Deposition of evaporites in a salinity- and density-layered sea is examined by theoretically predicting the large-scale circulation in a simplified model sea. In the constant depth model sea, vertical stratification is represented by two homogeneous layers; the upper layer is normal or slightly concentrated sea water, and the considerably denser lower layer is saturated with respect to halite. Each layer has a constant density and volume for all time.
The horizontal transport form of the time-dependent equations of motion and continuity for each layer are solved numerically by a finite-difference method. A forward time extrapolation of four transport components, upper layer depth, and free surface height is performed on a square lattice covering the model basin. Interface stresses acting between the two layers and bottom stresses acting between the lower layer and the bottom allow consideration of vertical turbulent friction. Forcing is by a constant and uniform wind stress acting on the free surface. Rotation and hydrostatic pressure gradient terms are also included in the equations of motion.
Several 140-hr (5.8 days) calculations were made for the Upper Silurian evaporites in Michigan Basin, using reasonable values of physical parameters. For an initially static sea 120 m deep with a 5-m-deep upper layer, mild easterly paleowinds cause upwelling of the lower layer at the north boundary. As the wind continues to blow, the region of upwelling slowly increases in area and migrates around the margin to the east boundary.
In an evaporite sea, salt would precipitate in the exposed lower-layer brine because of evaporation. The salt could precipitate at the free surface as hopper crystals, internally, or at the bottom. By assuming a modest evaporation rate of 10 cm per yr, model calculations show that the total Upper Silurian salt volume is easily accounted for by an average of fewer than two 140-hr wind events per year.
Model predicted upwelling at the north and east boundaries indicates that hopper crystals should be concentrated around the northeast margin of Michigan Basin. Other regional sedimentological and chemical variations related to circulation patterns, such as lithology and reef type, are suggested by the model calculations.