Semi-analytical expressions for the momentum flux associated with orographic internal gravity waves, and closed analytical expressions for its divergence, are derived for inviscid, stationary, hydrostatic, directionally-sheared flow over mountains with an elliptical horizontal cross-section. These calculations, obtained using linear theory conjugated with a third-order WKB approximation, are valid for relatively slowly-varying, but otherwise generic wind profiles, and given in a form that is straightforward to implement in drag parametrization schemes. When normalized by the surface drag in the

The dynamics of an asymmetric rainband complex leading into secondary eyewall formation (SEF) are examined in a simulation of Hurricane Matthew (2016), with particular focus on the tangential wind field evolution. Prior to SEF, the storm experiences an axisymmetric broadening of the tangential wind field as a stationary rainband complex in the downshear quadrants intensifies. The axisymmetric acceleration pattern that causes this broadening is an inward-descending structure of positive acceleration nearly 100 km wide in radial extent and maximizes in the low-levels near 50 km radius. Vertical advection from convective updrafts in the downshear-right quadrant largely contributes to the low-level acceleration maximum, while the broader inward-descending pattern is due to horizontal advection within stratiform precipitation in the downshear-left quadrant. This broad slantwise pattern of positive acceleration is due to a mesoscale descending inflow (MDI) that is driven by midlevel cooling within the stratiform regions and draws absolute angular momentum inward. The MDI is further revealed by examining the irrotational component of the radial velocity, which shows the MDI extending downwind into the upshear-left quadrant. Here, the MDI connects with the boundary layer, where new convective updrafts are triggered along its inner edge; these new upshear-left updrafts are found to be important to the subsequent axisymmetrization of the low-level tangential wind maximum within the incipient secondary eyewall.

Using idealized simulations, we examine the storm-scale wind field response of a dry, hurricane-like vortex to prescribed stratiform heating profiles that mimic tropical cyclone (TC) spiral rainbands. These profiles were stationary with respect to the storm center to represent the diabatic forcing imposed by a quasi-stationary rainband complex. The first profile was typical of stratiform precipitation with heating above and cooling below the melting level. The vortex response included a mesoscale descending inflow and a midlevel tangential jet, consistent with previous studies. An additional response was an inward-spiraling low-level updraft radially inside the rainband heating. The second profile was a modified stratiform heating structure derived from observations and consisted of a diagonal dipole of heating and cooling. The same features were found with stronger magnitudes and larger vertical extents. The dynamics and implications of the forced low-level updraft were examined. This updraft was driven by buoyancy advection because of the stratiform-induced low-level cold pool. The stationary nature of the rainband diabatic forcing played an important role in modulating the required temperature and pressure anomalies to sustain this updraft. Simulations with moisture and full microphysics confirmed that this low-level updraft response was robust and capable of triggering sustained deep convection that could further impact the storm evolution, including having a potential role in secondary eyewall formation.

The orographic gravity-wave drag produced in flow over an axisymmetric mountain when both vertical wind shear and non-hydrostatic effects are important was calculated using a semi-analytical two-layer linear model, including unidirectional or directional constant wind shear in a layer near the surface, above which the wind is constant. The drag behaviour is determined by partial wave reflection at the shear discontinuity, wave absorption at critical levels (both of which exist in hydrostatic flow) and total wave reflection at levels where the waves become evanescent (an intrinsically non-hydrostatic effect), which produces resonant trapped lee-wave modes. As a result of constructive or destructive wave interference, the drag oscillates with the thickness of the constant-shear layer and the Richardson number within it (Ri), generally decreasing at low Ri and when the flow is strongly non-hydrostatic. Critical-level absorption, which increases with the angle spanned by the wind velocity in the constant-shear layer, shields the surface from reflected waves, keeping the drag closer to its hydrostatic limit. Although, for the parameter range considered here, the drag seldom exceeds this limit, a substantial drag fraction may be produced by trapped lee waves, particularly when the flow is strongly non-hydrostatic, the lower layer is thick and Ri is relatively high. In directionally sheared flows with Ri = O(1), the drag may be misaligned with the surface wind in a direction opposite to the shear, a behaviour that is due totally to non-trapped waves. The trapped lee-wave drag, the reaction force of which is felt on the atmosphere at low levels, may therefore have a distinctly different direction from the drag associated with vertically propagating waves, which acts on the atmosphere at higher levels.