SPINS_ENERGETICS

This set of scripts is to help the user interrogate and analyse the energetics-related outputs from SPINS.

There are two toolboxes:

• Offline_Sorting : a MATLAB implementation of the sorting algorithm & checks for it's validity
• Analyse_Diagnos : Analysis of onboard SPINS diagnostics

Author: Sam Hartharn-Evans, 2022

Analyse Diagnostics - Analysis of onboard SPINS diagnostics:

Calculate Energetics

calc_energetics is a re-formulation of SPINSmatlab plot_diagnos, which works for even very large number of outputs. Unlike, it reduces the temporal frequency consistently onto a regularly spaced grid across all outputs, and implements a different filter onto BPE which works for any size array. The diagnostics are then used to calculate BPE, PE, KE, APE, etc using the same equations as Deepwell.

BPE Filters

filt_design is to explain the choice of timeseries filter used in calc_energetics BPE filter, compared to the one used in plot_diagnos. Three filters are explored, mlptdenoise, a spectral lowpass filter, and the MATLAB smooth filter (running mean).

Mixing Characteristics

mixing_characteristics calculates some characteristics which are relevant to mixing:

• Pycnocline thickness, Nz in pycnocline, Dz in pycnocline, $L_{pyc}/Dx$
• $Sc = \nu/\kappa_{\rho}$ : Schmidt number, indicating momentum diffusivity over molecular diffusivity
• Characterises the SPINS filter (exponential or hyperviscosity), assuming $k_{nyquist} = \frac{\pi}{Lx}(Nx-1)$

Offline Sorting - a MATLAB implementation of the sorting algorithm & checks for it's validity

Sort Energetics

sort_energetics.m employs the Winters (1995)-like sorting algorithm for a mapped case to calculate BPE for a mapped grid (based off sorted stratification across the entire domain, $\rho_b$), calculates PE, and APE & BPE, and then also calculates KE and packages into a structure: $$APE = 9.81 \sum_{j=1}^{Nx} \sum_{i=1}^{Nz} W^{i, j} (\rho^{i, j} - \rho_{b}^{i, j})z^{i, j}$$ $$BPE = 9.81 \sum_{j=1}^{Nx} \sum_{i=1}^{Nz} W^{i, j} \rho_{b}^{i, j}z^{i, j}$$ $$PE = 9.81 \sum_{j=1}^{Nx} \sum_{i=1}^{Nz} W^{i, j} (\rho^{i, j})z^{i, j}$$

Run sort energetics

run_sort_energetics.m calculates and saves the output of sort_energetics for each timestep.

Plot offline energetics

plot_offline_energetics.m plots timeseries of each energetic component, and can optionally compare these to all_diagnos.mat produced from plot_diagnos.m:

Check Rho b Hovmoller

check_rhob_hovmoller plots diagnostics related to the sorting algorithm

• a) Reference density profile ( $\rho_b$ ) hovmoller
• b) Change in reference density profile ( $\rho_b - \rho_b(0)$ ) hovmoller
• c) Mass deviation timeseries
• d) Change in BPE over time

(b) is very useful to indicate if things look correct, we'll see a dipole band appear around the pycnocline, intensifying through the timeseries. (c) indicates if things look very wrong, for example if the mass suddenly ramps up.