Salt Polygons are Caused by Convection Jana Lasser,1, 2, ∗ Joanna M. Nield,3 Marcel Ernst,1 Volker Karius,4 Giles F. S. Wiggs,5 and Lucas Goehring6, y 1Max Planck Institute for Dynamics and Self-Organization, Am Fassberg 17, 37077 Gottingen,¨ Germany 2Institute for Nonlinear Dynamics, Georg-August-University Gottingen,¨ Friedrich-Hund-Platz 1, 37077 Gottingen,¨ Germany 3Geography and Environment, University of Southampton, Highfield, Southampton SO17 1BJ, UK 4Geowissenschaftliches Zentrum, Georg-August-University, Goldschmidtstrasse 3, 37077 Gottingen,¨ Germany 5Aeolian Geomorphology, University of Oxford, Radcliffe Sq, Oxford OX1 4AJ, UK 6School of Science and Technology, Nottingham Trent University, Nottingham NG11 8NS, UK (Dated: November 6, 2019) From fairy circles to patterned ground and columnar joints, natural patterns spontaneously appear in many complex geophysical settings. Here, we shed light on the origins of polygonally patterned crusts of salt playa and salt pans. These beautifully regular features, approximately a meter in diameter, are found worldwide and are fundamentally important to the transport of salt and dust in arid regions. We show that they are consistent with the surface expression of buoyancy-driven convection in the porous soil beneath a salt crust. By combining quantitative results from direct field observations, analogue experiments, linear stability theory, and numerical simulations, we further determine the conditions under which salt polygons should form, as well as how their characteristic size emerges. INTRODUCTION ter and energy balances of fragile environments. Research on salt pans has typically focused on ei- Salt deserts are amongst the most inhospitable places ther the dynamics of their complex subsurface flows of our planet. Their otherworldly shapes inspire the [14–18] or their crusts, without considering how these imagination (e.g. Star Wars desert planet Crait [1], features could interact. Crust patterns have been at- or the million tourists annually visiting Death Valley tributed to buckling or wrinkling as expanding areas of [2]), and are an important drive of climate processes crust collide [5, 19, 20], or to surface cracks [6, 21– [3]. The immediately prominent feature of such land- 24]. For example, a model of crust patterns develop- scapes (Fig. 1) is a characteristic tiling of polygons, ing from contraction cracks in mud is given by Krins- formed by ridges in the salt-encrusted surface. These ley [21] whereas Christiansen [19] provides a quanti- patterns decorate salt pans around the world, including tative model based on buckling, and most subsequent Salar de Uyuni in Chile, Chott el Djerid in Tunisia [4], discussion reiterates these ideas. However, for such Badwater Basin in California and the periphery of the mechanical instabilities the expected feature size is a Dead Sea – always expressing the same size of about few times the thickness of the cracking [21, 25–27] or one meter. buckling [28, 29] layer. As well, buckling is known Salt crusts are dynamic over months to years [5–8], to favour parallel wrinkles rather than closed poly- and couple to other environmental processes. Wind gons [28, 29]. Salt playa crusts vary in thickness from sub-centimeter to meters [5, 6, 21], which cannot it- arXiv:1902.03600v2 [nlin.PS] 5 Nov 2019 over crust creates dust, the emission of which forms a significant proportion of the Earth’s global atmospheric self explain the consistent polygon diameters of 1– dust production [3, 9] and of mineral transport to the 2 m. Similarly, there is no clear reason why preex- oceans [10]. As one example, dust from the surface of isting mud-cracks, surface roughness or other hetero- the dry Owens Lake has posed a major health problem geneities would appear worldwide at the same length- for people living downwind of the lake [11, 12], and the scale and arrangement. For example, at Owens Lake site is the centre of a decades-long, intense remediation we observed crusts 1–20 cm thick, desiccation cracks effort. Salt crusts also modify evaporation and heat flux in crust-free mud of ∼10 cm spacing and intermit- from the playa surface [13], and hence the critical wa- tent buckling of crust (see Supplemental Movie) with wavelengths of ∼2 cm and parallel rather than polygo- nal features. While salt precipitation may take advan- tage of any such pre-existing surface structures, none ∗ [email protected] of these can adequately explain the patterns and scales y [email protected] observed in the crust polygons. 2 evaporation salt ridge high salinity B Z pore fluid flows low salinity X FIG. 2. Proposed dynamics of patterned salt crusts. Evapo- ration leaves the near-surface fluid enriched in salt, and heav- ier than the fluid beneath it. This drives convection, with A C downwellings of high salinity pore fluid co-localized with surface ridges. The dominant fluid motions are shown by the FIG. 1. Typical salt polygon patterns at A, C Badwater black arrows, and the water salinity is indicated by the colour Basin in Death Valley and B, Owens Lake, California (image contours. At downwellings, the weak salt gradients in the A courtesy Sarah Marino). groundwater enhance salt precipitation/crust growth, leading to ridges; at upwelling plumes the stronger gradients favour diffusive over advective transport, and crust growth is slower. Here we show that by instead considering the sur- MODEL OF SUBSURFACE CONVECTION face of a salt playa jointly with its subsurface flows, the origins, dynamics, length-scale and shape of the polyg- We consider the coupling of surface salt patterns to onal patterns in salt crusts can be apprehended. Specif- subsurface flows, as visualised in Fig. 2. Specifically, ically, by combining theoretical analysis, numerical we treat fluid and salt transport in a saturated porous simulations, analogue experiments and field observa- medium, driven by surface evaporation and fed from tions, we show that density-driven convective dynam- below by a reservoir of water with some background ics will lead to heterogeneity in the horizontal salin- salinity. The aquifer is deep, compared to the diame- ity distribution of evaporating groundwater, at the same ter of the salt polygons, and any corresponding near- scale as the observed polygons. These convective cells surface dynamics. This system will naturally develop can act to template the position of polygons, setting a salinity gradient below the surface, which can be- their size and shape. For example, we will show how come unstable to convective overturning [14–16]. To salt ridges should naturally develop over descending determine whether field conditions will support such a plumes of dense salty groundwater, where faster salt buoyancy-driven convective instability, we start from precipitation will be expected, and demonstrate such mass and momentum balances, as are used to describe co-location in the field. thermal [14] or solutal [16, 35] convection in porous media. We then perform a linear stability analysis to The salt polygons at Owens Lake (Fig. 1B) have a give the criteria for convection, and will confirm this typical pattern in a well-studied and controlled land- instability via simulations, experiments and field ob- scape; their summary also introduces our modelling as- servations. sumptions and main field site. This dry, terminal saline We model the volumetric flux q of a fluid driven by lake has an aquifer that extends from the near-surface pressure p through a porous medium of constant uni- to >150 m depth [30]. The groundwater carries dis- form porosity φ and permeability κ. The fluid has a solved salts [12, 31], which collect in an evaporite pan viscosity µ and carries dissolved salt, whose diffusivity of about 300 km2 [3, 30]. Efforts to control dust emis- D is corrected for the presence of different ions as well sion from the lake-bed involve shallow flooding [32], as tortuosity (see Methods). Using the Boussinesq ap- vegetation [33], gravel cover and crust growth [34]. As proximation, buoyancy is generated by a variable fluid shown in the online supplementary movie S1, after a density ρ = ρb + S∆ρ, where ρb is the density of the flooding event the soil is saturated with water, which reservoir fluid, and ρb + ∆ρ is that of the top bound- evaporates leaving behind salts that crystallize into a ary; the relative salinity S linearly mediates between continuous crust, covered by a network of ridges. the two limits. The model consists of the continuity 3 equation for incompressible fluid flow, Darcy’s law and tion (see [38] for derivation) are shown in Fig. 3A. At an advection-diffusion equation for salt transport: Rac the critical wavenumber, ac = 0:76, corresponds to a wavelength of about 1-2 m, under typical field con- r · q = 0 (1) ditions. κ q = − [r(p + ρ gz) + S∆ρgz^] (2) µ b @S INSTABILITY AND SCALE SELECTION. φ = φDr2S − q · rS (3) @t To determine the Rayleigh numbers relevant to field where g is the acceleration due to gravity, and z^ is an conditions, and to thus evaluate if they should lead to upward-pointing unit vector. convection and an associated pattern of crust precip- Taking the average evaporation rate E as the natural itation, we measured the relevant parameters at sites velocity scale for the system, we set the characteristic in Owens Lake (CA), Badwater Basin (CA) and Sua length and time as L = φD=E and T = φ2D=E2, Pan (Botswana) – see Methods for details. From grain- respectively. Non-dimensionalization of Eqs. 1-3 then size distributions we calculated ds, the Sauter diame- gives ter [39], of near-surface soil samples; results, from 4 to 138 µm, represent a silt to fine sand. A high soil r · U = 0 (4) porosity, φ = 0:70 ± 0:02, was previously measured ^ at Owens Lake [40]. For relative permeability we use U = −∇P − RaSZ (5) 5:6 2 the empirical relationship κ = 0:11 φ ds , which fits @S = r2S − U · rS (6) a broad set of experimental and simulation data [41].