[Paper Review] Stokes drift should not be added to ocean general circulation model velocities

Gregory LeClaire Wagner, Navid C. Constantinou+1 more|arXiv (Cornell University)|Oct 16, 2022

Oceanographic and Atmospheric Processes4 citations

TL;DR

This paper argues that Stokes drift should not be added to ocean general circulation model (OGCM) outputs, as wave-agnostic models already simulate the Lagrangian-mean velocity — the true total transport velocity — even when Stokes drift is significant. The authors reject the long-standing 'Eulerian-mean hypothesis' and instead propose the 'Lagrangian-mean hypothesis,' demonstrating via theoretical analysis and simulations that OGCMs inherently capture Lagrangian-mean dynamics without additional correction.

ABSTRACT

Studies of ocean surface transport often invoke the "Eulerian-mean hypothesis": that wave-agnostic general circulation models neglecting explicit surface waves effects simulate the Eulerian-mean ocean velocity time-averaged over surface wave oscillations. Acceptance of the Eulerian-mean hypothesis motivates reconstructing the total, Lagrangian-mean surface velocity by adding Stokes drift to model output. Here, we show that the Eulerian-mean hypothesis is inconsistent, because wave-agnostic models cannot accurately simulate the Eulerian-mean velocity if Stokes drift is significant compared to the Eulerian-mean or Lagrangian-mean velocity. We conclude that Stokes drift should not be added to ocean general circulation model velocities. We additionally show the viability of the alternative "Lagrangian-mean hypothesis" using a theoretical argument and by comparing a wave-agnostic global ocean simulation with an explicitly wave-averaged simulation. We find that our wave-agnostic model accurately simulates the Lagrangian-mean velocity even though the Stokes drift is significant.

Motivation & Objective

• To challenge the widely held assumption that wave-agnostic ocean general circulation models (OGCMs) simulate the Eulerian-mean velocity.
• To demonstrate that the Eulerian-mean hypothesis — which assumes OGCMs produce Eulerian-mean velocity and requires adding Stokes drift to obtain total Lagrangian-mean transport — is inconsistent when Stokes drift is significant.
• To propose and validate an alternative: the 'Lagrangian-mean hypothesis,' where OGCMs inherently simulate the Lagrangian-mean velocity.
• To show that resolved surface wave effects are negligible at typical OGCM resolutions, but that wave-averaged momentum balances are fundamental to accurate transport modeling.
• To reframe the fundamental momentum balance in ocean models, positioning the Lagrangian-mean velocity as the primary dynamical quantity rather than the Eulerian-mean.

Proposed method

• Conducting a scaling analysis of the wave-averaged Craik-Leibovich equations to assess the consistency of the Eulerian-mean hypothesis under significant Stokes drift.
• Comparing a wave-agnostic global ocean simulation with an explicitly wave-averaged simulation to evaluate whether the former accurately captures the Lagrangian-mean velocity.
• Using theoretical arguments based on momentum balance and wave-averaged equations to show that the Lagrangian-mean velocity is the fundamental mean velocity in ocean dynamics.
• Analyzing the role of parameterizations (e.g., K-profile and vertical momentum flux) in OGCMs, showing they are naturally formulated in terms of the Lagrangian-mean velocity.
• Evaluating the impact of resolved surface wave effects at different model resolutions, particularly at submesoscale and mesoscale levels.
• Utilizing MOM6 and WAVEWATCH III model codes to generate simulations and validate the Lagrangian-mean hypothesis across different oceanic regimes.

Experimental results

Research questions

• RQ1 Is the Eulerian-mean hypothesis — that wave-agnostic OGCMs simulate the Eulerian-mean velocity — consistent when Stokes drift is significant compared to the mean flow?
• RQ2 Can wave-agnostic ocean general circulation models accurately simulate the Lagrangian-mean velocity, even in the presence of strong Stokes drift?
• RQ3 What is the fundamental dynamical role of the Lagrangian-mean velocity in ocean momentum balance, and how does it differ from the Eulerian-mean velocity?
• RQ4 How do wave-averaged momentum equations and parameterizations in OGCMs relate to the Lagrangian-mean velocity, and why is this formulation more physically consistent?
• RQ5 At what spatial and temporal scales do resolved surface wave effects become relevant for ocean circulation modeling?

Key findings

• The Eulerian-mean hypothesis is inconsistent because wave-agnostic models cannot accurately simulate the Eulerian-mean velocity when Stokes drift is significant compared to the mean flow.
• Wave-agnostic ocean general circulation models already simulate the Lagrangian-mean velocity accurately, even when Stokes drift is large, supporting the 'Lagrangian-mean hypothesis'.
• The Lagrangian-mean velocity is the fundamental mean velocity in ocean dynamics, and momentum balance equations should be formulated in terms of this quantity.
• Parameterizations such as the K-profile and vertical momentum flux models are consistent with the Lagrangian-mean framework, as they dissipate mean kinetic energy associated with $\boldsymbol{u}^\mathrm{L}$.
• Resolved surface wave effects are negligible at $\nicefrac{1}{4}^\circ$ resolution, but become relevant at finer scales where $\left(\boldsymbol{\nabla}\times\boldsymbol{u}^\mathrm{S}\right)\times\boldsymbol{u}^\mathrm{L}$ terms are non-negligible.
• The practice of adding Stokes drift to OGCM outputs or observational products is therefore unnecessary and misleading, as it double-counts the wave-induced transport.