forked from NikAksamit/TRA_TSE
-
Notifications
You must be signed in to change notification settings - Fork 1
/
ReadMe
54 lines (41 loc) · 3.6 KB
/
ReadMe
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
--------------------------------------------------------------------------
Author: Nikolas Aksamit [email protected]
--------------------------------------------------------------------------
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% References:
[1] Haller, G., Aksamit, N. O., & Bartos, A. P. E. (2021). Quasi-Objective Coherent Structure Diagnostics from Single Trajectories.
Chaos, 31, 043131-1–17. https://doi.org/10.1063/5.0044151
[2] Aksamit, N.O., Haller, G. (2021). Objective Momentum Barriers in Wall Turbulence.
In Review, http://arxiv.org/abs/2106.07372
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% Calculate TRA and TSE diagnostics for 2D and 3D, steady and unsteady flows.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
The four “Advect_and_Calculate” scripts provide the tools to calculate TRA, and TSE values as described in [1] for both 2D and 3D, steady and unsteady flows. For the unsteady cases, the extended phase space versions are calculated which require a choice of v_0. The default choice is the spatio-temporal mean of the flow velocity magnitude in the domain of interest.
Each Advect_and_Calculate script uses similar input formats:
Advect_and_Calculate_2DSteady.m
% Input arguments:
tspan : Discrete advection timesteps used for RK4 advection scheme. This must include all intermediate steps between initial and final times(e.g. tspan=linspace(t_initial,t_final,100). For the steady case, these are dummy times as the velocity field is autonomous.
xx,yy : Initial positions for advection. These must be formatted as Nx1 vectors
U_Interp,V_Interp : Velocity field interpolants with inputs (xx,yy)
NCores : Number of Cores for parpool
% Output arguments:
xt,yt : xx-component, yy-component of trajectory final position.
time_note : tspan time if a trajectory left interpolant domain
TSE_Bar,TSE,TRA_Bar,TRA : Single trajectory metrics from section II and III in [1]
Advect_and_Calculate_2DUnsteady.m
% Input arguments:
tspan : Discrete advection timesteps used for RK4 advection scheme. This must include all intermediate steps between initial and final times(e.g. tspan=linspace(t_initial,t_final,100). For the unsteady case, these are times used in the velocity field interplant.
xx,yy : Initial positions for advection. These must be formatted as Nx1 vectors
U_Interp,V_Interp : Velocity field interpolants with inputs (time,xx,yy)
NCores : Number of Cores for parpool
% Output arguments:
xt,yt : xx-component, yy-component of trajectory final position.
time_note : tspan time if a trajectory left interpolant domain
TSE_Bar,TSE,TRA_Bar : Extended phase-space single trajectory metrics from section IV [1]
Note: For unsteady cases you can modify v_0, or leave as the mean of values used to define flow field interpolants. Advect_and_Calculate_3DSteady.m and Advect_and_Calculate_3DUnsteady.m are of the same format, with an extra z-component.
Demo_Unsteady2D.m
Demonstration of unsteady TRA and TSE calculations for geostrophic ocean current data as in [1].
Demo_Steady3D.m
Demonstration of steady TRA and TSE calculations for Johns Hopkins Turbulence Database Re=1000 Channel flow as in [2].
Demo_Steady3D_Geometry.m
Demonstration of steady NTRA and NTSE (normalized) calculations for Johns Hopkins Turbulence Database Re=1000 Channel flow as in [2].