DOI: 10.7280/d1tm4g
title: Diurnal thermally driven cross‐shore exchange in steady alongshore currents

description: Idealized numerical modeling of thermally-driven baroclinic exchange is
 performed to understand how cross-shore flow is modulated by steady
 alongshore currents and associated shear-generated turbulence. In general,
 we find that shear-driven vertical mixing reduces the temperature
 gradients responsible for establishing the baroclinic flow, such that
 cross-shore thermal exchange diminishes with alongshore current speed.
 Circulation in a base-case simulation of thermal exchange with no
 alongshore forcing contains a cooling response consisting of a midday flow
 in the form of a downslope current with a compensating onshore
 near-surface flow driving cross-shore exchange, followed by an afternoon
 warming response flow via an offshore-directed surface warm front, with a
 compensating return flow at the bottom. Nighttime convective cooling
 enhances vertical mixing and decelerates the warming response, and the
 diurnal cycle is renewed. In this base-case scenario, representative of
 tropical reef environments with optically clear water and weak alongshore
 flow, surface heating and cooling can drive cross-shore circulation with
 O(1) cm s-1 velocities. Alongshore flow forcing is implemented to induce
 upwelling- and downwelling-favorable cross-shore circulation. For mild
 alongshore forcing, the baroclinic cross-shore exchange flow is enhanced
 due to an increase in the horizontal temperature gradient. Stronger
 alongshore flow leads to diminished thermally-driven exchange, ultimately
 reaching a regime where the cross-shore exchange is due predominantly to
 Ekman dynamics. Though exchange velocities are relatively small (O(1) cm
 s-1), these persistent exchange flows are capable of flushing the
 nearshore region multiple times per day, with important implications for
 water properties of nearshore ecosystems.
description: We use the Regional Ocean Modeling System (ROMS), a
 terrain-following, free-surface model that solves finite differences of
 the Reynolds Averaged Navier Stokes equations using hydrostatic and
 Boussinesq approximations (Haidvogel et al., 2008; Shchepetkin &
 McWilliams, 2005). The model grid
 ("RotationGrid.nc") is an alongshore uniform wedge, of 10 m
 lateral (Δx, Δy) resolution, extending 1,000 m in the alongshore and 5,000
 m in the cross-shore. The grid has 30 vertical S-coordinate layers with
 control parameters (Song & Haidvogel, 1994) chosen for sufficient
 resolution near the surface and bottom. Horizontal viscosity and
 diffusivity coefficients are set to dampen noise occurring on a time scale
 of 120 s, with a horizontal Prandtl number of 7 following Marques and
 Özgökmen (2014). The bottom slope, β, and minimum depth are 3% and 1 m,
 respectively, resulting in a maximum domain depth of 151 m. At the onshore
 and alongshore boundaries, all prognostic fields are set to closed and
 periodic boundary conditions, respectively. At the
 offshore boundary, the free surface and barotropic momentum boundary
 conditions are set to those of Chapman (1985) and Mason et al. (2010),
 respectively, to allow signals moving at the shallow water speed to
 radiate out normal to the boundary; the offshore 3D momentum and tracer
 (temperature and salinity) boundaries are set to the radiation condition
 of Orlanski (1976). Finally, the offshore mixing
 turbulent kinetic energy field has a gradient boundary condition. To
 attenuate numerical noise associated with open (offshore) boundary
 conditions, a sponge layer that linearly increases the horizontal
 viscosity and diffusivities by a factor of 10 is inserted in the offshore
 500 m of the domain. We implement a modification of the two-equation k − ϵ
 (Rodi, 1987) version of the Generic Length Scale (Umlauf &
 Burchard, 2003; Warner et al., 2005) parameterization, in which the
 minimum turbulent kinetic energy value is 1E−12 m 2 s −2, and we use the
 multidimensional positive-definite advection transport algorithm (MPDATA).
 The domain is initially quiescent, with uniform temperature and salinity
 fields of 24°C and 35 psu, respectively. All model runs
 have a baroclinic time step of 2 s, with 35 barotropic time steps in
 between each baroclinic time step, and are run for a 28 day simulation.
 The thermal forcing common to all runs is an idealized analytical
 expression representing surface heat fluxes for a periodic diurnal cycle
 of heating and cooling, with periods and amplitudes of both phases
 informed by meteorological observations (see Section 2.3 of the
 publication). The baseline scenario, BA, is forced only by the diurnally
 periodic surface heat flux forcing, and additional simulations were forced
 with the same surface heat flux as that in BA, as well as with steady
 alongshore currents of varying magnitudes (see Table 1 of the
 publication). Within ROMS, the steady alongshore forcing was implemented
 by applying an alongshore-directed kinematic momentum flux with a
 magnitude scaled by the local depth; this is equivalent to a cross-shore
 uniform alongshore pressure gradient. The kinematic momentum flux was then
 applied as a bodyforce throughout the water column by activating the ROMS
 “BODYFORCE” C-preprocessor directive to distribute the stress vertically.
 At the 20 m isobath, this alongshore forcing is equivalent to an
 alongshore pressure gradient ranging from 9.9E−6 m s −2 for the weakest
 alongshore forcing to 9.0E−4 m s −2 for the strongest alongshore
 forcing. Simulations are identified by the ratio of
 u*/uf at the 20 m isobath in Table 1, where the value of u* is computed
 within the model using a logarithmic drag formulation with a uniform
 hydrodynamic roughness (i.e., “z0”) set to 2 cm. A final group of
 simulations was run with the same range of alongshore forcing, but with
 zero buoyancy flux to isolate cross-shore exchange driven solely by the
 Coriolis contribution to the cross-shore momentum budget. These
 simulations achieved equilibrium flow more quickly than the simulations
 with diurnal heating and cooling, so were run for only 10 days, and are
 identified with the prefix “N” in Table 1. Model output
 was analyzed using MATLAB (www.mathworks.com). Analysis is performed on
 the final 14 days of simulated output and all variables are averaged in
 the alongshore direction, from which a diurnal phase-averaged canonical
 day is computed.
description: The files within "ROMSsetups.zip" contain the code to
 be used with the Regional Ocean Modeling System (Haidvogel et al., 2008;
 Shchepetkin & McWilliams, 2005). The file
 "RotationGrid.nc" is the model grid domain. It is a NetCDF file
 that can be viewed with MATLAB, or alternatively, the freely available
 NCview from David W. Pierce (https://cirrus.ucsd.edu/ncview/).