SUMMARYInterest in the use of supercomputers for the direct numerical calculation of turbulence prompts the development of efficient numerical techniques so that calculation at higher Reynolds numbers might be made. This paper presents an efficient pseudo-spectral technique, similar to but different from others that have recently appeared, for the calculation of momentum and heat transfer to a constant-property, turbulent fluid in a two-dimensional channel with walls at different, uniform temperature. The code uses no empiricism, although periodic boundary conditions are used for fluctuating quantities in the streamwise and spanwise directions.Calculations were made for a Prandtl number of 072 and Reynolds number based on friction velocity and channel half-height of 180 or 2800 based on channel half-height and average velocity. Calculations of mean velocity profile, turbulence intensities, skewness, flatness, Reynolds stress and eddy diffusivity of heat near a wall compare favourably with experimental results. Representative contour plots of the temperature field near the wall and of the spanwise and streamwise two-point velocity correlations are given.Deficiencies are that the calculation requires many hours on a fast computer with a large high-speed memory and that the grid size in each direction for appropriate resolution is approximately proportional to the square of the Reynolds number and to the Prandtl number raised to some power greater than one.
Areas of improving and degrading groundwater-quality conditions in the State of California were assessed using spatial weighting of a new metric for scoring wells based on constituent concentrations and the direction and magnitude of a trend slope (Sen). Individual well scores were aggregated across 2135 equal-area grid cells covering the entire groundwater resource used for public supply in the state. Spatial weighting allows results to be aggregated locally (well or grid cell), regionally (groundwater basin), provincially, or statewide. Results differentiate degrading (increasing concentration trends) areas with low to moderate concentrations (unimpaired) from degrading areas with moderate to high concentrations (impaired). Results also differentiate improving areas (decreasing concentration trends) in the same manner. Multi-year to decadal groundwater-quality trends were computed from periodic, inorganic water-quality data for 38 constituents collected between 1974 and 2014 for compliance monitoring of nearly 13,000 public-supply wells (PSWs) in the State of California. Mann-Kendall (MK) rank correlations and Sen's slope estimator were used to detect statistically significant trends for the entire period of recorded data (long-term trend), for the period since 2000 (recent trend), for different pumping seasons (seasonal trend), and for reversals of trends. Statewide, the most frequently detected trends since 2000 were for nitrate (36%), gross alpha/uranium (10%), arsenic (14%), total dissolved solids (TDS) (23%), and the major ions that contribute to TDS (19-28%). The Transverse and Selected Peninsular Ranges (TSPR) and the San Joaquin Valley (SJV) hydrogeologic provinces had the largest percentage of areas with moderate to high nitrate concentrations and groundwater quality trends. Improving nitrate concentrations in parts of the TSPR is associated with long-term managed aquifer recharge that has replaced historical, agriculturally affected groundwater with low-nitrate recharge in parts of the TSPR. This example suggests that application of dilute, excess surface water to agricultural fields during the winter could improve groundwater-quality in the SJV over the long term.
SUMMARYThe possibility of improving heat transfer rates by the imposition of a wavy boundary led to this extension of direct simulation of heat transfer in turbulent flow in a channel. This part of the paper shows how a pattern of micro-riblets on the surface and parallel to the flow is incorporated into the solution of the Navier-Stokes and temperature equations. The channel is two-dimensional with walls at different but uniform temperatures, and the fluid properties are constant. The presence of the patterns presents a considerable computational problem that can be largely overcome by the use of a discrete Green function technique. The method is illustrated by making short-time calculations of the velocity and temperature fields for a Prandtl number of 0.72, a Reynolds number based on channel half-width and bulk velocity of 2800, and a sinusoidal pattern with a height of 5 wall units.
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