On the Generation of Roll Vortices due to the Inflection Point Instability of the Hurricane Boundary Layer Flow

Abstract

Horizontal roll vortices, or rolls, are frequently observed in the hurricane boundary layer (HBL). Previous studies suggest that these rolls can be generated by the inflection point instability of the HBL flow. In this study we investigate the formation of rolls due to this mechanism in the axisymmetric HBL using a numerical approach that explicitly resolves rolls. The effects of mean HBL wind and stratification distributions on rolls are evaluated. We identify two important factors of the mean HBL wind that affect the characteristics of rolls. The dynamical HBL height affects the wavelength of rolls, and the magnitude of the mean wind shear affects the growth rate of rolls. As a result, under neutrally stratified HBL, the wavelength of rolls increases with the radius (out of the radius of maximum wind), while the growth rate of rolls decreases. The stratification also plays an important role in the generation of rolls. The stable stratification suppresses the growth of rolls because of the negative work done by the buoyancy force. Nonuniform stratification with a mixed layer has less suppressing effect on rolls. Rolls can trigger internal waves in the stably stratified layer, which have both vertically propagating and decaying properties. We derive analytical solutions for the internal waves, which relate the properties of the internal waves to the boundary layer rolls. We find the properties of the internal waves are affected by the mixed-layer height.

On the Equilibrium-State Roll Vortices and Their Effects in the Hurricane Boundary Layer

“…In this study, the mean flow refers to the large-scale flow in the HBL, which consists of the primary cyclonic circulation and the secondary circulation induced by the surface friction; the perturbations refer to the smallscale features formed as a result of the dynamical instability of the mean flow, which consist of the boundary layer rolls and the internal waves triggered by them. Based on the above flow-separation assumption, the governing equations for the mean flow and the perturbations can be derived, as shown in the appendix of Gao and Ginis (2014). The equations for the mean flow and the perturbations are solved by two different numerical models, while the unresolved small-scale turbulence are parameterized using the traditional method.…”

“…A diagram illustrating the cylindrical coordinate system (r, l, z) for the mean flow and the local Cartesian coordinate system (x, y, z) for the perturbations (z axis is not shown) at r 5 R [as in Fig. 1 of Gao and Ginis (2014)]. The variable « is the angle between the along-roll direction y and the azimuthal direction l. Positive « means the along-roll direction is to the left of the azimuthal direction.…”

“…, where k is the von Kármán constant (k 5 0:4) and l ' is asymptotic mixing length, 2 which is set to 30 m. The impacts of the choice of l ' on the formation and characteristics of rolls were discussed in Gao and Ginis (2014). Here a relatively small value of l ' is used to ensure the mean flow is favorable for rolls to form.…”

“…They also suggested that rolls could interact with other small-scale features (such as internal waves and Kelvin-Helmholtz waves), and the rolls enhanced the vertical transports in the HBL. In a recent study by the authors (Gao and Ginis 2014), rolls were resolved by applying a two-dimensional high-resolution single-grid roll-resolving model (SRM) embedded into an axisymmetric HBL model. They found that rolls generated by the inflection point instability are affected by the stratification during the linear phase, in which the rolls grow exponentially with time.…”

“…Moreover, there is still limited understanding of the impacts of rolls on the mean HBL flow. In this study, we aim to advance the understanding on these important aspects of rolls in the HBL by extending the numerical approach used by Gao and Ginis (2014). Specifically, we address the following questions:…”