DOI: 10.5061/dryad.n2z34tn99
title: Data from: Fluxes and mixing of reacting biogeochemical scalars in a stratified shear layer

description: Biogeochemical scalars, representing many different species of
 phytoplankton, zooplankton, nutrients, etc., play an important role in
 marine ecosystems. Here we examine a simplified two-species system of
 generic phytoplankton and nutrient populations, modeled here as reacting
 scalars governed by advection-diffusion equations with added terms
 governing the biological reaction (nutrient uptake, phytoplankton
 death/remineralization). We perform direct numerical simulations of an
 idealized scenario in which initial layers of phytoplankton and nutrients
 are separated by an unstable stratified shear layer susceptible to either
 Kelvin-Helmholtz or Holmboe instability (canonical examples of overturning
 and scouring mixing events, respectively). We further vary the ratio of
 the reaction and flow timescales, considering cases of fast, slow, and
 comparable reaction rates. We find that turbulent advective fluxes show
 large oscillations during the evolution of the shear instabilities,
 associated with reversible fluid motions. To isolate the irreversible
 turbulent scalar fluxes, we instead calculate diascalar fluxes, that is,
 diffusive fluxes across isoscalar surfaces. This concept has been
 previously used to quantify irreversible mixing of buoyancy in stratified
 mixing events; here, we extend this approach to also account for the
 effects of biogeochemical reactions. With this analysis, we show that both
 instabilities accelerate phytoplankton growth, that the KH-driven mixing
 tends to have a larger impact on the phytoplankton growth than the Holmboe
 flow, and that the largest impact of the flow on the scalar evolution
 occurs when reaction timescales are comparable to the buoyancy period.
description: # Data from: Fluxes and mixing of reacting biogeochemical scalars in a
 stratified shear layer Dataset DOI:
 [10.5061/dryad.n2z34tn99](10.5061/dryad.n2z34tn99) ## Description of the
 data and file structure Data from two sets of fully three-dimensional
 stratified shear instability simulations (Kelvin-Helmholtz, Holmboe).
 Included are data directly from simulation output, as well as quantities
 calculated in post-processing. ### Files and variables #### File:
 Re1000_Pr7_R1_SEP.mat, Re1000_Pr7_R3_SEP.mat **Description:** These files
 contain horizontally averaged quantities for the Kelvin-Helmholtz case
 (R1) and Holmboe case (R3). These simulations included 13 scalar fields
 that are advanced in time along with the velocity and pressure. All
 variables involving the scalars have final dimension of size 13. Scalar 1
 is buoyancy. Scalars 4, 8, and 12 are phytoplankton at low, intermediate,
 and high Dahmköhler number as seen in the paper. Scalars 2, 6, and 10 are
 phytoplankton at low, intermediate, and high Dahmköhler number without any
 initial separation between the phytoplankton and nutrient layers (these do
 not appear in the paper). Scalars 3, 5, 7, 9, 11, and 13 are nutrients,
 each corresponding to the preceding phytoplankton scalar. Note that these
 simulations and their outputs are entirely non-dimensional. Using the
 initial tanh profiles for velocity, buoyancy, phytoplankton, and
 nutrients, lengths are nondimensionalized by the shear layer half-width,
 times by an advective timescale, velocities by initial maximum velocity,
 buoyancy by initial maximum buoyancy, and phytoplankton and nutrient by
 initial maximum magnitude. See equations (1-3) in the associated
 publication for more detail. ##### Variables * gyf: vertical grid * time:
 time * DA: Dahmköhler number * NU: viscosity [m^2/s] * Re: Reynolds number
 * R: ratio of velocity and buoyancy interface widths (R=1 is
 Kelvin-Helmholtz, R=3 is Holmboe) * RI: Richardson number * Pr: Prandtl
 number * ume,vme,wme: three components of velocity * thme: scalar fields *
 uv,uw,wv: fluctuation covariance (Reynolds stresses) * thth: fluctuation
 covariance between different scalars. This quantity represents the
 interaction between each pair of scalars (2&3, 4&5, 6&7,
 8&9, 10&11, 12&13), so thth(:,:,2)=thth(:,:,3) and so on for
 each pair. thth(:,:,1) has been set to NaN because the first scalar
 represents buoyancy and is not part of any phytoplankton-nutrient scalar
 pair. The array is constructed with third dimension size of 13 in order to
 be consistently sized with other variables. * thv: fluctuation covariance
 between scalar and vertical velocity * urms,vrms,wrms: root mean square of
 velocity fluctuation * thrms: root mean square of scalar fluctuation *
 dudy,dwdy,dthdy: vertical gradients of horizontal velocity and scalars *
 omega_x,omega_y,omega_z: three components of vorticity * epsilon:
 dissipation #### File: stable_Re1000_Pr7_R1_SEP.mat,
 stable_Re1000_Pr7_R3_SEP.mat **Description:** These files contain
 horizontally averaged values of the scalars as advanced by the simple 1D
 model including only diffusion and the biological reaction. #####
 Variables * ref_gyf: vertical grid (same as full 3D simulation) *
 ref_time: time (same as full 3D simulation) * ref_thme: scalar fields ####
 File: zstar_R1.mat, zstar_R3.mat **Description:** These files contain data
 of scalars after transformation into the sorted coordinate z_*. Note that
 this analysis required calculations using the full 3D velocity and scalar
 fields, which were saved less frequently than the horizontally averaged
 data in the files described above. These calculations involve
 rearrangement of the physical scalar fields, leading to occasional values
 of 'NaN' near boundaries where resolution is lower than in the
 center of the domain. These 'NaN' values can be neglected during
 interpretation of the data. ##### Variables * gyf: vertical grid * time:
 time * th_zstarmean: scalar field after being sorted into z_* space *
 rxn_zstarmean: reaction term after being sorted into z_* space * phid:
 diascalar flux (phi_d) * dphiddz: vertical gradient of diascalar flux
 (phi_d) #### File: input_R1.dat, input_R3.dat, input_chan.dat
 **Description:** These files contain numerical parameters, domain sizes,
 boundary conditions, etc. More information can be found on DIABLO input
 files at
 [https://github.com/johnryantaylor/DIABLO](https://github.com/johnryantaylor/DIABLO) #### File: grid_def, grid_def.all, grid_mpi, grid.h5 **Description:** These files contain the grid size, the grid size per processor, the processor parallelization breakdown, and the gridpoints in the vertical direction, respectively. More information can be found on DIABLO grid files at [https://github.com/johnryantaylor/DIABLO](https://github.com/johnryantaylor/DIABLO) #### File: user_rhs.f **Description:** This Fortran subroutine implements a user-inputted right-hand side of the governing equations. This file shows the implementation of the biological active terms in the governing phytoplankton and nutrient scalar equations. This is a modified version of the user_rhs.f that can be found at [https://github.com/johnryantaylor/DIABLO](https://github.com/johnryantaylor/DIABLO)