A strongly tilted, nearly axisymmetric vortex in dry air with asymmetric diabatic heating is analysed here by matched asymptotic expansions. The vortex is in gradient wind balance, with vortex Rossby numbers of order unity, and embedded in a quasigeostrophic (QG) background wind with weak vertical shear. With wind speeds of 60-120 km h −1, such vortices correspond to tropical storms or nascent hurricanes according to the Saffir-Simpson scale. For asymmetric heating, nonlinear coupling of the evolution equations for the vortex tilt, its core structure, and its influence on the QG background is found. The theory compares well with the established linear theory of precessing quasi-modes of atmospheric vortices, and it corroborates the relationship between vortex tilt and asymmetric potential temperature and vertical velocity patterns as found by Jones (Q. J. R. Meteorol. Soc., vol. 121, 1995, pp. 821-851) and Frank & Ritchie (Mon. Weath. Rev., vol. 127, 1999, pp. 2044-2061 in simulations of adiabatic tropical cyclones. A relation between the present theory and the local induction approximation for three-dimensional slender vortex filaments is established.

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We examine the unsteady response of a neutral atmospheric boundary layer (ABL) of depth h and friction velocity u à when a uniform surface heat flux is applied abruptly or decreased rapidly over a time scale t h less than about h/(10u à ). Standard Monin-Obukhov (MO) relationships are used for the perturbed eddy viscosity profile in terms of the changes to the heat flux and mean shear. Analytical solutions for changes in temperature, mean wind and shear stress profile are obtained for the surface layer, when there are small changes in h/|L MO | over the time scale t MO~| L MO |/(10u à ) (where L MO and t MO are the length and time scales, respectively). They show that a maximum in the wind speed profile occurs at the top of the thermal boundary layer for weak surface cooling, i.e. a wind jet, whereas there is a flattening of the profile and no marked maximum for weak surface heating. The modelled profiles are approximately the same as those obtained from the U.K. Met Office Unified Model when operating as a mesoscale model at 12-km horizontal resolution. The theoretical model is modified when strong surface heating is suddenly applied, resulting in a large change in h/ |L MO | () 1), over the time scale t MO . The eddy structure is predicted to change significantly and the addition of convective turbulence increases the shear turbulence at the ground. A lowlevel wind jet can form, with convective turbulence adding to the mean momentum of the flow. This was verified by our laboratory experiment and direct numerical simulations. Additionally, it is shown that the effects of Coriolis acceleration diminish (rather than as suggested in the literature, amplify) the formation of the wind jets in the situations considered here. Hence, only when the surface heat flux changes over time scales greater than 1/f (where f is the Coriolis parameter) does the ABL adjust monotonically between its equilibrium states. These results are also applicable to the ABL passing over spatially varying surface heat fluxes.