Quasi-two-dimensional roll vortices are frequently observed in hurricane boundary layers. It is believed that this highly coherent structure, likely caused by the inflection-point instability, plays an important role in organizing turbulent transport. Large-eddy simulations are conducted to investigate the impact of wind shear characteristics, such as the shear strength and inflection-point level, on the roll structure in terms of its spectral characteristics and turbulence organization. A mean wind nudging approach is used in the simulations to maintain the specified mean wind shear without directly affecting turbulent motions. Enhancing the radial wind shear expands the roll horizontal scale and strengthens the roll's kinetic energy. Increasing the inflection-point level tends to produce a narrow and sharp peak in the power spectrum at the wavelength consistent with the roll spacing indicated by the instantaneous turbulent fields. The spectral tangential momentum flux, in particular, reaches a strong peak value at the roll wavelength. In contrast, the spectral radial momentum flux obtains its maximum at the wavelength that is usually shorter than the roll's, suggesting that the roll radial momentum transport is less efficient than the tangential because of the quasi-two-dimensionality of the roll structure. The most robust rolls are produced in a simulation with the highest inflection-point level and relatively strong radial wind shear. Based on the spectral analysis, the roll-scale contribution to the turbulent momentum flux can reach 40 % in the middle of the boundary layer.

The hurricane boundary layer (HBL) is well known for its critical role in
evolution of tropical cyclones (TCs) as the air–sea interaction represents
both the most important source and sink of the moist available energy and the
kinetic energy, respectively. One of the frequently occurring features in the
HBL is horizontal roll vortices, which have quasi-two-dimensional coherent
and banded structure extending from the surface to the top of the HBL. The
observed horizontal roll scale, i.e., the average distance between two
neighboring rolls, ranges from sub-kilometer to

Previous studies have attributed the prevalence of the roll structure to the
existence of an inflection point in the mean HBL radial wind profile and
attempted to establish the link between the HBL environment and the roll
statistical characteristics (e.g., Foster, 2005; Nolan, 2005). These analyses
are generally consistent with observations: (1) the rolls are oriented at
0–10

There have been a few LES studies of HBL rolls. Zhu (2008) configured a
nested WRF (Weather Research Forecast) model to include an LES domain with a
horizontal resolution of 100 m and a vertical grid spacing varying from 5 to
65 m below 1.6 km. The WRF-LES was used to simulate a real case of
hurricane landfall. Organized large-eddy circulations with horizontal scales
ranging from 1 to 10 km were found to intensely enhance the vertical
momentum, heat, and moisture transport. He further proposed a framework of the
turbulent transport parameterization based on the conceptual model of
convective up- and down-draft representation for shallow cumulus convection.
While this mesoscale LES grid-nesting framework represents a realistic and
sophisticated numerical approach, it does not allow for sensitivity studies
to examine impact of various mean conditions, such as wind profiles, on the
roll structure. In an idealized study of HBL rolls, Nakanishi and
Niino (2012, hereafter NN12) adopted a traditional LES approach, which uses a
20

Among these LES studies, only the WRF-LES nesting approach used by Zhu (2008) explicitly simulates mesoscale circulations and thus their effects on the roll structure. Others neglect the horizontal advection effects by assuming a local balance among the turbulent mixing, gradient wind, Coriolis force, and hurricane-induced centripetal force. Consequently, the wind profile based on the local force balance may not represent the most relevant features with respect to the roll development in the HBL in the LES studies. For example, Morrison et al. (2005) provided both observed radial and tangential winds from WSR-88D radar data, and the IPLs estimated from these observations are about 300 to 800 m for the winds at the TC radius of 29 to 122 km, respectively. These IPLs are generally higher than those of the LES simulations by NN12 which are 100 and 300 m at the radius of 40 and 100 km, respectively. Therefore, there is a need to use more realistic wind profiles in the LES studies. The latest study of Bryan et al. (2017) provided an improved HBL LES framework that accounts for the influence of mesoscale advection on the wind profiles. The current work introduces an empirical approach as discussed in the next section.

Boundary layer rolls have been a subject of many studies since 1960s, as reviewed by Atkinson and Zhang (1996) and Young et al. (2002). Several physical mechanisms have been proposed for different environments, including combined surface shear–buoyancy instability (Moeng and Sullivan, 1994; Glendening, 1996), the surface shear–cloud convection–radiation instability (Chlond, 1992), parallel instability (Lilly, 1966), and inflection-point instability (Brown, 1970; Brown, 1972; Foster, 2005). As discussed at the beginning of the paper, the most relevant mechanism for the HBL rolls is the inflection-point instability. This work aims to gain a new understanding of the impact of the mean wind profile characteristics, that are directly associated with the inflection-point instability, the radial wind shear, and IPL, on the roll structure. We use a different LES approach, featuring a mean nudging method which is applied to the momentum equations to strongly regulate the mean wind profile. This approach enables us to conduct a systematic study of the roll response, including the growth of the HBL, turbulence intensity, and the spectral distribution, to changes in the mean wind profiles. The remainder of the paper is organized as follows. Section 2 describes the LES model and simulation setup. Sections 3 and 4 provide general description of the simulation results and spectral analysis, respectively. Further discussions on the wind shear are given in Sect. 5. Section 6 summarizes the work.

The Naval Research Laboratory Coupled Ocean/Atmosphere Mesoscale Prediction
System large-eddy simulation (COAMPS-LES) is used in this study. The LES
model was first introduced by Golaz et al. (2005) for the study of boundary
layer cloud systems. It has been applied to investigate various types of
boundary layer turbulence, including topographic flows, and stratocumulus
dynamics (Golaz et al., 2009; Wang et al., 2012; Jiang and Wang, 2013).
Readers are referred to these papers for detailed descriptions as well as its
various applications. Briefly, the model applies the anelastic approximation
for efficient numerical computation and uses the Deardorff's prognostic
turbulence kinetic energy approach for the subgrid-scale model (Deardorff,
1980). The model coordinate is configured such that

As discussed in the introduction, the mean wind profiles from the LES
simulations that do not include the mesoscale circulations (e.g., HBL inflow)
may not adequately represent the wind characteristics in a hurricane
environment. It is highly desirable that observationally based wind profiles
be used and approximately maintained throughout the simulations. We adopt a
modeling approach that strongly regulates the mean wind profile according to
our specifications. A special relaxation term is added to each horizontal
momentum equation to nudge the mean wind toward a specified target wind
profile. A unique feature of these nudging terms is that they only nudge the
horizontally averaged wind. That is, at each time step, the horizontal mean
wind profile, which is dependent only on

The momentum equations with the nudging terms can be written as

We are interested in two sets of LES quasi-equilibrium solutions
corresponding to different mean wind characteristics with regard to both the
wind shear strength and IPL. These two parameters are chosen because,
according to previous studies, they are key parameters related to
inflection-point instability. The former is the main source of turbulence and
the latter is linked to the roll scales (e.g., Chlond, 1992; GG14). The
vertical shear of the radial wind above the surface layer is a main focus of
this study. The shear layer, where the inflection point is located, usually
extends from

The target wind profiles are formulated based on the normalized typical
hurricane wind profiles obtained from a dynamical model of Foster (2005) and
from the observations by Morrison et al. (2005). The LES mean winds are
nudged toward the target profiles, which are formulated to represent various
wind shear conditions. This approach facilitates the study of the response of
roll formation and dynamics to wind profiles through sensitivity simulations.
We have experimented with dozens of LES simulations using a variety of target
wind profiles. The two groups of the target wind profiles (i.e., groups H and
L; see Fig. 1) are chosen from these additional trial simulations, and they
exhibit systematic variations in shear strength and infection-point levels.
The target radial wind

Target wind profiles used in simulations of groups L and
H:

In summary, group L simulations are forced with the target radial wind
profiles (

Simulation conditions and results with the following parameters:
individual experiments (Exp), maximum radial wind shear (RSH

While there is some quantitative difference between the target wind profiles defined above and the ones derived from the basic HBL balance equations, such as those of Foster (2005), they carry some essential features that are similar to the model-derived or observed wind profiles, such as an inflection point in the radial wind, the super-gradient wind in HBL, and the gradient wind balance above the HBL. Given our objective of investigating the impact of the wind shear (including both the shear strength and the inflection-point level) on the roll structure, our choices of the target winds are justified in the sense that they retain the basic HBL mean wind features and provide a simple way to make a meaningful comparative study.

This section is centered on comparing instantaneous turbulence fields and statistics between group L and H simulations (see Table 1). Special attention is given to the roll structure manifested by the coherent and organized turbulent flow. All the profiles presented here are obtained from ensemble averaging applied over the entire horizontal domain and between 8 and 10 h with a sample interval of 30 s. A time series of an average variable is constructed by taking the horizontal mean every minute.

To gain a general impression of the HBL development and differences among the
simulations, the time series of the HBL heights (

HBL height evolution and mean vertical profiles.

For all the simulations, the parameter,

Plan view of

Because the mean wind profiles are nudged toward the target winds, the last
hour average winds exhibit the characteristics that bear resemblance to the
target wind profiles (Figs. 1 and 2). For instance, the radial shear
increases with the radial wind speed within each group. Group L has stronger
radial wind shears and lower IPLs than group H. The mean tangential winds
are very similar within each group. The mean potential temperature
(

Two major differences in the wind forcing among the simulations are
associated with the radial wind shear strength and the IPLs. How do these
differences affect the roll structure as well as turbulence in general? The
link between the wind shear profiles and flow pattern is evident in the
horizontal cross sections of

It is evident that the rolls appear stronger, in terms of the maximum

These simulations also show a strong signature of gravity waves. For example,
the linear roll patterns are well defined near the inversion base (i.e.,

Many of the above-discussed aspects of the roll structure are also evident in
the horizontal cross sections of other perturbation variables. Figure 4 shows
the wind component perturbations (

Plan views of turbulent perturbations at 9 h from H3 at

This argument is supported by further quantitative analysis. A coordinate
transformation is performed on the instantaneous fields so that the resultant

Phase differences between the along-roll-averaged
perturbation

Turbulence statistics respond strongly to the different wind profiles as
demonstrated in Fig. 7. The negative radial momentum flux (

Vertical cross section of along-roll-averaged
perturbations from H3. The cross-roll velocity

Profiles of LES turbulence statistics. The variables are

The buoyancy flux (

Some important features emerging from the above diagnosis are worthy of
emphasis: (1) all simulations except H1 produce well-defined roll structure
manifested by a quasi-linear pattern through the depth of the HBLs; (2) increasing
the vertical shear of the radial wind results in enhanced
turbulence, higher HBL height, and larger roll spatial scales; (3) rising IPL
also leads to a larger roll spatial scale in spite of the weakened radial
shear; (4) the vertical tilting (in the radial direction) of the low-level
convergence zone enhances the radial momentum flux associated with HBL roll
circulations, which is consistent with other studies (e.g., GG14); and (5) the
presence of internal gravity waves is strongly suggested by the
“roll-like” pattern above the HBL and the 90

To understand how the turbulent flow at various scales respond to the
changes in the wind forcing and how effective rolls are in vertical momentum
transfer, we examine the 2-D power density spectra of the simulated

All the spectra are calculated using the data collected between 8 and 10 h
with a sampling interval of 5 min. They are functions of the magnitude of the
horizontal wave number vector

The 2-D power spectra of

Many of the essential features discussed for the

A major feature of the cospectrum of

The 2-D co-spectra of

The following features associated with H3 are worth noting: (1) the highest

It is also noteworthy that the presence of a significant narrow peak in the
momentum flux spectra is consistent with the observational analysis by Zhang
et al. (2008), which shows sharp peaks in all the cospectra of

Decomposition of turbulent fluxes for H3. Various spectral
components for turbulent flux profiles are presented in top panels;
fractional contributions from the components in bottom panels. Three spectral
groups are small scale (< 1 km), large eddy (1–2.5 km), and roll
(> 2.5 km), respectively.

How significant are the HBL roll contributions to turbulent fluxes compared to other turbulent eddies in the LES simulations? This issue has been addressed previously with a decomposition method based on the roll coherence feature. For example, the updraft–downdraft roll circulation can be defined based on the quasi-linear longitudinal coherence of the roll structure (Glendening, 1996); the roll-scale characteristics may also be represented as conditional means of the turbulent flow based on the convection model (Zhu, 2008). Because a key feature of the rolls is that turbulence is organized in such a way that various flux spectral distributions reach their maxima at the roll wavelength, a decomposition method based on spectral analysis provides a more fundamental representation of roll characteristics. This approach is also consistent with the observational analyses of HBL rolls by Zhang et al. (2008).

To compute the contributions from different wave numbers, we integrate each flux over three spectral bands to yield the subtotals at each model level. The spectral bands are chosen, in principle, to represent turbulent fluxes from the small scale, the large-eddy scale, and the roll scale based on the H3 spectra (Figs. 8 and 9). The small scale ranges from 0.1 to 1 km; the large-eddy 1 to 2.5 km; the roll 2.5 to 12 km. The calculation is carried out from the surface to 2 km.

To emphasize the relative importance of the fluxes from the different
spectral groups, we calculate both the fluxes and the flux fractions defined
by the ratio of the specific group flux to the total, as shown in Fig. 10.
The small-scale contribution to

The longitudinal momentum fluxes (

We have argued that the correlation between the roll-scale

Vertical profiles of roll characteristics derived from
H3:

The results of the roll contribution to the third moment

The spectral analysis in this section confirms that both the roll's
horizontal scale and intensity are highly dependent on the shear and IPL in
the radial wind profile. The stronger the radial wind shear is and the higher
the IPL is, the stronger and larger the rolls are. More importantly,
increasing IPL tends to produce a robust roll structure in the sense that a
narrow and sharp peak is present in the

The momentum transfer coefficient, defined by the negative ratio of the
momentum flux to the mean wind shear according to the

These transfer coefficients of both wind components are shown in Fig. 12. The
values of

Momentum transfer coefficients for three spectral groups of H3 for

Overall, there are marked differences between

We have so far emphasized the impact of the radial wind shear on both turbulence intensity and spectral distribution. However, both the radial and tangential winds may have significant shear above the surface layer (Fig. 2b and c). What roles does the tangential wind shear play in regulating the roll structure? This section attempts to address this issue by comparing the simulations H3, L3, L3H, and H3L, which are forced with different radial and tangential wind shear in the target profiles (Table 1). The simulation L3H uses the same target radial wind profile as the L3, but the same target tangential wind as the group H simulations (i.e., the profile H in Fig. 1). Correspondingly, the H3L adopts the same target radial wind profile as the H3, but the target tangential wind of the group L (i.e., the profile L in Fig. 1). This target wind specification is designed to examine how the roll structure responds to a change in one wind component while the other remains the same.

The comparison of the turbulence statistics profiles from H3 and H3L with
those from L3 and L3H (Fig. 13) suggests that the radial wind plays a
dominant role in determining the turbulence intensity. The target radial
wind with a high IPL from H3 and H3L leads to both the stronger

Comparison among simulations H3, L3, H3L and L3H with
different wind shear.

The spectral response of the turbulence is displayed in Fig. 14. A dominant
feature is that there is a peak in the power spectrum of

The above results suggest that the radial wind shear plays a more dominant
role in determining the roll characteristics with regard to the scale
selection, while the tangential wind shear strongly influences the
tangential momentum flux

Comparison of the power spectra of

A series of LES simulations have been conducted to examine the response of
the roll structure to different mean wind shear conditions in terms of the
radial wind shear strength and the IPL in an idealized HBL. A unique feature
in our approach is that a mean wind nudging technique with specified target
wind profiles is used to maintain the horizontal-domain average wind profiles
without directly affecting turbulent perturbations. Two groups of simulations
(L and H) are conducted. Each group uses the same target tangential wind
profile, but three radial wind profiles with different shear. Group H is
designed to have higher IPLs (

All simulations except H1, which has the weakest radial wind shear, produce
the rolls manifested by a quasi-linear structure with the horizontal scale
ranging from 1 to 3.6 km. The roll structure extends from the
near-surface level (

One of the important features regarding the roll contribution to the vertical momentum flux is that the tangential wind is better correlated with the vertical motion than the radial wind in the lower half of the HBL. It is because the low-level convergence mainly comes from the radial wind, whose roll-scale perturbation is close to zero where the upward motion is maximized. The convergence zone is tilted with height toward the rotation center to generate broader updrafts in the area of negative radial wind perturbations. Consequently, the negative correlation of upward motion and radial wind perturbation increases with height, which is supported by the roll momentum correlation coefficients calculated based on the spectral analysis.

Effects of tangential wind shear are also investigated. A sensitivity
simulation, in which the upper-level tangential wind shear is reduced, shows
that the basic roll structure is not significantly impacted in the sense
that both the power spectrum and the momentum flux co-spectra generally
maintain their distributions. The tangential momentum flux, however, changes
significantly with the tangential wind shear, which feeds back to the
turbulence generation and leads to some difference in the overall turbulence
intensity. This effect is also reflected in the

The results of the spectral analysis are used to compute the roll
contributions to various turbulent fluxes. The contribution from the
roll-scale (

This study highlights the critical roles of the radial wind shear in regulating the roll structure. As discussed in the introduction, the mean wind shear should be a strong function of both the local rotational forcing and the mesoscale tendencies. The mean nudging approach used in this work is intended to bridge the gap between the commonly used LES configuration and the need for including the mesoscale effects, and to facilitate sensitivity simulations. Because of the strong nudging it is difficult to isolate the impact of the rolls on the mean wind profile in this study. A more comprehensive study of the roll structure requires incorporating effects of the hurricane mesoscale environment such as radial wind advection. The LES approach recently proposed by Bryan et al. (2017) and the nested LES in a mesoscale model of Zhu (2008) provide attractive modeling frameworks that can be used to address issues related to the feedback of the rolls to the mean wind profiles in HBLs.

All data are available from Shouping Wang (shouping.wang@nrlmry.navy.mil).

Comparison of the evolution of the boundary layer height

The mean wind nudging method introduced in Sect. 2 is used to maintain LES-simulated
mean wind profiles and to make systematic changes in the mean wind
for sensitivity simulations; it has no direct influence on the resolved
turbulence. Three LES simulations are presented here to evaluate these
statements. The first simulation (RN1) uses the horizontal momentum equations
with the rotation terms (i.e., the square bracket terms with

In general, all the variables are in excellent agreement among the three
simulations, as shown in Figs. A1–A2. The simulations RN1 and RN2 have very
consistent

Comparison of test simulations for the mean nudging
approach. All the profiles are averages between 9 and 10 h at a sampling
interval 30 s. Panel

The authors declare that they have no conflict of interest.

We thank James Doyle for discussions on the LES model setup and gravity waves. The careful reviews and valuable comments by Kun Gao and Ralph Foster greatly improved the clarity of the manuscript. This research was funded by the Office of Naval Research (ONR) under program element (PE) 0602435N. Edited by: H. Wernli Reviewed by: R. Foster and K. Gao

^{™}LES: Model evaluation and analysis of second and third moment vertical velocity budgets, Bound.-Lay. Meteorol., 116, 487–517, 2005.