Tsunamis—long-wavelength, high-energy wave trains generated by sudden water-column displacement—require a substantial body of water. Deserts, by definition, lack the necessary volume and fetch. Here's the scientific breakdown.
All mechanisms share one prerequisite: a deep, laterally extensive water body (ocean, marginal sea, or very large lake).
Deserts receive < 250 mm annual precipitation. Surface water is ephemeral—playas, intermittent streams, small saline lakes (e.g., Lake Eyre, Great Salt Lake). Even the largest desert lakes are orders of magnitude too small and shallow to sustain tsunami propagation. Wave energy dissipates via bottom friction and lateral spreading long before reaching shore.
No credible geological or hydrodynamic model supports tsunami generation within a desert. The hazard is exclusively coastal or lacustrine (in very large lakes).