# Reduced-Order Quasilinear Model of Ocean Boundary-Layer Turbulence

## TL;DR

This paper demonstrates that a reduced-order quasilinear model, using a small subset of modes, can accurately reproduce key statistics of ocean boundary-layer turbulence, offering a computationally efficient approach.

## Contribution

It introduces a novel combination of model reduction via proper orthogonal decomposition with quasilinear approximation for ocean turbulence modeling.

## Key findings

- Less than 0.2% of modes retain key turbulence statistics within 30% error
- Basis reduction can improve accuracy over full quasilinear models
- Convergence to correct statistics is non-monotonic as modes increase

## Abstract

The combined effectiveness of model reduction and the quasilinear approximation for the reproduction of the low-order statistics of oceanic surface boundary-layer turbulence is investigated. Idealized horizontally homogeneous problems of surface-forced thermal convection and Langmuir turbulence are studied in detail. Model reduction is achieved with a Galerkin projection of the governing equations onto an subset of modes determined by proper orthogonal decomposition. For less than 0.2% of the modes retained, the reduced quasilinear model is able to reproduce vertical profiles of horizontal mean fields as well as certain energetically important second-order turbulent transport statistics and energies to within 30% error. For intermediate sizes of the basis truncation some statistics approach those found in the fully nonlinear simulations. Thus basis reduction can actually improve upon the accuracy of quasilinear dynamics. A test model with a small total number of modes demonstrates the non-monotonic convergence toward the correct statistics as the size of the basis is increased.