Numerical schemes for stochastic backscatter in the inverse cascade of quasigeostrophic turbulence

Ian Grooms, Yoonsang Lee, Andrew J. Majda

Research output: Contribution to journalArticle

Abstract

Backscatter is the process of energy transfer from small to large scales in turbulence; it is crucially important in the inverse energy cascades of geophysical turbulence, where the net transfer of energy is from small to large scales. One approach to modeling backscatter in underresolved simulations is to add a stochastic forcing term. This study, set in the idealized context of the inverse cascade of two-layer quasigeostrophic turbulence, focuses on the importance of spatial and temporal correlation in numerical stochastic backscatter schemes when used with low-order finite-difference spatial discretizations. A minimal stochastic backscatter scheme is developed as a stripped-down version of stochastic superparameterization [Grooms and Majda, J. Comput. Phys., 271, (2014), pp. 78-98]. This simplified scheme allows detailed numerical analysis of the spatial and temporal correlation structure of the modeled backscatter. Its essential properties include a local formulation amenable to implementation in finite difference codes and nonperiodic domains, and tunable spatial and temporal correlations. Experiments with this scheme in the idealized context of homogeneous two-layer quasigeostrophic turbulence demonstrate the need for stochastic backscatter to be smooth at the coarse grid scale when used with low-order finite-difference schemes in an inverse-cascade regime. In contrast, temporal correlation of the backscatter is much less important for achieving realistic energy spectra. It is expected that the spatial and temporal correlation properties of the simplified backscatter schemes examined here will inform the development of stochastic backscatter schemes in more realistic models.

Original languageEnglish (US)
Pages (from-to)1001-1021
Number of pages21
JournalMultiscale Modeling and Simulation
Volume13
Issue number3
DOIs
StatePublished - 2015

Fingerprint

Cascades (fluid mechanics)
Temporal Correlation
backscatter
Numerical Scheme
Cascade
Turbulence
cascades
turbulence
Spatial Correlation
Finite Difference
Energy transfer
Numerical analysis
energy
Forcing Term
Correlation Structure
numerical analysis
Energy Transfer
Energy Spectrum
Energy
Finite Difference Scheme

Keywords

  • Backscatter
  • Quasigeostrophic turbulence
  • Stochastic modeling

ASJC Scopus subject areas

  • Modeling and Simulation
  • Chemistry(all)
  • Computer Science Applications
  • Ecological Modeling
  • Physics and Astronomy(all)

Cite this

Numerical schemes for stochastic backscatter in the inverse cascade of quasigeostrophic turbulence. / Grooms, Ian; Lee, Yoonsang; Majda, Andrew J.

In: Multiscale Modeling and Simulation, Vol. 13, No. 3, 2015, p. 1001-1021.

Research output: Contribution to journalArticle

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