Atmospheric Boundary-Layer Dynamics with Constant Bowen Ratio

Motivated by the observation that the diurnal evolution of sensible and latent heat fluxes tends to maintain a constant Bowen ratio, we derive approximate solutions of the ordinary differential equations of a simplified atmospheric boundary-layer (ABL) model. Neglecting the early morning transition, the potential temperature and specific humidity of the mixed layer are found to be linearly related to the ABL height. Similar behaviour is followed by the inversion strengths of temperature and humidity at the top of the ABL. The potential temperature of the mixed layer depends on the entrainment parameter and the free-atmosphere temperature lapse rate, while the specific humidity also depends on the free-atmosphere humidity lapse rate and the Bowen ratio. The temporal dynamics appear only implicitly in the evolution of the height of the boundary layer, which in turn depends on the time-integrated surface sensible heat flux. Studying the limiting behaviour of the Bowen ratio for very low and very large values of net available energy, we also show how the tendency to maintain constant Bowen ratio during midday hours stems from its relative insensitivity to the atmospheric conditions for large values of net available energy. The analytical expression for the diurnal evolution of the ABL obtained with constant Bowen ratio is simple and provides a benchmark for the results of more complex model

Forest Soil Carbon and Nitrogen Cycles under Biomass Harvest: Stability, Transient Response, and Feedback

Biomass harvest generates an imbalance in forest carbon (C) and nitrogen (N) cycles and the nonlinear biogeochemical responses may have long-term consequences for soil fertility and sustainable management. We analyze these dynamics and characterize the impact of biomass harvest and N fertilization on soil biogeochemistry and ecosystem yield with an ecosystem model of intermediate complexity that couples plant and soil C and N cycles. Two harvest schemes are modeled: continuous harvest at low intensity and periodic clear-cut harvest. Continuously-harvested systems sustain N harvest at steady-state under net mineralization conditions, which depends on the C:N ratio and respiration rate of decomposers. Further, linear stability analysis reveals steady-state harvest regimes are associated with stable foci, indicating oscillations in C and N pools that decay with time after harvest. Modeled ecosystems under periodic clear-cut harvest operate in a limit-cycle with net mineralization on average. However, when N limitation is strong, soil C–N cycling switches between net immobilization and net mineralization through time. The model predicts an optimal rotation length associated with a maximum sustainable yield (MSY) and minimum external N losses. Through non-linear plant–soil feedbacks triggered by harvest, strong N limitation promotes short periods of immobilization and mineral N retention, which alter the relation between MSY and N losses. Rotational systems use N more efficiently than continuous systems with equivalent biomass yield as immobilization protects mineral N from leaching losses. These results highlight dynamic soil C–N cycle responses to harvest strategy that influence a range of functional characteristics, including N retention, leaching, and biomass yield

Thermodynamic relations among isotropic material properties in conditions of plane shear stress

We present new general relationships among the material properties of an isotropic material kept in homogeneous stress conditions with hydrostatic pressure and plane shear. The derivation is not limited to the proximity of the zero shear-stress and -strain condition, which allows us to identify the relationship between adiabatic and isothermal shear compliances (inverse of the moduli of rigidity) along with new links, among others, between isobaric and isochoric shear thermal expansion coefficients, heat capacities at constant stress and constant shear strain. Such relationships are important for a variety of applications, including characterization of nanomaterials as well as identification of properties related to earthquakes precursors and complex media (e.g., soil) behaviors. The results may be useful to investigate the behavior of materials during phase transitions involving shear or in non-homogeneous conditions within a local thermodynamic equilibrium framework