka$ flame is
predominantly governed by local interactions of the isotherms. It is found that
enhancement in $\widetilde{S_d}$ in regions of large negative curvature occurs
as a result of these interactions, evincing that the interaction model is
useful for high $Ka$ turbulent premixed flames as well.
