# Stochastic circulation dynamics in the ocean mixed layer

@article{Holm2020StochasticCD, title={Stochastic circulation dynamics in the ocean mixed layer}, author={Darryl D. Holm and Erwin Luesink and Wei Pan}, journal={arXiv: Fluid Dynamics}, year={2020} }

In analogy with similar effects in adiabatic compressible fluid dynamics, the effects of buoyancy gradients on incompressible stratified flows are said to be `thermal'. The thermal rotating shallow water (TRSW) model equations contain three small nondimensional parameters. These are the Rossby number, the Froude number and the buoyancy parameter. Asymptotic expansion of the TRSW model equations in these three small parameters leads to the deterministic thermal versions of the Salmon's L1 (TL1…

## 2 Citations

Theoretical and computational analysis of the thermal quasi-geostrophic model

- Mathematics
- 2021

This work involves theoretical and numerical analysis of the Thermal Quasi-Geostrophic (TQG) model of submesoscale geophysical fluid dynamics (GFD). Physically, the TQG model involves thermal…

Stochastic Wave-Current Interaction in Thermal Shallow Water Dynamics

- Computer ScienceJ. Nonlinear Sci.
- 2021

In the entire family of nonlinear stochastic wave-current interaction equations derived here using this approach, Kelvin’s circulation theorem reveals a barotropic mechanism for wave generation of horizontal circulation or convection (cyclogenesis) which is activated whenever the gradients of wave elevation and/or topography are not aligned with the gradient of the vertically averaged buoyancy.

## References

SHOWING 1-10 OF 54 REFERENCES

The quasi-geostrophic theory of the thermal shallow water equations

- PhysicsJournal of Fluid Mechanics
- 2013

Abstract The thermal shallow water equations provide a depth-averaged description of motions in a fluid layer that permits horizontal variations in material properties. They typically arise through…

Stochastic wave-current interaction in stratified shallow water dynamics

- Physics, Mathematics
- 2019

Holm (Proc. Roy. Soc 2015) introduced a variational framework for stochastically parametrising unresolved scales of hydrodynamic motion. This variational framework preserves fundamental features of…

The role of mixed-layer instabilities in submesoscale turbulence

- GeologyJournal of Fluid Mechanics
- 2015

Upper-ocean turbulence at scales smaller than the mesoscale is believed to exchange surface and thermocline waters, which plays an important role in both physical and biogeochemical budgets. But what…

Extended-geostrophic Hamiltonian models for rotating shallow water motion

- Physics
- 1996

Abstract By using a small Rossby number expansion in Hamilton's principle for shallow water dynamics in a rapidly rotating reference frame, we derive new approximate extended-geostrophic equations…

Modelling uncertainty using circulation-preserving stochastic transport noise in a 2-layer quasi-geostrophic model

- Physics, Mathematics
- 2018

The stochastic variational approach for geophysical fluid dynamics was introduced by Holm (Proc Roy Soc A, 2015) as a framework for deriving stochastic parameterisations for unresolved scales. The…

Pattern of vertical velocity in the Lofoten vortex (the Norwegian Sea)

- GeologyOcean Dynamics
- 2018

Mean radial distributions of various dynamic characteristics of the permanently existing anticyclonic Lofoten vortex (LV) in the Norwegian Sea are obtained from an eddy-permitting regional…

Geophysical fluid dynamics: understanding (almost) everything with rotating shallow water models

- PhysicsContemporary Physics
- 2018

Random motions can be found all across science and engineering. Examples of random motions include: diffusion of particles in physics and chemistry, turbulent flows, search patterns of foraging…

On the vertical structure and stability of the Lofoten vortex in the Norwegian Sea

- 2017

The Lofoten Vortex (LV), a quasi-permanent anticyclonic eddy in the Lofoten Basin of the Norwegian Sea, is investigated with an eddy-permitting primitive equation model nested into the ECCO2 ocean…

Variational principles for stochastic fluid dynamics

- Mathematics, PhysicsProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- 2015

The circulation properties of the stochastic Stratonovich fluid equations are found to closely mimic those of the deterministic ideal fluid models.

Numerically Modeling Stochastic Lie Transport in Fluid Dynamics

- Physics, Computer ScienceMultiscale Model. Simul.
- 2019

New methodology to implement this velocity decomposition is developed and then numerically integrate the resulting stochastic partial differential equation using a finite element discretisation for incompressible 2D Euler fluid flows.