In Lagrangian dynamics, the detection of coherent clusters can help understand the organization of transport by identifying regions with coherent trajectory patterns. Many clustering algorithms, however, rely on user-input parameters, requiring a priori knowledge about the flow and making the outcome subjective. Building on the conventional spectral clustering method of Hadjighasem et al (2016), a new parameter-free spectral clustering approach is developed that automatically identifies parameters and does not require any user-input choices. A noise-based metric for quantifying the coherence of the resulting coherent clusters is also introduced. The parameter-free spectral clustering is applied to two benchmark analytical flows, the Bickley Jet and the asymmetric Duffing oscillator, and to a realistic, numerically-generated oceanic coastal flow. In the latter case, the identified model-based clusters are tested using observed trajectories of real drifters. In all examples, our approach succeeded in performing the partition of the domain into coherent clusters with minimal inter-cluster similarity and maximum intra-cluster similarity. For the coastal flow, the resulting coherent clusters are qualitatively similar over the same phase of the tide on different days and even different years, whereas coherent clusters for the opposite tidal phase are qualitatively different.

The Lagrangian and Eulerian structure and dynamics of a strong wind event in the Tokar Gap region are described using a WRF model hindcast for 2008. Winds in the Tokar Gap reach 25 m s-1 and remain coherent as a jet far out over the Red Sea, whereas equally strong wind jets occurring in neighboring gaps are attenuated abruptly by a jump-like hydraulic transition that occur just offshore of the Sudan coast. The transition is made possible by the supercritical nature of the jets, which are fed by air that spills down from passes at relatively high elevation. By contrast, the spilling flow in the ravine-like Tokar Gap does not become substantially supercritical and therefore does not undergo a jump, and also carries more total horizontal momentum. The Tokar Wind Jet carries some air parcels across the Red Sea and into Saudi Arabia, whereas air parcel trajectories in the neighboring jets ascend as they cross through the jumps, then veer sharply to the southeast and do not cross the Red Sea. The mountain parameter Nh/U is estimated to lie in the rage 1.0-4.0 for the general region, a result roughly consistent with a primary gap jet having a long extension, and supercritical jets spilling down from higher elevation passes. The strong event is marked by the formation of a cyclonic cell near the upstream entrance to the Tokar Gap, a feature absent from the more moderate events that occur throughout the summer. The cell contains descending air parcels that are fed into the primary and secondary jets. An analysis of the Bernoulli function along air parcel trajectories reveals an approximate balance between the loss of potential energy and gain of internal energy and pressure, with surprisingly little contribution from kinetic energy, along the path of the descending flow. All jets attain the critical wind speed nominally required to loft dust into the atmosphere, though only the Tokar Gap has a broad, delta region with plentiful deposits of silt.