A scale-dependent dynamic model for large-eddy simulation: application to a neutral atmospheric boundary layer

A scale-dependent dynamic subgrid-scale model for large-eddy simulation of turbulent flows is proposed. Unlike the traditional dynamic model, it does not rely on the assumption that the model coefficient is scale invariant. The model is based on a second test-filtering operation which allows us to determine from the simulation how the coefficient varies with scale. The scale-dependent model is tested in simulations of a neutral atmospheric boundary layer. In this application, near the ground the grid scale is by necessity comparable to the local integral scale (of the order of the distance to the wall). With the grid scale and/or the test-filter scale being outside the inertial range, scale invariance is broken. The results are compared with those from (a) the traditional Smagorinsky model that requires specification of the coefficient and of a wall damping function, and (b) the standard dynamic model that assumes scale invariance of the coefficient. In the near-surface region the traditional Smagorinsky and standard dynamic models are too dissipative and not dissipative enough, respectively. Simulations with the scale-dependent dynamic model yield the expected trends of the coefficient as a function of scale and give improved predictions of velocity spectra at different heights from the ground. Consistent with the improved dissipation characteristics, the scale-dependent model also yields improved mean velocity profiles

Groundwater waves in a coastal aquifer: A new governing equation including vertical effects and capillarity

Groundwater waves, that is, water table fluctuations, are a natural phenomenon in coastal aquifers. They represent an important part of the interaction between the ocean and aquifer and affect the mass exchange between them. This paper presents a new groundwater wave equation. Because it includes the effects of vertical flows and capillarity, the new equation is applicable to both intermediate-depth aquifers and high-frequency waves. Compared with the wave equation derived by Nielsen ed al. [1997], the present equation provides a closer representation of groundwater waves. In particular, it predicts high-frequency water table fluctuations as observed in the field. A validation of the new equation has been carried out by comparing the analytical solutions to it with predictions from direct simulations using the numerical model SUTRA. The effects of various physical parameters and their relative importance are also discussed

On Monin-Obukhov similarity in the stable atmospheric boudary layer

Atmospheric measurements from several field experiments have been combined to develop a better understanding of the turbulence structure of the stable atmospheric boundary layer. Fast response wind velocity and temperature data have been recorded using 3-dimensional sonic anemometers, placed at several heights (≈ 1 m to 4.3 m) above the ground. The measurements were used to calculate the standard deviations of the three components of the wind velocity, temperature, turbulent kinetic energy (TKE) dissipation and temperature variance dissipation. These data were normalized and plotted according to Monin–Obukhov similarity theory. The non-dimensional turbulence statistics have been computed, in part, to investigate the general applicability of the concept of z-less stratification for stable conditions. From the analysis of a data set covering almost five orders of magnitude in the stability parameter ζ = z/L (from near-neutral to very stable atmospheric stability), it was found that this concept does not hold in general. It was only for the non-dimensional standard deviation of temperature and the average dissipation rate of turbulent kinetic energy that zless behaviour has been found. The other variables studied here (non-dimensional standard deviations of u, v, and w velocity components and dissipation of temperature variance) did not follow the concept of z-less stratification for the very stable atmospheric boundary layer. An imbalance between production and dissipation of TKE was found for the near-neutral limit approached from the stable regime, which matches with previous results for near-neutral stability approached from the unstable regime

Atmospheric stability effect on subgrid scale physics for large-eddy simulation

Field measurements in the atmospheric boundary layer were carried out to identify the effect of atmospheric stability on subgrid-scale physics for large-eddy simulation. The basic instrumentation setup consisted of 12 three-dimensional sonic anemometers arranged in two parallel horizontal arrays (seven sensors in the lower array and five sensors in the upper array). Data from this setup are used to compute the subgrid-scale (SGS) heat fluxes and SGS dissipation of the temperature variance under stable and unstable stability conditions. The relative contribution of the SGS vertical flux to the total turbulent flux increases when going from unstable to stable conditions. The relative importance of negative SGS dissipation (backscatter) events becomes larger under stable conditions. The model coefficients for two well-known SGS models (eddy-viscosity and non-linear) are computed. Model coefficients are found to depend strongly on stability. Under both stable and unstable conditions, large negative SGS dissipation is associated with the onset of ejection events while large positive SGS dissipation tends to occur during the onset of sweep events. These findings are also supported by conditionally sampled 2D velocity and temperature fields obtained using the 12 anemometers placed in a vertical array

Analytical approximation for the recession of a sloping aquifer

An approximation is obtained for the recession of a sloping aquifer. The analytical approximation can provide a useful tool to analyze data and obtain physical properties of the aquifer. In contrast to the case of a horizontal aquifer, when plotting the time derivative of the flux versus the flux on a log scale, the result shows that the flux derivative reaches a minimum value and that the curve can have a slope of unity as often observed. Illustration of the application of the analytical results to the Mahantango Creek data is also discussed

Mixture of time scales in land-atmosphere interaction: Desorption and self-similarity of energy fluxes

The time evolution of evaporation from a bare soil, over a 9-d period following irrigation, is described by a combination of daily and hourly drying patterns. From the second day, the daily evaporation shows a second stage of drying that can be described as a desorptive process (evaporation proportional to (t - to)-1/2, where t is time in days and to is the day when the second stage starts). The short time (hourly) evaporation rate can be modeled on the basis of a type of self-similarity in the energy balance components. Combining the evaporative flux behavior at the two time scales, desorption at the daily timescale and self-similarity for the diurnal variations, a robust description of evaporation for drying land surfaces is obtained. This approach is tested using accurate measurements of the different com-ponents of the energy balance at the soil surface, obtained at 20-min intervals. The model accurately describes the time evolution of the evaporative flux and could be used for the disaggregation of daily or weekly evaporation into hourly values

Predicting Shallow Groundwater Tables for Sloping Highland Aquifers

While hydrological science has made great strides forward during the last 50 years with the advance of computing power and availability of satellite images, much is unknown about the sustainable development of water for irrigation, domestic use, and livestock consumption for millions of households in the developing world. Specifically, quantification of shallow underground water resources for irrigation in highland regions remains challenging. The objective is to better understand the hydrology of highland watersheds with sloping hillside aquifers. Therefore, we present a subsurface flow model for hillside aquifers with recharge that varied from day to day. Recharge to the aquifer was estimated by the Thornthwaite Mather procedure. A characteristic time was identified for travel time of water flowing from the upper part of the hillside to the river or well. Using the method of characteristics, we found that the height of shallow groundwater level can be predicted by determining the total recharge over the characteristic time divided by drainable porosity. We apply the model to farmer‐dug wells in the Ethiopian highlands using observed rainfall, potential evaporation, and a fitted travel time. We find that the model performs well with maximum water table heights being determined by the soil surface and minimum heights by the presence or absence of volcanic dikes downhill. Our application shows that unless the water is ponded behind a natural or artificial barrier, hillslope aquifers are unable to provide a continuous source of water during the long, dry season. This clearly limits any irrigation development in the highlands from shallow sloping groundwater

Analytical approximation for the recession of a sloping aquifer

An approximation is obtained for the recession of a sloping aquifer. The analytical approximation can provide a useful tool to analyze data and obtain physical properties of the aquifer. In contrast to the case of a horizontal aquifer, when plotting the time derivative of the flux versus the flux on a log scale, the result shows that the flux derivative reaches a minimum value and that the curve can have a slope of unity as often observed. Illustration of the application of the analytical results to the Mahantango Creek data is also discussed