A fully-coupled (hydrodynamic and morphologic) numerical model is presented, and utilized for the simulation of tsunami-induced scour around a monopile structure, representative of those commonly utilized as offshore wind turbine foundations at moderate depths i.e. for depths less than 30 m. The model is based on solutions to Reynolds-averaged Navier-Stokes equations, coupled with two-equation k a, turbulence closure, with additional bed and suspended load descriptions forming the basis for sea bed morphology. The model is first validated for flow, bed shear stresses, and scour within a steady current, where a generally excellent match with experimentally-based results is found. A methodology for maintaining and assessing hydrodynamic and morphologic similarity between field and (laboratory) model-scale tsunami events is then presented, combining diameter-based Froude number similarity with that based on the dimensionless wave boundary layer thickness-tomonopile diameter ratio. This methodology is utilized directly in the selection of governing tsunami wave parameters (i.e. velocity magnitude and period) used for subsequent simulation within the numerical model, with the tsunami-induced flow modelled as a long sinusoidally-varying current. The flow, sediment transport, and scour processes beneath up to ten tsunami waves are simulated in succession. These illustrate a generally accumulative scour process i.e. a-relatively rapid scour induced by the leading wave, with an additional build-up of the scour depth during additional trailing waves. The resulting scour seems to approach an equilibrium value after sufficient time duration, which corresponds reasonably to that predicted by existing steady-current scour depth expressions, after accounting for the finite boundary layer thickness induced by the unsteady tsunami wave, i.e. it is important to incorporate both current-like, as well as wave-like aspects of the long tsunami event. Based on the simulated results, a simple methodology for predicting the tsunami-induced scour depth in engineering practice is finally developed. This methodology is demonstrated to match the predicted scour development for all of the simulated flows considered, ranging from the series of transient tsunami waves to the steady-current limit.