Roll Wavelength Research Articles

Two-dimensional structure functions for characterizing convective rolls in the marine atmospheric boundary layer from Sentinel-1 SAR images

ABSTRACT We study the shape of convective rolls in the Marine Atmospheric Boundary Layer from Synthetic Aperture Radar images of the ocean. We propose a multiscale analysis with structure functions which allow an easy generalization to analyse high-order statistics and so to finely describe the shape of the rolls. The two main results are 1) second-order structure function characterizes the wavelength and direction of rolls just like correlation or power spectrum do, 2) high-order statistics can be studied with skewness and flatness which characterize the asymmetry and intermittency of rolls, respectively. This is the first time that the asymmetry and intermittency of rolls are shown from radar images of the ocean surface.

Enigmatic surface rolls of the Ellesmere Ice Shelf

Abstract The once-contiguous Ellesmere Ice Shelf, first reported in writing by European explorers in 1876, and now almost completely disintegrated, has rolling, wave-like surface topography, the origin of which we investigate using a viscous buckling instability analysis. We show that rolls can develop during a winter season (~ 100 d) if sea-ice pressure (depth-integrated horizontal stress applied to the seaward front of the Ellesmere Ice Shelf) is sufficiently large (1 MPa m) and ice thickness sufficiently low (1–10 m). Roll wavelength initially depends only on sea-ice pressure, but evolves over time depending on amplitude growth rate. This implies that a thinner ice shelf, with its faster amplitude growth rate, will have a shorter wavelength compared to a thicker ice shelf when sea-ice pressure is equal. A drawback of the viscous buckling mechanism is that roll amplitude decays once sea-ice pressure is removed. However, non-Newtonian ice rheology, where effective viscosity, and thus roll change rate, depends on total applied stress may constrain roll decay rate to be much slower than growth rate and allow roll persistence from year to year. Whether the viscous-buckling mechanism we explore here ultimately can be confirmed as the origin of the Ellesmere Ice Shelf rolls remains for future research.

Rayleigh–Bénard convection in non-Newtonian fluids: Experimental and theoretical investigations

We present an experimental and theoretical study of Rayleigh–Bénard convection in shear-thinning fluids with temperature-dependent properties. Experiments were performed using a cylindrical cell with a radius R̂=60 mm and height adjustable at d̂=15 and 20 mm giving a radius-to-height ratio L = 4 and 3, respectively. The fluids used are glycerol (Newtonian fluid) and aqueous xanthan gum solutions (shear-thinning fluids) at 1000 and 1200 ppm. Convection patterns are visualized by the shadowgraph method. In the theoretical part of this study, the weakly nonlinear analysis performed by Varé et al. [J. Fluid Mech. 905, A33 (2020)] is extended to take into account the variation of the thermal expansion coefficient with temperature. For the xanthan gum solutions used, the temperature dependence of the fluid parameters is sufficiently strong to obtain hexagonal cells at the onset of convection. It has been observed that their size decreases with the increase in the temperature difference across the fluid layer above the critical value. This result provides an experimental support to our theoretical study where it is shown that for hexagons, the band of stable wavenumbers is bent toward higher wavenumbers. For the glycerol, Newtonian fluid with a large Prandtl number, a slight increase in the wavelength of rolls is observed in agreement with the literature.

Two Modes of Vibrational Double-Diffusive Instability in a Superposed Fluid-Porous Layer Heated from Below: The Effect of Buoyancy Ratio

The convective double-diffusive instability in a two-layer system consisting of a binary fluid layer overlaying a fluid-saturated porous layer is investigated numerically. The system moves periodically in a vertical direction under the conditions of gravity field. The layers are heated from below and oscillate with high frequency and small amplitude. The instability threshold for the convection onset and the wavelength of convective rolls, which induce as soon as the fluid equilibrium state has lost its stability, are found. The buoyancy ratio and vibrational parameter effects are studied. A region of parameters for the bimodal marginal stability curves is obtained and divided it into parts for the local and large-scale convection onset values. It is revealed that wavelength of stationary convection rolls varies non-monotonically as the buoyancy ratio decreases. The longitudinal scale of rolls reduces sharply at first and then increases gradually. Vibration produces the greatest stabilizing effect on the fluid equilibrium state in a narrow range of small negative and positive buoyancy ratios, which are responsible for a considerable change in the wavelength of rolls. The buoyancy ratio effect on the oscillatory convection rolls is rather weak. The vibration effect on their marginal stability threshold and wavelength is more pronounced.

On the Characteristics of Linear-Phase Roll Vortices under a Moving Hurricane Boundary Layer

Abstract Previous theoretical and numerical studies only focused on the formation of roll vortices (rolls) under a stationary and axisymmetric hurricane. The effect of the asymmetric wind structure induced by the storm movement on the roll characteristics remains unknown. In this study, we present the first attempt to investigate the characteristics of linear-phase rolls under a moving hurricane by embedding a linear two-dimensional (2D) roll-resolving model into a 3D hurricane boundary layer model. It is found that the roll horizontal wavelength under the moving hurricane is largely determined by the radial-shear-layer depth, defined as the thickness of the layer with positive radial wind shear. The horizontal distribution of the roll wavelength resembles the asymmetric pattern of the radial-shear-layer depth. Interestingly, the roll growth rate is not only affected by the radial wind shear magnitude alluded to in previous studies but also by the radial-shear-layer depth. A deeper (shallower) radial shear layer tends to decrease (increase) the roll growth rate. Such an effect is due to the presence of the bottom boundary. The bottom boundary constrains the lower-level roll streamlines and reduces the efficiency of rolls in extracting kinetic energy from the radial shear. This effect is more pronounced under a deeper shear layer, which favors the formation of larger-size rolls. This study improves the understanding of the main factors affecting the structure and growth of rolls and will provide guidance for interpreting the spatial distribution of rolls under realistic hurricanes in observations and high-resolution simulations.

Tropical Cyclone Boundary Layer Rolls in Synthetic Aperture Radar Imagery

AbstractMarine atmospheric boundary layer (MABL) roll plays an important role in the turbulent exchange of momentum, sensible heat, and moisture throughout MABL of tropical cyclone (TC). Hence, rolls are believed to be closely related to TC's development, intensification, and decay processes. Spaceborne synthetic aperture radar (SAR) provides a unique capability to image the sea surface imprints of quasi‐linear streaks induced by the MABL rolls within a TC. In this study, sixteen SAR images, including three images acquired during three major hurricanes: Irma, Jose, and Maria in the 2017 Atlantic hurricane season, were utilized to systematically map the distribution and wavelength of MABL rolls under the wide range of TC intensities. The images were acquired by SAR onboard RADARSAT‐1/2, ENVISAT, and SENTINEL‐1 satellites. Our findings are in agreement with the previous one case study of Hurricane Katrina (2005), showing the roll wavelengths are between 600 and 1,600 m. We also find that there exist roll imprints in eyewall and rainbands, although the boundary layer heights are shallower there. Besides, the spatial distribution of roll wavelengths is asymmetrical. The roll wavelengths are found to be the shortest around the storm center, increase and then decrease with distance from storm center, reaching the peak values in the range of , where is defined as the physical location to TC centers normalized by the radius of maximum wind. These MABL roll characteristics cannot be derived using conventional aircraft and land‐based Doppler radar observations.

Impact of vertical wind shear on roll structure in idealized hurricane boundary layers

Abstract. 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.

MERIS full‐resolution total column water vapor: Observing horizontal convective rolls

AbstractThis study presents the first analysis of small‐scale convective structures observed in a total column water vapor (TCWV) field obtained from full‐resolution Medium Resolution Imaging Spectrometer (MERIS) near‐infrared measurements. The high‐resolution MERIS TCWV field for a high‐pressure event occurring in May over central Europe allows the detection of horizontal convective rolls, due to the observation of parallel bands of alternating low‐ and high‐TCWV values. The bands are aligned parallel to the boundary layer winds obtained from a numerical weather prediction model and radiosonde data. Closer examination further reveals that cloud streets observed in the east extend along bands of maximum TCWV. From a quantitative analysis of the TCWV data, combined with auxiliary data, it is shown that the roll wavelength and aspect ratio can be determined, which are found to be 6.5 km and 4.2, respectively, for this case study.

Response of roll wave to suspended load and hydraulics of overland flow on steep slope

A roll wave is frequently observed in overland flow and it can accelerate the soil erosion on slopes. However, the feedback effect of eroded sediment on roll wave has not been studied. The aim of this study was to investigate the response of roll wave to sediment concentration and overland flow hydraulics on steep slope. The experiment was carried out in a hydraulic flume. The unit flow rate varied from 1.0 to 3.0×10−3m3s−1, and sediment concentration from 0 to 400kgm−3. The sediment transport was dominated by suspension. Slope gradient was 9°. As the sediment concentration increased, the critical slope length for roll wave formation increased, implying that the suspended sediment in flow could inhibit the formation of a roll wave. The roll wave in overland flow is a short water long wave. The roll wave length increased with the increasing sediment concentration, while the wave frequency and velocity decreased. The decreased wave velocity meant a decrease in flow erosion potential caused by a roll wave. Roll wave frequency and velocity significantly increased with Reynolds number, Froude number and mean flow velocity, and decreased with the hydraulic resistance, while there were no notable relationships between roll wave length and overland flow hydraulics. Both roll wave frequency and velocity had the strongest dependency on Froude number and could be estimated by the linear equations between them. When the sediment concentration was larger than 300kgm−3, all the roll waves in overland flow disappeared due to the high sediment supply. The results indicated that the suspended sediment can ease the acceleration influence of a roll wave on soil erosion and should be considered in the soil erosion models.

Toward Improved Forecasts of Sea-Breeze Horizontal Convective Rolls at Super High Resolutions. Part I: Configuration and Verification of a Down-Scaling Simulation System (DS3)

Abstract Horizontal convective rolls (HCRs) that develop in sea breezes greatly influence local weather in coastal areas. In this study, the authors present a realistic simulation of sea-breeze HCRs over an urban-scale area at a resolution of a few meters. An advanced Down-Scaling Simulation System (DS3) is built to derive the analyzed data using a nonhydrostatic model and data assimilation scheme that drive a building-resolving computational fluid dynamics (CFD) model. The mesoscale-analyzed data well capture the inland penetration of the sea breeze in northeastern Japan. The CFD model reproduces the HCRs over Sendai Airport in terms of their coastal initiation, inland growth, streamwise orientation, specific locations, roll wavelength, secondary flows, and regional differences due to complex surfaces. The simulated HCRs agree fairly well with those observed by dual-Doppler lidar and heliborne sensors. Both the simulation and observation analyses suggest that roll updrafts typically originate in the narrow bands of low-speed streaks and warm air near the ground. The HCRs are primarily driven and sustained by a combination of wind shear and buoyancy forces within the slightly unstable sea-breeze layer. In contrast, the experiment without data assimilation exhibits a higher deficiency in the reproduction of roll characteristics. The findings highlight that CFD modeling, given reliable mesoscale weather and surface conditions, aids in high-precision forecasting of HCRs at unprecedented high resolutions, which may help determine the roll structure, dynamics, and impacts on local weather.

Toward Improved Forecasts of Sea-Breeze Horizontal Convective Rolls at Super High Resolutions. Part II: The Impacts of Land Use and Buildings

Abstract Horizontal convective rolls form in coastal areas around Sendai Airport during sea-breeze events. Using a building-resolving computational fluid dynamics model nested in an advanced forecast system with a data assimilation scheme, the authors perform a series of sensitivity experiments to investigate the impacts of land use and buildings on these rolls. The results show that the roll positions, intensities, and structures are significantly affected by variations in land use and the presence of buildings. Land-use heterogeneity is responsible for generating rolls with evident regional features. Major rolls tend to develop downwind of warm surfaces, and they dominate over neighboring rolls; thus, a heterogeneity-scale mode is imposed on the inherent roll wavelength. The roll’s rapid growth is attributable to warm surfaces that initiate a strong coupling among turbulent thermals, convective updrafts, pressure perturbations, and secondary flows in sea breezes. The heterogeneity-induced features differ considerably from the nearly homogeneous features that form over uniform surfaces. Additionally, the wake flow behind buildings helps organize near-surface warm air into streamwise bands that drive streaky ejections. The building-induced turbulence acts to modify secondary flows and displace roll updrafts toward building wakes. Such effects are most effective over villages with scattered houses that are aligned with the ambient wind. Building signatures are elongated in downwind open areas due to sustained secondary circulations. An analysis of turbulent kinetic energy shows that both land use and buildings regulate energy generation and transport, resulting in a clear response in roll growth. Thus, including complex surfaces in forecast models helps determine detailed characteristics and structures of roll convection over coastal regions.

On the impact of forced roll convection on vertical turbulent transport in cold air outbreaks

AbstractWe investigated the impact of roll convection on the convective boundary layer and vertical transports in different cold air outbreak (CAO) scenarios using large eddy simulations (LES). The organization of convection into rolls was triggered by upstream heterogeneities in the surface temperature, representing ice and water. By changing the sea ice distribution in our LES, we were able to simulate a roll and a nonroll case for each scenario. Furthermore, the roll wavelength was varied by changing the scale of the heterogeneity. The characteristics of the simulated rolls and cloud streets, such as aspect ratios, orientation of the roll axes, and downstream extensions of single rolls agreed closely with observations in CAO situations. The vertical turbulent fluxes, calculated for each simulation, were decomposed into contributions from rolls and from unorganized turbulence. Even though our results confirmed that rolls triggered by upstream heterogeneities can substantially contribute to vertical turbulent fluxes, the total fluxes were not affected by the rolls.

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.

Simulating the IHOP_2002 Fair-Weather CBL with the WRF-ARW–Noah Modeling System. Part II: Structures from a Few Kilometers to 100 km across

Abstract Fair-weather data along the May–June 2002 International H2O Project (IHOP_2002) eastern track and the nearby Argonne Boundary Layer Experiments (ABLE) facility in southeast Kansas are compared to numerical simulations to gain insight into how the surface influences convective boundary layer (CBL) structure, and to evaluate the success of the modeling system in replicating the observed behavior. Simulations are conducted for 4 days, using the Advanced Research version of the Weather Research and Forecasting (WRF) model coupled to the Noah land surface model (LSM), initialized using the High-Resolution Land Data Assimilation System (HRLDAS). Because the observations focus on phenomena less than 60 km in scale, the model is run with 1-km grid spacing, offering a critical look at high-resolution model behavior in an environment uncomplicated by precipitation. The model replicates the type of CBL structure on scales from a few kilometers to ∼100 km, but some features at the kilometer scales depend on the grid spacing. Mesoscale (tens of kilometers) circulations were clearly evident on 2 of the 4 days (30 May and 20 June), clearly not evident on 1 day (22 June), with the situation for the fourth day (17 June) ambiguous. Both observed and modeled surface-heterogeneity-generated mesoscale circulations are evident for 30 May. On the other hand, 20 June satellite images show north-northwest–south-southeast cloud streets (rolls) modulated longitudinally, presumably by tropospheric gravity waves oriented normal to the roll axis, creating northeast–southwest ridges and valleys spaced 50–100 km apart. Modeled cloud streets showed similar longitudinal modulation, with the associated two-dimensional structure having maximum amplitude above the CBL and no relationship to the CBL temperature distribution; although there were patches of mesoscale vertical velocity correlated with CBL temperature. On 22 June, convective rolls were the dominant structure in both model and observations. For the 3 days for which satellite images show cloud streets, WRF produces rolls with the right orientation and wavelength, which grows with CBL depth. Modeled roll structures appeared for the range of CBL depth to Obukhov length ratios (−zi/L) associated with rolls. However, sensitivity tests show that the roll wavelength is also related to the grid spacing, and the modeled convection becomes more cellular with smaller grid spacing.

Wavelength selection in convection near a lateral boundary

This paper considers the way in which a lateral boundary restricts the wavelength of convective rolls parallel to the boundary. Unlike previous theories of wave number selection, the present work allows for perpendicular cross rolls adjacent to the boundary, the existence of which is indicated by stability considerations. The present theory also incorporates forcing at the boundary, equivalent to a wall that is imperfectly insulated, as in many experimental investigations of Rayleigh-Benard convection. The results are based on weakly non-linear solutions of amplitude equations derived from the Swift-Hohenberg model and are compared with numerical solutions of the full non-linear Swift-Hohenberg equation.

Small-scale convection under the back-arc occurring in the low viscosity wedge

Water released from subducting slabs through a dehydration reaction may lower the viscosity of the mantle significantly. Thus, we may expect a low viscosity wedge (LVW) above the subducting slabs. The LVW coupled with a large-scale flow induced by the subducting slabs may allow the existence of roll-like small-scale convection whose axis is normal to the strike of the plate boundary. Such a roll structure may explain the origin of along-arc variations of mantle temperature proposed recently in northeast Japan. We study this possibility using both 2D and 3D models with/without pressure- and temperature-dependent viscosity. 2D models without pressure and temperature dependence of viscosity show that, with a reasonable geometry of the LVW and subduction speed, small-scale convection is likely to occur when the viscosity of the LVW is less than 1019 Pa s. Corresponding 3D model studies reveal that the wavelength of rolls depends on the depth of the LVW. The inclusion of temperature-dependent viscosity requires the existence of further low viscosity in the LVW, since temperature dependence suppresses the instability of the cold thermal boundary layer. Pressure (i.e. depth) dependence coupled with temperature dependence of the viscosity promotes short wavelength instabilities. The model, which shows a relatively moderate viscosity decrease in the LVW (most of the LVW viscosity is 1018∼1019 Pa s) and a wavelength of roll ∼80 km, has a rather small activation energy and volume (∼130 kJ/mol and ∼4 cm3/mol) of the viscosity. This small activation energy and volume may be possible, if we regard them as an effective viscosity of non-linear rheology.

Horizontal Convective Rolls: Determining the Environmental Conditions Supporting their Existence and Characteristics

Abstract Data from the Convection and Precipitation/Electrification (CaPE) project, as well as results from numerical simulations, are used to study horizontal convective rolls. The environmental conditions necessary for sustaining rolls and for influencing the aspect ratio, ratio of roll wavelength to convective boundary layer (CBL) depth, and orientation are examined. Observations and numerical model simulations both suggest that a moderate surface sensible heat flux and some vertical wind shear are necessary for roll existence. Unlike some previous studies, however, it is shown that rolls occurred within very low CBL shear conditions (∼2 × 10−3 s−1). In addition, the low-level (i.e., ∼200 m) shear seems to be more important than the shear through the depth of the CBL in roll sustenance. The aspect ratio is shown to be proportional to the CBL instability, measured in terms of the Monin–Obukhov length. The roll orientation is similar to the wind direction at 10 m AGL, the CBL wind direction, the inversio...

Electrohydrodynamics in Nematics Subject to Parallel Electric and Magnetic Fields

Abstract Under parallel electric and magnetic fields, electrohydrodynamic instabilities in nematic liquid crystals having negative dielectric anisotropy are predicted to exhibit a strong dependence of roll spacing on applied magnetic field. We report studies of the parallel magnetic field dependence of the threshold electric field for instabilities and the roll wavelength at threshold. The threshold electric field exhibits fascinating re-entrant behaviour not predicted by theory. We describe qualitatively new mechanisms for the creation and destruction of the convecting state at higher magnetic fields.

A new roll-type instability in an oscillating fluid plane

A new roll-type instability has been discovered experimentally. When fluid between two closely spaced, parallel plates is oscillated about an axis midway between the plates, it exhibits an instability that takes the form of longitudinal rolls aligned perpendicular to the axis of rotation. The basic-state oscillatory shear flow, before the onset of rolls, may be viewed as driven by the $\dot{\bm \Omega}\times \hat{\bm r}$ term of the Navier–Stokes equation in the oscillatory reference frame. A regime diagram is presented in a parameter space defined by the maximum amplitude of angular oscillation, α, and the non-dimensional frequency, Φ = ωd2/ν. The equilibrium wavelength of the rolls scales with d, the gap spacing between the plates, and it increases as Φ increases. Supercritical to a weak-roll onset, an abrupt transition to stronger roll amplitude occurs. Photographs of the cell after an impulsive start show the roll development and initial increase in roll wavelength. A variety of phenomena are observed, including wavelength selection via defect creation and elimination, front propagation, secondary wave instabilities, and the transition to turbulence. We also present solutions of the Navier–Stokes equation for the basic-state shear flow in a near-axis approximation. We develop a simple resonance model which shows some promise in understanding the low-α, high-Φ behaviour of strong rolls. A theoretical analysis of this instability is presented by Hall (1994).

The Three‐Dimensional Nature of ‘Symmetric’ Instability

AbstractThe importance of three‐dimensional effects in a flow with negative potential vorticity is considered here; this is the three‐dimensional counterpart of symmetric instability. the term symmetric instability refers to a two‐dimensional flow with negative potential vorticity which develops roll circulations aligned along the thermal wind. the requirement for exact two‐dimensionality is here relaxed by using three‐dimensional numerical simulations. Two classes of simulation are described; both take a two‐dimensional basic flow.In the first part we explore the response of a flow with uniform negative potential vorticity to localized initial perturbations. It is found that circulations become established which elongate at an angle to the thermal wind. This angle, it is shown, is determined by viscous effects and is in accord with the structure of linear viscous tilted modes for this flow. If, as happens on occasions, such an angle formed by rainbands to the thermal wind is observed in nature, it gives an indication of the importance of viscous effects. In the cases presented here the orientation is such that the rolls tilt towards the warm air as viewed in the direction of the thermal wind; i.e. they are rotated anticyclonically relative to the front. It is shown that these structures, when at finite amplitude, are stable to perturbations imposed along their length.In the second part localized regions of instability are produced which are confined along the thermal wind direction by prescribing in these zones a reduced static stability for vertical motion. This represents the effects of latent‐heat release and it is only in these zones that the effective potential vorticity is negative. It is found that if the length of the zone along the thermal wind direction is smaller than about twice the roll wavelength across that direction then the growth rate is substantially reduced; otherwise it is relatively unaffected by this confinement. It therefore appears that a flow with negative potential vorticity is not only unstable in the pathological two‐dimensional case.