Geophysical fluid models with simple energy backscatter: explicit flows and unbounded exponential growth

@article{Prugger2022GeophysicalFM,
  title={Geophysical fluid models with simple energy backscatter: explicit flows and unbounded exponential growth},
  author={A. Prugger and J. D. M. Rademacher and Junliang Yang},
  journal={Geophysical \& Astrophysical Fluid Dynamics},
  year={2022}
}
Motivated by numerical schemes for large scale geophysical flow, we consider the rotating shallow water and Boussinesq equations on the whole space with horizontal kinetic energy backscatter source terms built from constant negative viscosity and stabilising hyperviscosity. We study the impact of this energy input through various explicit flows, which are simultaneously solving the nonlinear equations and the linear equations that arise upon dropping the transport nonlinearity, i.e., the… 
View PDF on arXiv
1 Citations

One Citation

Citation Type

Citation Type

Explicit superposed and forced plane wave generalized Beltrami flows
We revisit and present new linear spaces of explicit solutions to incompressible Euler and Navier-Stokes equations on $\mathbb{R}^n$, as well as the rotating Boussinesq equations on $\mathbb{R}^3$.…

References

SHOWING 1-10 OF 30 REFERENCES
Explicit superposed and forced plane wave generalized Beltrami flows
We revisit and present new linear spaces of explicit solutions to incompressible Euler and Navier-Stokes equations on $\mathbb{R}^n$, as well as the rotating Boussinesq equations on $\mathbb{R}^3$.…
Simulating turbulent mixing caused by local instability of internal gravity waves
Abstract With the aim of assessing internal wave-driven mixing in the ocean, we develop a new technique for direct numerical simulations of stratified turbulence. Since the spatial scale of oceanic…
A Kinematic Kinetic Energy Backscatter Parametrization: From Implementation to Global Ocean Simulations
Ocean models at eddy‐permitting resolution are generally overdissipative, damping the intensity of the mesoscale eddy field. To reduce overdissipation, we propose a simplified, kinematic energy…
Single-scale two-dimensional-three-component generalized-Beltrami-flow solutions of incompressible Navier-Stokes equations
Testing of kinetic energy backscatter parameterizations in the NEMO ocean model
Abstract Eddy-permitting numerical ocean models resolve mesoscale turbulence only partly, that leads to underestimation of eddy kinetic energy (EKE). Mesoscale dynamics can be amplified by using…
Exact Solutions to the Three-Dimensional Navier–Stokes Equations Using the Extended Beltrami Method
In a 1966 publication, Chi-Yi Wang used the streamfunction in concert with the vorticity equations to develop a methodology for obtaining exact solutions to the incompressible Navier–Stokes…
Three-dimensional small-scale instabilities of plane internal gravity waves
We study the evolution of three-dimensional (3-D), small-scale, small-amplitude perturbations on a plane internal gravity wave using the local stability approach. The plane internal wave is…
Toward Consistent Subgrid Momentum Closures in Ocean Models
State-of-the-art global ocean circulation models used in climate studies are only passing the edge of becoming “eddy-permitting” or barely eddy-resolving. Such models commonly suffer from…
Toward an Energetically Consistent, Resolution Aware Parameterization of Ocean Mesoscale Eddies
A subgrid‐scale eddy parameterization is developed, which makes use of an explicit eddy kinetic energy budget and can be applied at both “non‐eddying” and “eddy‐permitting” resolutions. The…
An in-depth numerical study of the two-dimensional Kuramoto–Sivashinsky equation
TLDR
An extensive numerical study of the Kuramoto–Sivashinsky equation (2D KSE) is performed to complement this analytical work and explores in detail the statistics of chaotic solutions and classify the solutions that arise for domain sizes where the trivial solution is unstable and the long-time dynamics are completely two-dimensional.
...
1
2
3
...