A recent study examined the predictability of an idealized baroclinic wave amplifying in a conditionally unstable atmosphere through numerical simulations with parameterized moist convection. It was demonstrated that with the effect of moisture included, the error starting from small random noise is characterized by upscale growth in the short-term (0-36 h) forecast of a growing synoptic-scale disturbance. The current study seeks to explore further the mesoscale error-growth dynamics in idealized moist baroclinic waves through convection-permitting experiments with model grid increments down to 3.3 km. These experiments suggest the following three-stage error-growth model: in the initial stage, the errors grow from small-scale convective instability and then quickly [O(1 h)] saturate at the convective scales. In the second stage, the character of the errors changes from that of convective-scale unbalanced motions to one more closely related to large-scale balanced motions. That is, some of the error from convective scales is retained in the balanced motions, while the rest is radiated away in the form of gravity waves. In the final stage, the large-scale (balanced) components of the errors grow with the background baroclinic instability. Through examination of the error-energy budget, it is found that buoyancy production due mostly to moist convection is comparable to shear production (nonlinear velocity advection). It is found that turning off latent heating not only dramatically decreases buoyancy production, but also reduces shear production to less than 20% of its original amplitude.

Numerical simulations of nonrotating flow with uniform basic wind and stability past long three-dimensional (3D) ridges are compared to the corresponding two-dimensional (2D) limit to reveal the importance of 3D effects. For mountain heights smaller than the threshold for breaking waves, the low-level flow over the interior of the ridge is well described by 2D theory when the horizontal aspect ratio is roughly 10 or greater. By contrast, in flows with wave breaking significant discrepancies between 2D and 3D results remain apparent even for 12. It is found that the onset of wave breaking and the transition to the high-drag state is accompanied in 3D by an abrupt increase in deflection of the low-level flow around the ridge. The increased flow deflection is produced at least in part by upstream-propagating columnar disturbances forced by the transition to the high-drag state. The deflection of the incident flow reduces the amplitude of the mountain wave aloft relative to 2D and acts as a negative feedback on the surface form drag. As a result, the nonlinear enhancement of the surface drag associated with wave breaking for a ridge with 7.5 is found to be roughly half the enhancement obtained for a 2D ridge.

The development of orographic wakes and vortices is revisited from the dynamical perspective of a three-dimensional (3D) vorticity-vector potential formulation. Particular emphasis is given to the role of upstream blocking in the formation of the wake. Scaling arguments are first presented to explore the limiting form of the 3D vorticity inversion for the case of flow at small dynamical aspect ratio δ. It is shown that in the limit of small δ the inversion is determined completely by the two horizontal vorticity components—that is, the part of the velocity induced by the vertical component of vorticity vanishes in the small-δ limit. This result leads to an approximate formulation of small-δ fluid mechanics in which the three governing prognostic variables are the two horizontal vorticity components and the potential temperature. The remainder of the study then revisits the problem of orographic wake formation from the perspective of this small-δ vorticity dynamics framework. Previous studies have suggested that one of the potential routes to stratified wake formation is through the blocking of flow on the upstream side of the barrier. This apparent link between blocking and wake formation is shown to be relatively straightforward in the small-δ vorticity context. In particular, it is shown that blocking of the flow inevitably leads to a horizontal vorticity distribution that favors deceleration of the leeside flow at the ground. This process of leeside flow deceleration, as well as the subsequent time evolution of the wake, is illustrated through a series of numerical initial-value problems involving flows past 2D and 3D barriers. It is proposed that the initiation of the wake flow in these stratified problems resembles the flow produced by a retracting piston in shallow-water theory.

The effect of an inland plateau on the tropical sea breeze is considered in terms of idealized numerical experiments, with a particular emphasis on offshore effects. The sea breeze is modeled as the response to an oscillating interior heat source over land. The parameter space for the calculations is defined by a nondimensional wind speed, a scaled plateau height, and the nondimensional heating amplitude. The experiments show that the inland plateau tends to significantly strengthen the land-breeze part of the circulation, as compared to the case without terrain. The strengthening of the land breeze is tied to blocking of the sea-breeze density current during the warm phase of the cycle. The blocked sea breeze produces a pool of relatively cold, stagnant air at the base of the plateau, which in turn produces a stronger land-breeze density current the following morning. Experiments show that the strength of the land breeze increases with the terrain height, at least for moderate values of the height. For very large terrain, the sea breeze is apparently blocked entirely, and further increases in terrain height lead to only small changes in land-breeze intensity and propagation. Details of the dynamics are described in terms of the transition from linear to nonlinear heating amplitudes, as well as for cases with and without background winds. The results show that for the present experiments, significant offshore effects are tied to nonlinear frontal propagation, as opposed to quasi-linear wave features.

The equatorial coastal circulation is modeled in terms of the linear wave response to a diurnally oscillating heat source gradient in a background wind. A diurnal scaling shows that the solution depends on two parameters: a nondimensional coastal width ℒ and a nondimensional wind speed 𝒰. The solutions are interpreted by comparing to the 𝒰 = 0 theory of Rotunno. For 𝒰 ≠ 0 the Fourier integral solution consists of three distinct wave branches. Two of these branches correspond to the prior no-wind solution of Rotunno, except with Doppler shifting and associated wave dispersion. The third branch exists only for 𝒰 ≠ 0 and is shown to be broadly similar to flow past a steady heat source or a topographic obstacle. The relative importance of this third branch is determined largely by the parameter combination 𝒰/ℒ. For sufficiently large 𝒰/ℒ the third branch becomes the dominant part of the solution. The spatial structures of the three branches are described in terms of group velocity arguments combined with a desingularized quadrature method.