International audienceThe somewhat counter-intuitive effect of how stratification destabilizes shear flows and the rationalization of the Miles-Howard stability criterion are re-examined in what we believe to be the simplest example of action-at-a-distance interaction between 'buoyancy-vorticity gravity wave kernels'. The set-up consists of an infinite uniform shear Couette flow in which the Rayleigh-Fjortoft necessary conditions for shear flow instability are not satisfied. When two stably stratified density jumps are added, the flow may however become unstable. At each density jump the perturbation can be decomposed into two coherent gravity waves propagating horizontally in opposite directions. We show, in detail, how the instability results from a phase-locking action-at-a-distance interaction between the four waves (two at each jump) but can as well be reasonably approximated by the interaction between only the two counter-propagating waves (one at each jump). From this perspective the nature of the instability mechanism is similar to that of the barotropic and baroclinic ones. Next we add a small ambient stratification to examine how the critical-level dynamics alters our conclusions. We find that a strong vorticity anomaly is generated at the critical level because of the persistent vertical velocity induction by the interfacial waves at the jumps. This critical-level anomaly acts in turn at a distance to dampen the interfacial waves. When the ambient stratification is increased so that the Richardson number exceeds the value of a quarter, this destructive interaction overwhelms the constructive interaction between the interfacial waves, and consequently the flow becomes stable. This effect is manifested when considering the different action-at-adistance contributions to the energy flux divergence at the critical level. The interfacial-wave interaction is found to contribute towards divergence, that is, towards instability, whereas the critical-level-interfacial- wave interaction contributes towards an energy flux convergence, that is, towards stability

Oscillatory pumping tests were conducted at the Boise Hydrological Research Site. A periodic pressure signal is generated by pumping and injecting water into the aquifer consecutively and the pressure response is recorded at many points around the source. We present and analyze the data from the

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Characterizing aquifer heterogeneity is paramount for accurate flow and transport modeling. In this work, we present a new approach for statistical analysis of hydraulic properties in continuous pumping tomography tests of a phreatic aquifer. The method entails determining equivalent hydraulic conductivity (Keq), specific storage (Ss,eq), and specific yield (Sy,eq) at many locations in the field and then calculating statistical moments of the equivalent properties, assuming they are random space variables. Equivalent properties are defined as the ones pertinent to a homogeneous aquifer for which the head time dependent signal fits the one observed in the pumping test. Calculation is carried out in a novel approach, by matching measured head data to two separate semianalytical solutions considering two time periods, early and late. We apply this approach to the Boise Hydrogeophysical Research Site and find that the equivalent property spatial averages decrease with horizontal distance from the pumping well and appear to stabilize at sufficiently large distances, in line with existing theory for Keq. The squared coefficient of variation shows similar behavior, with values indicating a weakly heterogeneous aquifer. Furthermore, estimated values for Keq, Ss,eq, and Sy,eq are in agreement with literature values for the site.

We present an analytical method for calculating two‐phase effective relative permeability, krjeff, where j designates phase (here CO2 and water), under steady state and capillary‐limit assumptions. These effective relative permeabilities may be applied in experimental settings and for upscaling in the context of numerical flow simulations, e.g., for CO2 storage. An exact solution for effective absolute permeability, keff, in two‐dimensional log‐normally distributed isotropic permeability (k) fields is the geometric mean. We show that this does not hold for krjeff since log normality is not maintained in the capillary‐limit phase permeability field ( Kj=k·krj) when capillary pressure, and thus the saturation field, is varied. Nevertheless, the geometric mean is still shown to be suitable for approximating krjeff when the variance of ln⁡k is low. For high‐variance cases, we apply a correction to the geometric average gas effective relative permeability using a Winsorized mean, which neglects large and small Kj values symmetrically. The analytical method is extended to anisotropically correlated log‐normal permeability fields using power law averaging. In these cases, the Winsorized mean treatment is applied to the gas curves for cases described by negative power law exponents (flow across incomplete layers). The accuracy of our analytical expressions for krjeff is demonstrated through extensive numerical tests, using low‐variance and high‐variance permeability realizations with a range of correlation structures. We also present integral expressions for geometric‐mean and power law average krjeff for the systems considered, which enable derivation of closed‐form series solutions for krjeff without generating permeability realizations.