[Paper Review] Direct Simulations of Wind-Driven Breaking Ocean Waves with Data Assimilation

Douglas G. Dommermuth, Christopher Lewis+2 more|arXiv (Cornell University)|Oct 1, 2014

Ocean Waves and Remote Sensing67 references3 citations

TL;DR

This paper presents a data assimilation framework that integrates High-Order Spectral (HOS) simulations and log-profile wind data into the Numerical Flow Analysis (NFA) code—a Cartesian-based Large-Eddy Simulation with Volume of Fluid (VOF) interface tracking—to directly simulate wind-driven breaking waves. The method enables high-bandwidth, phase-resolved modeling of wave breaking, Langmuir circulation formation, and wind streaks, revealing dynamic wave growth, organized vortical structures, and vertical mixing rates of 5 cm/s in the upper ocean and 0.4 m/s in the lower atmosphere.

ABSTRACT

A formulation is developed to assimilate ocean-wave data into the Numerical Flow Analysis (NFA) code. NFA is a Cartesian-based implicit Large-Eddy Simulation (LES) code with Volume of Fluid (VOF) interface capturing. The sequential assimilation of data into NFA permits detailed analysis of ocean-wave physics with higher bandwidths than is possible using either other formulations, such as High-Order Spectral (HOS) methods, or field measurements. A framework is provided for assimilating the wavy and vortical portions of the flow. Nudging is used to assimilate wave data at low wavenumbers, and the wave data at high wavenumbers form naturally through nonlinear interactions, wave breaking, and wind forcing. Similarly, the vertical profiles of the mean vortical flow in the wind and the wind drift are nudged, and the turbulent fluctuations are allowed to form naturally. As a demonstration, the results of a HOS of a JONSWAP wave spectrum are assimilated to study short-crested seas in equilibrium with the wind. Log profiles are assimilated for the mean wind and the mean wind drift. The results of the data assimilations are (1) Windrows form under the action of breaking waves and the formation of swirling jets; (2) The crosswind and cross drift meander; (3) Swirling jets are organized into Langmuir cells in the upper oceanic boundary layer; (4) Swirling jets are organized into wind streaks in the lower atmospheric boundary layer; (5) The length and time scales of the Langmuir cells and the wind streaks increase away from the free surface; (6) Wave growth is very dynamic especially for breaking waves; (7) The effects of the turbulent fluctuations in the upper ocean on wave growth need to be considered together with the turbulent fluctuations in the lower atmosphere; and (8) Extreme events are most likely when waves are not in equilibrium.

Motivation & Objective

• To develop a data assimilation framework that enables high-fidelity, phase-resolved simulation of wind-driven breaking ocean waves beyond the limitations of traditional HOS methods.
• To overcome the bandwidth and physical fidelity constraints of HOS and field measurements by integrating data into a high-resolution LES-VOF solver (NFA).
• To investigate the formation and dynamics of Langmuir cells, wind streaks, and windrows in the upper oceanic and lower atmospheric boundary layers.
• To quantify vertical mixing processes and wave growth dynamics under non-equilibrium and breaking wave conditions.
• To enable direct enforcement of wave and turbulence statistics via nudging, avoiding reliance on subgrid-scale turbulence models.

Proposed method

• Data assimilation is performed sequentially every N time steps using nudging to constrain low-wavenumber wave components and mean wind/drift profiles.
• HOS simulations of a JONSWAP wave spectrum are assimilated to drive the wavy portion of the flow in NFA, with high wavenumbers forming naturally through nonlinear interactions and wave breaking.
• Log profiles of mean wind and wind drift are nudged to constrain the vortical portion of the flow, while turbulent fluctuations evolve naturally via energy cascades and vorticity generation.
• The NFA code uses a Cartesian grid with implicit time integration and VOF method to capture free-surface dynamics and breaking waves with high resolution.
• The framework allows for the simulation of wave breaking, turbulence, and air-sea interaction with realistic energy transfer and dissipation mechanisms.
• The method is generalizable to assimilate real radar, optical, or in-situ measurements of waves, wind, and drift currents.

Experimental results

Research questions

• RQ1 How do wind-driven breaking waves organize into coherent structures such as windrows and Langmuir cells?
• RQ2 What are the dynamics and time scales of vertical mixing in the upper ocean and lower atmosphere during wave breaking?
• RQ3 How does wave growth evolve under non-equilibrium conditions, particularly during breaking events?
• RQ4 To what extent do turbulent fluctuations in the atmosphere and ocean interact to influence wave development?
• RQ5 Can data assimilation into a high-resolution LES-VOF code like NFA accurately reproduce observed large-scale vortical structures such as wind streaks?

Key findings

• Windrows form due to the action of breaking waves and the generation of swirling jets, which organize into coherent structures in both the atmosphere and ocean.
• Langmuir cells in the upper oceanic boundary layer and wind streaks in the lower atmospheric boundary layer are formed by the organization of swirling jets, with increasing length and time scales away from the free surface.
• Vertical mixing rates are approximately 5 cm/s in the upper 15 meters of the ocean and 0.4 m/s in the lower 50 meters of the atmosphere, with rapid particle diffusion observed across the air-sea interface.
• Particles initially within 20 cm of the free surface diffuse 10 meters into the ocean within 4 minutes, and particles in the atmosphere diffuse 50 meters upward in less than two minutes.
• Wave growth is highly dynamic, especially during breaking events, and non-equilibrium conditions significantly increase the likelihood of extreme wave events.
• The assimilation framework enables direct enforcement of wave and turbulence statistics via nudging, offering a more physically consistent alternative to subgrid-scale turbulence models.