loop

Thermohaline loop, written in Fortran.

Motivation

The thermohaline loop model consists of a fluid loop with infinitesimal section area along which a circulation is induced by applying fluxes of temperature and salt and/or by directly applying a torque. The thermohaline model can serve as a conceptual model of the global ocean overturning circulation. It does not only find application in physical oceanography but also in nuclear and solar energy engineering in the form of the so-called thermosyphons. Despite its simple setup, the thermohaline loop exhibits a variety of dynamical behaviors including instability and chaos. Apart from being interesting in its own right, the loop model has great educational value when it comes to the analysis of overturning flows.

More information on the model equations can be found in the following publications:

• Pollmann, F., Roquet, F., and Madec, G., 2015. Effects of the Asymmetry between Surface and Interior Flow on the Dynamics of a Thermohaline Loop. Journal of Physical Oceanography. doi: 10.1175/JPO-D-15-0022.1
• Roquet F., Lindqvist R., Pollmann F., Ferreira D., Madec G., 2017. Stability of the thermohaline circulation examined with a one-dimensional fluid loop. Tellus A. doi: 10.1080/16000870.2017.1380490

Versions

Two versions of the fluidloop are available. The first fluidloop_v1 was used in Roquet et al. (2017). It is advised to use the more recent version fluidloop_v2 which has been modified in a number of way:

1. Outputs are available in netcdf format, with machine precision. This format can be easily read with scientific programming tools such as python or Matlab.
2. The diffusion and forcing are computed by default using an implicit scheme, which is unconditionally stable. This means that fluidloop_v2 can be run with much greater time steps than fluidloop_v1.
3. An option is now available in fluidloop_v2 to set variable diffusivities based on a constant energy of mixing scheme. This enables studying the impact of variable stratification on the loop flow.

Installation

Instructions for installation and execution of either fluidloop_v1 or fluidloop_v2 are available the README.md files of their respective directory.

Configuration files (for fluidloop_v2)

1. The namelist is the configuration file that allows to configure the loop model. The structure of the namelist must be as follows:

```
&namrun
  name_exp       = 'TEST'           ! name of experiment (used to name outputs). file max characters: 50
  nl             = 360              ! number of points around loop
  niter_t1       = 10000            ! number of iterations at t=1
  niter_max      = 10000  		  	  ! maximum number of timesteps
  niter_write    = 1000             ! number of iterations between writing output of output_1D
  use_netcdf     = .TRUE.           ! out put in netcdf or text file
  init_from_file = .TRUE.           ! start from init_state (T) or from rest (F)
  init_state = 'init_state.txt'     ! initial state for temperature, salinity and velocity. max characters: 50
/

&namconfig
  Zf = 0.5               	  	      ! height of source and sink of buoyancy -1<Zf<1
  R = 0.1                           ! inverse Rayleigh number
  lambda = 0.                     	! cabbeling parameter
  mu = 0.                           ! thermobaric parameter
  foldtrue = .TRUE.               	! Is the loop folded or not
  constant_diffusion = .FALSE.       ! Is the diffusion constant or not
  implicit_diffusion = .TRUE.       ! solve diffusion and forcing implicit (.FALSE. explicit)
/

&namforcing
  tau   = 0.                		    ! applied torque
  ref_t = 5.             	  	      ! Reference toward which temperature is relaxed
  xi_t  = 1.                        ! Temperature relaxation parameter
  F_s   = 0.15              	  	  ! Strength of fixed salinity forcing
/
```

2. Initial state

If init_from_file in namelist is .FALSE., all state variables are set to 0.

Otherwise, initial values are read in the file named after the entry init_state in the namelist. The format is: - First line: initial velocity w - Line 2 to nl+1: index j, temperature t(j), salinity s(j)

3. Forcing input

Forcing parameters are read in the namelist and they are kept constant throughout the simulation.

• tau : applied torque
• ref_t : Reference temperature for relaxation (relaxed toward +ref_t at source, and -ref_t at sink)
• xi_t : Temperature relaxation parameter
• F_s : Magnitude of fixed salinity flux (+F_s applied at source and -F_s applied at sink)

Output files (for fluidloop_v2)

Two output files are created in the working directory, whose prefix $EXP is set by the name_exp entry in the namrun section of the namelist:

1. $EXP_config.txt outputs the loop configuration, including namelist parameters and loop geometry factors

2. $EXP_output.nc provides snapshots of the properties of the loop at a frequency set by the niter_write entry in the namrun section of the namelist: * index: loop index, =1 at the top of the loop, then increasing in the clockwise direction, up to nl * record: number of snapshots * w: velocity * z: vertical height of tracer grid points * time: non-dimensional time variable for each record * theta: non-dimensional temperature (index from 1 to nl) * salt: salinity (index from 1 to nl) * sigma: density (index from 1 to nl) * N2: stratification, defined on a staggered grid (index from 0 to nl-1, with staggered index 0 to the left of the tracer index 1)

3. $EXP_restart.txt gives a snapshot of the last time step of the run, that can be used as an init_state file.

Matlab tools

Matlab tools are provided to:

• compute equilibrium tracer distribution when fixed-flux or relaxation forcings are applied: loop_tracer_fixed.m and loop_tracer_relax.m
• compute equilibrium state of the loop model with a semi-analytical value: loop_equilibrium.m
• analyze the linear stability of steady-states: loop_jacobian.m
• generate an initial-state file for the loop model: loop_init_state.m
• read model outputs in Matlab: loop_read_out.m

An example of use of Matlab tools is provided in the script loop_test.m

Python tools

Python script loop.py is available thanks to the generous work of Julien Emile-Geay. Also, a Jupyter notebook plot_outputs_fluidloop.ipynb developed by Eléa Lastes is also provided as an example of python scripts to analyse outputs of the model.

Contributors

Fabien Roquet (Department of Marine Sciences at the University of Gothenburg). More information on the author on his personal webpage

Other contributors:

• Eléa Lastes (University of Marseille)
• Friederike Pollmann (University of Hamburg)
• Rickard Lindqvist (previously at Stockholm University)

License

This software is distributed under the terms of the GNU GENERAL PUBLIC LICENSE v3. The GNU General Public License is a free, copyleft license for software and other kinds of works.