Reduced-Order Quasilinear Model of Ocean Boundary-Layer Turbulence

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 a subset of modes determined by proper orthogonal decomposition (POD). When applied to boundary layers that are horizontally homogeneous, POD and a horizontally averaged quasilinear approximation both assume flow features that are horizontally wavelike, making the pairing very efficient. 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. Reduced-basis quasilinear statistics must approach the full-basis statistics as the basis size approaches completion; however, some quasilinear statistics resemble those found in the fully nonlinear simulations at smaller basis truncations. Thus, model reduction could possibly improve upon the accuracy of quasilinear dynamics.

Generation of attached Langmuir circulations by a suspended macroalgal farm

“…(1997), which serves as benchmark case in the literature on Langmuir turbulence (Polton et al. 2008; Skitka, Marston & Fox-Kemper 2020). A constant wind stress is applied at the air–sea interface and aligned with the wave field in the downstream direction.…”

Reduced Order Models for the Quasi-Geostrophic Equations: A Brief Survey

“…Homogeneous flow are one such example. Indeed, for homogeneous flows, it was proved in [40,99] that one of the most popular ROM techniques yields a ROM basis that is identical to the Fourier basis. Thus, in this case, the resulting ROM is nothing but a spectral method, which does not reduce the FOM dimension.…”

Dimensional reduction of direct statistical simulation

“…It would be interesting to explore dimensional reduction of DSS for more realistic models such as those explored in Ait-Chaalal et al (2016). Dimensional reduction by POD has been tested in a quasilinear model of the ocean boundary layer (Skitka et al 2020). It would also be interesting to determine whether or not a dimensional reduction algorithm could be constructed that acts dynamically on DSS, bypassing the step of first acquiring statistics for the full non-truncated problem, as in the current work.…”

“…Other methods such as those developed by Kolmogorov (Batchelor 1947), Kraichnan (Frisch 1995) and others (Holloway & Hendershott 1977;Legras 1980;Huang, Galperin & Sukoriansky 2001) provide an approximate description of some statistical properties of turbulent flows but assume homogeneity and usually isotropy. Many flows in geophysics and astrophysics spontaneously develop features such as coherent vortices and zonal banding (Marston et al 2019;Skitka, Marston & Fox-Kemper 2020). Furthermore, in engineering applications turbulence often interacts with non-trivial mean flows (see e.g.…”