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1. Single-Mode Solutions for Convection and Double-Diffusive Convection in Porous Media

   https://doi.org/10.3390/fluids7120373  

   Liu, Chang ; Knobloch, Edgar ( December 2022 , Fluids)

   This work employs single-mode equations to study convection and double-diffusive convection in a porous medium where the Darcy law provides large-scale damping. We first consider thermal convection with salinity as a passive scalar. The single-mode solutions resembling steady convection rolls reproduce the qualitative behavior of root-mean-square and mean temperature profiles of time-dependent states at high Rayleigh numbers from direct numerical simulations (DNS). We also show that the single-mode solutions are consistent with the heat-exchanger model that describes well the mean temperature gradient in the interior. The Nusselt number predicted from the single-mode solutions exhibits a scaling law with Rayleigh number close to that followed by exact 2D steady convection rolls, although large aspect ratio DNS results indicate a faster increase. However, the single-mode solutions at a high wavenumber predict Nusselt numbers close to the DNS results in narrow domains. We also employ the single-mode equations to analyze the influence of active salinity, introducing a salinity contribution to the buoyancy, but with a smaller diffusivity than the temperature. The single-mode solutions are able to capture the stabilizing effect of an imposed salinity gradient and describe the standing and traveling wave behaviors observed in DNS. The Sherwood numbers obtained from single-mode solutions show a scaling law with the Lewis number that is close to the DNS computations with passive or active salinity. This work demonstrates that single-mode solutions can be successfully applied to this system whenever periodic or no-flux boundary conditions apply in the horizontal. 

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2. Supporting Information for The Future of Ground Magnetometer Arrays in Support of Space Weather Monitoring and Research

   Engebretson, Mark ; Zesta, Eftyhia ( July 2017 , Space weather)

   This file contains three tables and one figure. Table S1 lists the institutions represented at the initial Ground Magnetometer Array Workshop. Table S2 contains information about all NSF-AGS supported and USGS ground-based magnetometer arrays as of Fall 2016 and Figure S1 is a map showing these arrays. Table S3 lists web sites serving ground magnetometer data. 

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3. Site U1595

   Druitt, TH ; Kutterolf, S ; Ronge, TA ; Beethe, S ; Bernard, A ; Berthod, C ; Chen, H ; Chiyonobu, S ; Clark, A ; DeBari, S ; et al ( July 2024 , Proceedings of the International Ocean Discovery Program Expedition reports)

   Site U1595 (proposed Site CSK-08B) is located in the southern basin of the Santorini caldera at 291 meters below sea level (mbsl) (Figure F1). It was drilled in three holes (U1595A–U1595C) to a maximum recovery depth of 127.0 meters below seafloor (mbsf) (all depths below seafloor are given using the core depth below seafloor, Method A [CSF-A], scale, except in Operations where the drilling depth below seafloor [DSF] scale is used). Average hole core recoveries range 46%–77%. Site U1594 addresses the same drilling objectives and lies northeast of Site U1595. Two additional sites (U1596 and U1597) lie in the northern caldera basin. Four seismic units (S1–S4) were previously recognized in the Santorini caldera (Johnston et al., 2015; Nomikou et al., 2016) (Figure F2). Seismic Units S1–S3 were thought to consist of muds and sands from cliff mass wasting (Unit S1); compacted (possibly lithified) sandy volcaniclastics from Kameni Volcano (Unit S2); and consolidated coarse blocky intracaldera tuffs, landslide debris, and/or flood gravels (Unit S3). Unit S4 was thought to be intracaldera tuff from the Late Bronze Age eruption. The four caldera sites were planned to sample Units S1–S3; test the published correlations between the two caldera basins; penetrate below Unit S3 into Unit S4; and address scientific Objectives 1, 4, 5, and 7 of the Expedition 398 Scientific Prospectus (Druitt et al., 2022). By drilling both caldera basins and exploiting our dense seismic reflection coverage, we gained access to the 3D architecture of the entire caldera fill. We also targeted the question of why the northern basin is 100 m deeper than the southern one. Finally, we tested whether Unit S3 consisted of flood debris from the caldera flooding event (Nomikou et al., 2016) or whether it was Late Bronze Age intracaldera tuff (Johnston et al., 2015). The intracaldera sites were used for microbiological work of Objective 7. 

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4. Suppression of internal waves by thermohaline staircases

   https://doi.org/10.1017/jfm.2020.563  

   Radko, Timour ( November 2020 , Journal of Fluid Mechanics)

   null (Ed.)

   This study attempts to quantify and explain the systematic weakening of internal gravity waves in fingering and diffusive thermohaline staircases. The interaction between waves and staircases is explored using a combination of direct numerical simulations (DNS) and an asymptotic multiscale model. The multiscale theory makes it possible to express the wave decay rate $({\lambda _d})$ as a function of its wavenumbers and staircase parameters. We find that the decay rates in fully developed staircases greatly exceed values that can be directly attributed to molecular dissipation. They rapidly increase with increasing wavenumbers, both vertical and horizontal. At the same time, ${\lambda _d}$ is only weakly dependent on the thickness of layers in the staircase, the overall density ratio and the diffusivity ratio. The proposed physical mechanism of attenuation emphasizes the significance of eddy diffusion of temperature and salinity, whereas eddy viscosity plays a secondary role in damping internal waves. The asymptotic model is successfully validated by the DNS performed in numerically accessible regimes. We also discuss potential implications of staircase-induced suppression for diapycnal mixing by overturning internal waves in the ocean. 

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5. The Formation of Double‐Diffusive Layers in a Weakly Turbulent Environment

   https://doi.org/10.1029/2018JC014625  

   Shibley, N. C. ; Timmermans, M. ‐L. ( March 2019 , Journal of Geophysical Research: Oceans)

   Double‐diffusive stratification in the ocean is characterized by staircase structures consisting of mixed layers separated by high‐gradient interfaces in temperature and salinity. These double‐diffusive layers, which flux heat vertically, are observed over a vast region of the Arctic Ocean at the top boundary of the relatively warm and salty Atlantic water layer. In one formalism for the origin of double‐diffusive layers, staircase formation arises when a heat source is applied at the base of water that is stably stratified in salinity. This framework is extended to consider the effect of intermittent shear‐driven turbulence on diffusive‐convective staircase formation. One‐dimensional numerical model results indicate that there is a critical level of intermittent turbulence above which a staircase cannot form. This is framed in terms of a critical diffusivity ratio (ratio of effective salinity diffusivity to effective thermal diffusivity) that cannot be exceeded for a staircase to persist. This critical ratio is not a universal constant but rather differs for each staircase. Model results further indicate that layer thicknesses decrease with height in a staircase, with the variation in thickness over a staircase being more pronounced in the presence of intermittent turbulence. Finally, results suggest that increased diffusivity ratios lead to decreased heat fluxes across interfaces; if a staircase is subject to intermittent turbulence levels (below the critical level), vertical heat fluxes will be smaller than in the absence of shear‐driven turbulence. Findings are related to double‐diffusive staircases, and associated heat fluxes, in the weakly turbulent Arctic Ocean.

    

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