Life-cycle simulations of shallow frontal waves and the impact of deformation strain

The life-cycle of shallow frontal waves and the impact of deformation strain on their development is investigated using the idealised version of the Met Office non-hydrostatic Unified Model which includes the same physics and dynamics as the operational forecast model. Frontal wave development occurs in two stages; first, a deformation strain is applied to a front and a positive potential vorticity (PV) strip forms, generated by latent heat release in the frontal updraft; second, as the deformation strain is reduced the PV strip breaks up into individual anomalies. The circulations associated with the PV anomalies cause shallow frontal waves to form. The structure of the simulated frontal waves is consistent with the conceptual model of a frontal cyclone. Deeper frontal waves are simulated if the stability of the atmosphere is reduced. Deformation strain rates of different strengths are applied to the PV strip to determine whether a deformation strain threshold exists above which frontal wave development is suppressed. An objective method of frontal wave activity is defined and frontal wave development was found to be suppressed by deformation strain rates $\ge 0.4\times10^{-5}\mbox{s}^{-1}$. This value compares well with observed deformation strain rate thresholds and the analytical solution for the minimum deformation strain rate needed to suppress barotropic frontal wave development. The deformation strain rate threshold is dependent on the strength of the PV strip with strong PV strips able to overcome stronger deformation strain rates (leading to frontal wave development) than weaker PV strips.

Damage rate is a predictor of fatigue life and creep strain rate in fatigue of tensile human cortical bone samples

We present results on the growth of damage in 29 fatigue tests of human femoral cortical bone from four individuals, aged 53–79. In these tests we examine the interdependency of stress, cycles to failure, rate of creep strain, and rate of modulus loss. The behavior of creep rates has been reported recently for the same donors as an effect of stress and cycles (Cotton, J. R., Zioupos, P., Winwood, K., and Taylor, M., 2003, "Analysis of Creep Strain During Tensile Fatigue of Cortical Bone," J. Biomech. 36, pp. 943–949). In the present paper we first examine how the evolution of damage (drop in modulus per cycle) is associated with the stress level or the "normalized stress" level (stress divided by specimen modulus), and results show the rate of modulus loss fits better as a function of normalized stress. However, we find here that even better correlations can be established between either the cycles to failure or creep rates versus rates of damage than any of these three measures versus normalized stress. The data indicate that damage rates can be excellent predictors of fatigue life and creep strain rates in tensile fatigue of human cortical bone for use in practical problems and computer simulations.