Lagrangian modelling of multi-dimensional advection-diffusion with space-varying diffusivities: theory and idealized test cases

Spivakovskaya, D.; Heemink, A.W.; Deleersnijder, Éric

doi:10.1007/s10236-007-0102-9

Cited by 44 publications

(37 citation statements)

References 41 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Because of this correction term the particles do not accumulate in regions of low diffusivity (Hunter et al, 1993;Visser, 1997;Ross and Sharples , 2004). This random walk model can be introduced by using the theory of stochastic differential equations (SDE) (Heemink, 1990;Dimou and Adams, 1993;Stijnen et al, 2006;Spivakovskaya et al, 2007). The advectiondiffusion equation is interpreted as the Fokker-Planck equation (Oksendal, 1985) and the corresponding SDE inÎto sense can be derived.…”

Section: Introductionmentioning

confidence: 99%

The backward Îto method for the Lagrangian simulation of transport processes with large space variations of the diffusivity

Spivakovskaya

Heemink²,

Deleersnijder³

2007

Ocean Sci.

View full text Add to dashboard Cite

Abstract. Random walk models are a powerful tool for the investigation of transport processes in turbulent flows. However, standard random walk methods are applicable only when the flow velocities and diffusivity are sufficiently smooth functions. In practice there are some regions where the rapid but continuous change in diffusivity may be represented by a discontinuity. The random walk model based on backwardÎto calculus can be used for these problems. This model was proposed by LaBolle et al. (2000). The latter is best suited to the problems under consideration. It is then applied to two test cases with discontinuous diffusivity, highlighting the advantages of this method.

show abstract

Section: Introductionmentioning

confidence: 99%

The backward Îto method for the Lagrangian simulation of transport processes with large space variations of the diffusivity

Spivakovskaya

Heemink²,

Deleersnijder³

2007

Ocean Sci.

View full text Add to dashboard Cite

show abstract

“…This is why it is suggested to turn to a vertical problem in which transport is due to vertical turbulent diffusion, with the possible addition of settling processes (e.g. Spivakovskaya et al (2007a); Gräwe and Wolff (2010);de Brauwere and Deleersnijder (2010)). Hence, horizontal transport processes are not taken into account.…”

Section: Motivationmentioning

confidence: 99%

“…An additional positive side effect of the proposed test case is that the particletracking schemes are tested for the weak and strong convergence (Arnold 1974). Previous publications focused either on the weak convergence (Stijnen et al 2006;Spivakovskaya et al 2007a;Gräwe and Wolff 2010;Gräwe 2011) or on the strong convergence (Shah et al 2011), but not on a combination of both.…”

Section: Introductionmentioning

confidence: 99%

“…However, the marine modelling community is progressively realising that the Euler scheme is far from optimal (e.g. Stijnen et al (2006); Spivakovskaya et al (2007a); Gräwe and Wolff (2010)). Turning to higherorder schemes is one of the improvements that are now believed to be needed.…”

Section: Introductionmentioning

confidence: 99%

“…In recent years, a battery of test cases was developed to asses the accuracy and convergence of particletracking schemes (Thomson 1987;LaBolle et al 2000;Brickman and Smith 2001;Deleersnijder et al 2006a;Spivakovskaya et al 2007a;Shah et al 2011). Most of these test cases were designed to compare an analytical solution with the numerical approximations.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Why the Euler scheme in particle tracking is not enough: the shallow-sea pycnocline test case

et al. 2012

Self Cite

View full text Add to dashboard Cite

During the last decades, the Euler scheme was the common "workhorse" in particle tracking, although it is the lowest-order approximation of the underlying stochastic differential equation. To convince the modelling community of the need for better methods, we have constructed a new test case that will show the shortcomings of the Euler scheme. We use an idealised shallow-water diffusivity profile that mimics the presence of a sharp pycnocline and thus a quasi-impermeable barrier to vertical diffusion. In this context, we study the transport of passive particles with or without negative buoyancy. A semi-analytic solutions is used to assess the performance of various numerical particle-tracking schemes (first-and secondorder accuracy), to treat the variations in the diffusivity profile properly. We show that the commonly used Euler scheme exhibits a poor performance and that widely used particle-tracking codes shall be updated to either the Milstein scheme or second-order schemes. It is further seen that the order of convergence is not the only relevant factor, the absolute value of the error also is.

show abstract

Simulating Lagrangian Subgrid-Scale Dispersion on Neutral Surfaces in the Ocean

Reijnders

Deleersnijder

Sebille

2021

Preprint

Self Cite

View full text Add to dashboard Cite

Turbulent stirring in the ocean disperses tracers and suspended material over time. The eddies, jets, and fronts that characterize this turbulent motion occur at a range of spatial and temporal scales. Since ocean models have a finite resolution, structures with spatial s cales of the order of the grid resolution or smaller are not resolved explicitly. Current state-of-the-art global ocean models use nominal 1/48° grid resolutions (Fox-Kemper et al., 2019;Su et al., 2018), resolving the mesoscale and part of the submesoscale spectrum. Still, computational constraints limit the simulation length of models at such resolutions to only a few years. Many of the latest generation of Earth system models that are used for CMIP6 use ocean grid resolutions of 1° and 1/4° (Hewitt et al., 2020). The models at 1° do not resolve any mesoscale eddies. While the 1/4° models are eddy-permitting in parts of the ocean, much higher resolutions are required to resolve the first baroclinic Rossby radius at higher latitudes, such

show abstract

Lagrangian modelling of multi-dimensional advection-diffusion with space-varying diffusivities: theory and idealized test cases

Cited by 44 publications

References 41 publications

The backward Îto method for the Lagrangian simulation of transport processes with large space variations of the diffusivity

The backward Îto method for the Lagrangian simulation of transport processes with large space variations of the diffusivity

Why the Euler scheme in particle tracking is not enough: the shallow-sea pycnocline test case

Simulating Lagrangian Subgrid-Scale Dispersion on Neutral Surfaces in the Ocean

Contact Info

Product

Resources

About