Simulation of slender vortex filaments

This page has been setup to support the preprint and the paper titled On the motion of hairpin filaments in the atmospheric boundary layer which can be found in arXiv: https://arxiv.org/abs/2303.09302 and Physics of Fluids webpage: https://doi.org/10.1063/5.0151078

Velocity profiles

The velocity profiles have been uploaded with the permission of Dr. Cedrick Ansorge for three Ekman flow cases: N, S_1, S_2. Case N corresponds to a neutrally stratified case and cases S_1 and S_2 are the stably stratified cases. Details of the simulation can be found in the preprint, Ansorge and Mellado (2014, 2016) and the PhD thesis of Ansorge (2016). The code used for the simulation can be found here: https://github.com/turbulencia/tlab.

python3 plotProfiles.py

Slender vortex filament code

• This code computes the motion of slender vortex filaments with two methods: Local induction approximation (LIA) and the M1 Klein-Knio (M1 KK) scheme. Details of both methods can be found in the preprint.
• It is based on the ezvortex code, written in C, by Dr. Daniel Margerit. See the original C code and the corresponding publications here: https://github.com/danielmargerit/ezvortex.

Setting up the code

The code can run in four modes,

• full python mode
• python with numba library (for details regarding the library, see https://numba.pydata.org/)
• partial FORTRAN (only for computing the thin tube velocity in M1 KK method, time integration is handled by python)
• full FORTRAN (only for M1 KK method, python simply acts as a wrapper in this scenario)

To compile FORTRAN code, run the following:

cd src/partial_fortran/
make
cd ../full_fortran/
make

Stagnant background flow

Example python templates for a stagnant background flow are given (Simulation_stagnant_*.py). Comments have been added to explain the various parameters and flags. Simulation_stagnant_LIA.py and Simulation_stagnant_M1KK.py run with LIA and M1 KK methods respectively in python with numba mode. Simulation_stagnant_M1KK_PF.py and Simulation_stagnant_M1KK_FF.py are templates which run the partial FORTRAN and full FORTRAN modes respectively. NOTE: FORTRAN code has to be compiled before running these templates.

Performance

The following is tested for the stagnant background flow case given in the template.
For LIA, ts = 0.00001, nsteps = 1000, writeEveryNSteps = 100
For M1 KK, ts = 0.001, nsteps = 10, writeEveryNSteps = 1

At t = 0.01, the temporal evolution of the hairpin filament for LIA (left) and M1 KK (right),

Method	Mode	Number of nodes	Time taken (s)
LIA	full python	700	45.264
	python with numba	700	23.04
	full python	900	60.86
	python with numba	900	26.81
M1 KK	python with numba	900	95.547
	partial FORTRAN	900	38.497
	full FORTRAN	900	6.179

Difference between LIA and M1 KK methods

At t = 0.1, the temporal evolution of the hairpin filament for LIA (left) and M1 KK (right),

Shear background flow

An example template for a shear background flow is given (Simulation_simpleshear_M1KK_FF.py). With the M1 KK method and the full FORTRAN mode, the result is plotted below:

ABL background flow

Finally, an example template for an ABL background flow is given (Simulation_BL_M1KK_PF_wall.py). With the M1 KK method and the partial FORTRAN mode with wall boundary condition, the result is plotted below:

These codes have been tested on a Linux machine running Debian 11 (bullseye) with python 3.9.2 and matplotlib 3.3.4. Some codes have been tested on a Mac OS as well. The codes may need to be adapted to work well on other machines.

Additional references

Ansorge, C., & Mellado, J. P. (2014). Global intermittency and collapsing turbulence in the stratified planetary boundary layer. Boundary-layer meteorology, 153(1), 89-116.

Ansorge, C., & Mellado, J. P. (2016). Analyses of external and global intermittency in the logarithmic layer of Ekman flow. Journal of Fluid Mechanics, 805, 611-635.

Ansorge, C. (2016). Analyses of turbulence in the neutrally and stably stratified planetary boundary layer. Springer.