Cattle (Bos spp.) grazing on weed–mixed forage biomass may potentially spread weed seeds, leading to plant invasions across pasturelands. Understanding the possibility and intensity of this spread is crucial for developing effective weed control methods in grazed areas. This research undertook an in vitro experiment to evaluate the germination and survival of five dominant weed species in the southern United States [Palmer amaranth (Amaranthus palmeri S. Watson), yellow foxtail [Setaria pumila (Poir.) Roem. & Schult.], johnsongrass [Sorghum halepense (L.) Pers.], field bindweed (Convolvulus arvensis L.) and pitted morningglory (Ipomoea lacunosa L.)] upon incubation in rumen fluid for eight time periods (0, 4, 8, 12, 24, 24, 48, 72, and 96 h). For the 96-h treatment, a full Tilley and Terry procedure was applied after 48 h for stopping fermentation, followed by incubation for another 48 h simulating abomasum digestion. Seed germination, upon incubation, varied significantly among weed species, with I. lacunosa reaching zero germination after only 24 h of incubation, whereas A. palmeri and S. halepense retained up to 3% germination even after 96 h of incubation. The hard seed coats of A. palmeri and S. halepense likely made them highly resistant, whereas the I. lacunosa seed coat became easily permeable and ruptured under rumen fluid incubation. This suggests that cattle grazing can selectively affect seed distribution and invasiveness of weeds in grazed grasslands and rangelands, including the designated invasive and noxious weed species. As grazing is a significant component in animal husbandry, a major economic sector in the U.S. South, our research provides important insights into the potential role of grazing as a dispersal mechanism for some of the troublesome arable weeds in the United States. The results offer opportunities for devising customized feeding and grazing practices combined with timely removal of weeds in grazeable lands at the pre-flowering stage for effective containment of weeds.

A small-disturbance model for a steady, two-dimensional, inviscid and transonic flow of a single-phase real gas around a thin airfoil is presented. The approach explores the nonlinear interactions among near-sonic speed of the flow, small thickness ratio of the airfoil and upstream properties of the fluid. The gas thermodynamic properties are related by a general equation of state. Information about thermodynamic modelling of the gas is lumped into one similarity parameter, $K_G$, related to the fundamental derivative of gas dynamics. The flow field is described by a modified transonic small-disturbance problem. The theory applies to any working fluid of interest. Model problems are derived for steam flows described by the perfect, van der Waals, virial and Redlich–Kwong gas equations of state. Predictions are compared according to the various gas models under various free-stream operating conditions from low subcritical to high supercritical thermodynamic states to gain insights into the sensitivity of the small-disturbance problem solution to thermodynamic modelling of the gas. Results show that transonic flows are independent of gas modelling at low subcritical thermodynamic conditions. However, at near-critical and supercritical thermodynamic conditions, transonic flow behaviour is significantly sensitive to gas modelling and variations of $K_G$. The upstream flow critical Mach number increases as the flow approaches thermodynamic critical state and a wider range of upstream Mach numbers can be found where pressure drag is zero. However, at supercritical conditions, $K_G$ increases, resulting in lower critical Mach numbers and higher pressure drags.

A small-disturbance asymptotic model is derived to describe the complex nature of a pure water vapour flow with non-equilibrium and homogeneous condensation around a thin airfoil operating at transonic speed and small angle of attack. The van der Waals equation of state provides real-gas relationships among the thermodynamic properties of water vapour. Classical nucleation and droplet growth theory is used to model the condensation process. The similarity parameters which determine the flow and condensation physics are identified. The flow may be described by a nonlinear and non-homogeneous partial differential equation coupled with a set of four ordinary differential equations to model the condensation process. The model problem is used to study the effects of independent variation of the upstream flow and thermodynamic conditions, airfoil geometry and angle of attack on the pressure and condensate mass fraction distributions along the airfoil surfaces and the consequent effect on the wave drag and lift coefficients. Increasing the upstream temperature at fixed values of upstream supersaturation ratio and Mach number results in increased condensation and higher wave drag coefficient. Increasing the upstream supersaturation ratio at fixed values of upstream temperature and Mach number also results in increased condensation and the wave drag coefficient increases nonlinearly. In addition, the effects of varying airfoil geometry with a fixed thickness ratio and chord on flow properties and condensation region are studied. The computed results confirm the similarity law of Zierep & Lin (Forsch. Ing. Wes. A, vol. 33 (6), 1967, pp. 169–172), relating the onset condensation Mach number to upstream stagnation relative humidity, when an effective specific heat ratio is used. The small-disturbance model is a useful tool to analyse the physics of high-speed condensing steam flows around airfoils operating at high pressures and temperatures.