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Past major changes in sea level have had a significant influence on global-and shelf sea tidal dynamics. Some of these changes are preserved in sedimentary records from the shelf seas, and so appropriate proxy data have the potential to constrain tidal model outputs over the recent geological past. Tidal models which simulate the evolution of tide-dependent parameters over geological timescales are fundamental to understanding the response of the tides to sea-level rise and climate change. This study explores a potential new sedimentary proxy for validating past shelf sea tidal dynamics, interrogating the relationship between tidally-modulated bed shear stress and seabed sediment grain size at discrete sediment core locations over the northwest European shelf seas. Radiocarbon-dated sediment grain size profiles were generated for four British Geological Survey UK shelf sediment vibrocores, spanning a range of physical environments. Changes in observed sediment grain size through time were compared with simulated changes in tidal-induced bed shear through time, using temporal and spatial outputs from the most recently developed palaeotidal model of the Northwest European shelf seas. Although a positive correlation between observed grain size and simulated bed shear stress was observed at three of the four sediment cores sites, no robust relationship could be quantified. The palaeotidal model output failed to resolve the details of the actual sediment dynamics, since only tidal-induced bed shear stresses were considered. Wave processes were neglected, and the model was not sensitive enough to constrain simulated past tidal conditions at point locations; rather it is suitable for examining general trends. There remains a need to develop new proxies for past shelf sea hydrodynamic conditions which can be used to constrain numerical model output of tidal currents at regional scales.

Buoyant, finite-size, or inertial particle motion is fundamentally unlike neutrally buoyant, infinitesimally small, or Lagrangian particle motion. The de-jure fluid mechanics framework for the description of inertial particle dynamics is provided by the Maxey-Riley equation. Derived from first principles-a result of over a century of research since the pioneering work by Sir George Stokes-the Maxey-Riley equation is a Newton-type law with several forces including (mainly) flow, added mass, shear-induced lift, and drag forces. In this paper, we present an overview of recent efforts to transfer the Maxey-Riley framework to oceanography. These involved: (1) including the Coriolis force, which was found to explain behavior of submerged floats near mesoscale eddies; (2) accounting for the combined effects of ocean current and wind drag on inertial particles floating at the air-sea interface, which helped understand the formation of great garbage patches and the role of anticyclonic eddies as plastic debris traps; and (3) incorporating elastic forces, which are needed to simulate the drift of pelagic Sargassum. Insight into the nonlinear dynamics of inertial particles in every case was possible to be achieved by investigating long-time asymptotic behavior in the various Maxey-Riley equation forms, which represent singular perturbation problems involving slow and fast variables.