Six recent Langmuir turbulence parameterization schemes and five traditional schemes are implemented in a common single-column modeling framework and consistently compared. These schemes are tested in scenarios versus matched large eddy simulations, across the globe with realistic forcing (JRA55-do, WAVEWATCH-III simulated waves) and initial conditions (Argo), and under realistic conditions as observed at ocean moorings. Traditional non-Langmuir schemes systematically underpredict large eddy simulation vertical mixing under weak convective forcing, while Langmuir schemes vary in accuracy. Under global, realistic forcing Langmuir schemes produce 6% (−1% to 14% for 90% confidence) or 5.2 m (−0.2 m to 17.4 m for 90% confidence) deeper monthly mean mixed layer depths than their non-Langmuir counterparts, with the greatest differences in extratropical regions, especially the Southern Ocean in austral summer. Discrepancies among Langmuir schemes are large (15% in mixed layer depth standard deviation over the mean): largest under wave-driven turbulence with stabilizing buoyancy forcing, next largest under strongly wave-driven conditions with weak buoyancy forcing, and agreeing during strong convective forcing. Non-Langmuir schemes disagree with each other to a lesser extent, with a similar ordering. Langmuir discrepancies obscure a cross-scheme estimate of the Langmuir effect magnitude under realistic forcing, highlighting limited understanding and numerical deficiencies. Maps of the regions and seasons where the greatest discrepancies occur are provided to guide further studies and observations.

We analyze the geometry of Lagrangian motion and material barriers in a time-dependent, three-dimensional, Ekman-driven, rotating cylinder flow, which serves as an idealization for an isolated oceanic eddy and other overturning cells with cylindrical geometry in the ocean and atmosphere. The flow is forced at the top through an oscillating upper lid, and the response depends on the frequency and amplitude of lid oscillations. In particular, the Lagrangian geometry changes near the resonant tori of the unforced flow, whose frequencies are rationally related to the forcing frequencies. Multi-scale analytical expansions are used to simplify the flow in the vicinity of resonant trajectories and to investigate the resonant flow geometries. The resonance condition and scaling can be motivated by simple physical argument. The theoretically predicted flow geometries near resonant trajectories have then been confirmed through numerical simulations in a phenomenological model and in a full solution of the Navier-Stokes equations.

We investigate and quantify stirring due to chaotic advection within a steady, three-dimensional, Ekman-driven, rotating cylinder flow. The flow field has vertical overturning and horizontal swirling motion, and is an idealization of motion observed in some ocean eddies. The flow is characterized by strong background rotation, and we explore variations in Ekman and Rossby numbers, E and R o , over ranges appropriate for the ocean mesoscale and submesoscale. A high-resolution spectral element model is used in conjunction with linear analytical theory, weakly nonlinear resonance analysis and a kinematic model in order to map out the barriers, manifolds, resonance layers and other objects that provide a template for chaotic stirring. As expected, chaos arises when a radially symmetric background state is perturbed by a symmetrybreaking disturbance. In the background state, each trajectory lives on a torus and some of the latter survive the perturbation and act as barriers to chaotic transport, a result consistent with an extension of the KAM theorem for three-dimensional, volume-preserving flow. For shallow eddies, where E is O(1), the flow is dominated by thin resonant layers sandwiched between KAM-type barriers, and the stirring rate is weak. On the other hand, eddies with moderately small E experience thicker resonant layers, wider-spread chaos and much more rapid stirring. This trend reverses for sufficiently small E, corresponding to deep eddies, where the vertical rigidity imposed by strong rotation limits the stirring. The bulk stirring rate, estimated from a passive tracer release, confirms the non-monotonic variation in stirring rate with E. This result is shown to be consistent with linear Ekman layer theory in conjunction with a resonant width calculation and the Taylor-Proudman theorem. The theory is able to roughly predict the value of E at which stirring is maximum. For large disturbances, the stirring rate becomes monotonic over the range of Ekman numbers explored. We also explore variation in the eddy aspect ratio.

Using a moving‐mesh, nonhydrostatic, spectral element model, we simulate Langmuir circulation with Navier‐Stokes equations under explicit, freely propagating surface waves. For comparison, Langmuir circulation is also simulated with Craik‐Leibovich (C‐L) equations. In both simulations, the Langmuir circulations are very similar, including temporal formation progresses and spatial structures; however, the strength of Langmuir circulation in the C‐L simulation is a bit weaker, which we suggest is due to the lack of Eulerian mean drift induced by fluid viscosity in the presence of explicit surface waves.