Vertical Flux Of Horizontal Momentum Research Articles

Turbulence structures and entrainment length scales in large offshore wind farms

Abstract. The flow inside and around large offshore wind farms can range from smaller structures associated with the mechanical turbulence generated by wind turbines to larger structures indicative of the mesoscale flow. In this study, we explore the variation in turbulence structures and dominant scales of vertical entrainment above large offshore wind farms located in the North Sea, using data obtained from a research aircraft. The aircraft was flown upstream, downstream, and above wind farm clusters. Under neutrally stratified conditions, there is high ambient turbulence in the atmosphere and an elevated energy dissipation rate compared to stable conditions. The intensity of small-scale turbulence structures is increased above and downstream of the wind farm, and it prevails over mesoscale fluctuations. But in stable stratification, mesoscale flow structures are not only dominant upstream of the wind farm but also downstream. We observed that the vertical flux of horizontal momentum is the main source of energy recovery in large offshore wind farms, and it strongly depends on the magnitude of the length scales of the vertical wind velocity component. The dominant length scales of entrainment range from 20 to ∼60 m above the wind farm in all stratification strengths, and in the wake flow these scales range from 10 to ∼100 m only under near-neutral stratification. For strongly stable conditions, negligible vertical entrainment of momentum was observed even just 2 km downstream of large wind farms. We also observed that there is a significant lateral momentum flux above the offshore wind farms, especially under strongly stable conditions, which suggests that these wind farms do not satisfy the conditions of an “infinite wind farm”.

Numerical Simulation of Mountain Waves over the Southern Andes. Part II: Momentum Fluxes and Wave–Mean-Flow Interactions

AbstractA companion paper by Lund et al. employed a compressible model to describe the evolution of mountain waves arising due to increasing flow with time over the southern Andes, their breaking, secondary gravity waves and acoustic waves arising from these dynamics, and their local responses. This paper describes the mountain wave, secondary gravity wave, and acoustic wave vertical fluxes of horizontal momentum, and the local and large-scale three-dimensional responses to gravity breaking and wave–mean-flow interactions accompanying this event. Mountain wave and secondary gravity wave momentum fluxes and deposition vary strongly in space and time due to variable large-scale winds and spatially localized mountain wave and secondary gravity wave responses. Mountain wave instabilities accompanying breaking induce strong, local, largely zonal forcing. Secondary gravity waves arising from mountain wave breaking also interact strongly with large-scale winds at altitudes above ~80 km. Together, these mountain wave and secondary gravity wave interactions reveal systematic gravity wave–mean-flow interactions having implications for both mean and tidal forcing and feedbacks. Acoustic waves likewise achieve large momentum fluxes, but typically imply significant responses only at much higher altitudes.

Departure from Flux-Gradient Relation in the Planetary Boundary Layer

It is well known that when eddies are small, the eddy fluxes can be directly related to the mean vertical gradients, the so-called flux-gradient relation, but such a relation becomes weaker the larger the coherent structures. Here, we show that this relation does not hold at heights relevant for wind energy applications. The flux–gradient relation assumes that the angle (β) between the vector of vertical flux of horizontal momentum and the vector of the mean vertical gradient of horizontal velocity is zero, i.e., these vectors are aligned. Our observations do not support this assumption, either onshore or offshore. Here, we present analyses of a misalignment between these vectors from a Doppler wind lidar observations and large-eddy simulations. We also use a real-time mesoscale model output for inter-comparison with the lidar-observed vertical profiles of wind speed, wind direction, momentum fluxes, and the angle between the horizontal velocity vector and the momentum flux vector up to 500 m, both offshore and onshore. The observations show this within the height range 100–500 m, β=−18∘ offshore and β=−12∘ onshore, on average. However, the large-eddy simulations show β≈0∘ both offshore and onshore. We show that observed and mesoscale-simulated vertical profiles of mean wind speed and momentum fluxes agree well; however, the mesoscale results significantly deviate from the wind-turning observations.

Mesospheric Gravity Wave Momentum Flux Associated With a Large Thunderstorm Complex

AbstractWe report on estimates of the vertical flux of horizontal momentum associated with an extensive and bright mesospheric gravity wave event that occurred over the El Leoncito Observatory, Argentina (31.8°S, 69.3°W), during the night of 17–18 March 2016. Using a combination of ground‐based and space‐based data sources, we propose that the event was generated by a large and distant thunderstorm complex located to the southeast of the observation site. The nightglow, including the wave structures, was easily visible to naked eye observers, a phenomenon known as a Bright Night. Such “extreme events” illuminate the important role of upward coupling in space weather research.

The Impact of Mountain Waves on an Idealized Baroclinically Unstable Large-Scale Flow

Abstract The feedback of mountain waves and low-level blocking on an idealized baroclinically unstable wave passing over an isolated ridge is examined through numerical simulation. Theoretical analysis implies that the volume-integrated perturbation momentum budget is dominated by mean-flow deceleration, the divergence of vertical fluxes of horizontal momentum, and the Coriolis force acting on the perturbation ageostrophic wind. These do indeed appear as the dominant balances in numerically computed budgets averaged over layers containing 1) wave breaking in the lower stratosphere, 2) flow blocking with wave breaking near the surface, and 3) a region of pronounced horizontally averaged mean-flow deceleration in the upper troposphere where there is no wave breaking. The local impact of wave breaking on the jet in the lower stratosphere is dramatic, with winds in the jet core reduced by almost 50% relative to the no-mountain case. Although it is the layer with the strongest average deceleration, the local patches of decelerated flow are weakest in the upper troposphere. The cross-mountain pressure drag over a 2-km-high ridge greatly exceeds the vertical momentum flux at mountain-top level because of low-level wave breaking, blocking, and lateral flow diversion. These pressure drags and the low-level momentum fluxes are significantly different from corresponding values computed for simulations with steady forcing matching the instantaneous conditions over the mountain in the evolving large-scale flow.

On the distortions in calculated GW parameters during slanted atmospheric soundings

Abstract. The significant distortions introduced in the measured atmospheric gravity wavelengths by soundings other than those in vertical and horizontal directions, are discussed as a function of the elevation angle of the sounding path and the gravity wave aspect ratio. Under- or overestimation of real vertical wavelengths during the measurement process depends on the value of these two parameters. The consequences of these distortions on the calculation of the energy and the vertical flux of horizontal momentum are analyzed and discussed in the context of two experimental limb satellite setups: GPS-LEO radio occultations and TIMED/SABER ((Atmosphere using Broadband Emission Radiometry/Thermosphere–Ionosphere–Mesosphere–Energetics and Dynamics)) measurements. Possible discrepancies previously found between the momentum flux calculated from satellite temperature profiles, on site and from model simulations, may to a certain degree be attributed to these distortions. A recalculation of previous momentum flux climatologies based on these considerations seems to be a difficult goal.

Simultaneous observation of gravity waves at PMC altitude from AIM/CIPS experiment and PANSY radar over Syowa (69°S, 39°E)

Simultaneous observation of gravity waves (GWs) in the polar summer mesosphere over Syowa (69°S, 39°E) by a ground-based radar and satellite instrument are presented. On 21 January 2016, at 2.3 UT, the CIPS instrument on the AIM satellite observed Polar Mesospheric Clouds (PMCs) with GW structures over Syowa. The orientation of the wave crests suggests north-west propagation direction. A periodogram analysis indicates GWs with horizontal wavelengths of 105 ± 5 and 60 ± 5 km. Cross-spectral analysis of the PANSY radar horizontal wind components at the same time, location, and altitude indicate two dominant waves with apparent periods of 15 and 9 h, with respective horizontal wavelengths of 100 ± 5 km and 302 ± 130 km. At the PMC altitude of ∼83 km, the mean zonal component of the vertical momentum flux spectra of the observed GWs is westward and the meridional component is northward. The comparable horizontal wavelengths of the 15 h wave observed by PANSY radar and the CIPS instrument, along with the agreement between the direction of vertical flux of horizontal momentum from PANSY, the propagation direction estimated from the cross-spectral analysis, and the orientation of the wave crests from CIPS i.e. north-west propagation direction suggests that the same wave is observed by both instruments. This simultaneous observation of the same wave by CIPS and PANSY radar provide a distinctive view of both the horizontal and vertical extent of a GW in the Antarctic summer mesosphere.

The QBO, gravity waves forced by tropical convection, and ENSO

AbstractBy means of theory, a simplified cartoon illustrating wave forcing of the stratospheric quasi‐biennial oscillation (QBO), and general circulation modeling of the QBO, it is argued that the period of the QBO is mainly controlled by the magnitude of the gravity wave (GW) vertical fluxes of horizontal momentum (GWMF) forcing the QBO, while the QBO amplitude is mainly determined by the phase speeds of the GWs that make up this momentum flux. It is furthermore argued that it is the zonally averaged GWMF that principally determines the QBO period irrespective of the longitudinal distribution of this GW momentum flux. These concepts are used to develop a hypothesis for the cause of a previously reported El Niño–Southern Oscillation (ENSO) modulation of QBO periods and amplitudes. Some observational evidence is reported for the ENSO modulation of QBO amplitudes to have been different before the 1980s than after about 1990. A hypothesis is also given to explain this in terms of the different ENSO modulation of tropical deep convection that took place before the 1980s from that which occurred after about 1990. The observational evidence, while consistent with our hypotheses, does not prove that our hypotheses are correct given the small number of El Niños and La Niñas that occurred in the early and later periods. Further research is needed to support or refute our hypotheses.

Vertical Momentum Transports Associated with Moist Convection and Gravity Waves in a Minimal Model of QBO-like Oscillation

Abstract A self-sustained oscillation dynamically analogous to the equatorial quasi-biennial oscillation (QBO) was obtained as a radiative–moist-convective quasi-equilibrium state in a minimal model of the stratosphere–troposphere coupled system, which is a two-dimensional cloud-system-resolving nonhydrostatic model with a periodic lateral boundary condition. The QBO-like oscillation shows downward propagation of the zonal mean signals in the stratosphere. In addition, in the troposphere there are periodic variations associated with the QBO-like oscillation, including organized features of moist-convective systems characterized as squall-line- or back-building-type precipitation patterns. Details of the momentum budget variation are examined to study the stratosphere–troposphere dynamical coupling associated with the QBO-like oscillation. The vertical flux of horizontal momentum is separated into three contributions of convective momentum transport (CMT) and momentum transports by upward- and downward-propagating gravity waves—that is, upward and downward gravity wave momentum transports (GWMTs)—and the time–height variations of each contribution are evaluated quantitatively. The method is based on the linear theory of gravity waves to separate upward- and non-upward-propagating contributions and uses the phase speed spectra of the total cloud mixing ratio to identify the CMT contribution. The upward GWMT predominates in the stratosphere and contributes to the acceleration of the zonal mean zonal wind. The CMT and downward GWMT are confined to the troposphere, and the former predominates. The variations of the mean zonal wind modulate the organization of convective systems, and the squall-line- and back-building-type patterns appear alternately. According to the modulation of convective systems, the spectral features of every momentum transport vary periodically.

Stratospheric gravity wave momentum flux from radio occultations

AbstractTriples of GPS radio occultation (RO) temperature data are used to derive horizontal and vertical gravity wave (GW) parameters in the stratosphere between 20 km and 40 km from which the vertical flux of horizontal momentum is determined. Compared to previous studies using RO data, better limiting values for the sampling distance (Δd≤250 km) and the time interval (Δt≤15 min) are used. For several latitude bands the mean momentum fluxes (MFs) derived in this study are considerably larger than MF from other satellite missions based on horizontal wavelengths calculated between two adjacent temperature profiles along the satellite track. Error sources for the estimation of MF from RO data and the geometrical setup for the applied method are investigated. Another crucial issue discussed in this paper is the influence of different background separation methods to the final MF. For GW analysis a measured temperature profile is divided into a fluctuation and a background and it is assumed that the fluctuation is caused by GWs only. For the background separation, i.e., the detrending of large‐scale processes from the measured temperature profile, several methods exist. In this study we compare different detrending approaches and for the first time an attempt is made to detrend RO data with ERA‐Interim data from the European Centre for Medium‐Range Weather Forecasts. We demonstrate that the horizontal detrending based on RO data and ERA‐Interim gives more consistent results compared with a vertical detrending.

Investigation of gravity wave activity based on operational radiosonde data from 13 years (1997-2009): Climatology and possible induced variability

Atmospheric gravity waves (GWs) are important for the dynamics of the atmosphere. The analysis of 13 years of routine radiosonde data from Prague (50.01°N, 14.27°E) with temporal highly resolved temperature, pressure and wind measurements is presented in order to derive a climatology of gravity wave activity in the lower stratosphere. An annual cycle with a maximum during winter and a minimum during summer is identified. Gravity wave activity is twice as high during winter as during summer. Winter periods are investigated by wavelet analysis. They show similar periods in vertical flux of horizontal momentum and pressure variance time series. These features may be attributed to planetary waves. When analyzing individual years, maxima of gravity wave activity and vertical flux of horizontal momentum often appears together with minima in surface pressure. We speculate therefore that at least parts of the interannual variations of gravity wave activity may due to cyclones.

Characteristics of Vertical Wind Fluctuations in the Lower Troposphere at Syowa Station in the Antarctic Revealed by the PANSY Radar

Using wind data over three years from July 2012-June 2015 from the PANSY radar, an MST radar, newly installed at Syowa Station (39.59°E, 69.0°S), statistical characteristics of vertical winds and vertical momentum fluxes in the Antarctic lower troposphere are examined. Frequency spectra covering a wide frequency range from (30 d)−1 to (8 min)−1 are divided into three frequency regions obeying power laws with different scaling exponents. The transition frequencies are different between horizontal and vertical wind spectra. Vertical fluxes of horizontal momentum were estimated for two wave period ranges of 8 min–2 h and 2 h–1 d which have almost equal logarithmic scales. The momentum fluxes are larger for longer period components. There are evidences showing that the vertical wind disturbances in the lower troposphere are due to gravity waves forced by topography aligned in the north-south direction. First, the strong disturbances are observed when horizontal winds are strong near the surface. Second, zonal winds tend to almost zero around the top of the disturbances. Third, frequency spectra are large at a wide range of frequency below a critical level, as is consistent with the phase modulation of mountain waves by unsteady mean flow.

Energy dissipation and transfer processes during the breaking of modulated wave trains

In this work numerical simulation of the breaking induced by the modulational instability are presented. The study is focused on the energy and momentum exchanged taking place at the air-water interface during the breaking process. Simulations are performed by a two-fluids Navier-Stokes solver combined with the VOF technique, which provides a detailed description of the flow in both phases. Results obtained by two different initial conditions are presented in terms of free surface shapes, energy in air and water, vertical fluxes of horizontal momentum and vorticity.

Multi-year observations of gravity wave momentum fluxes at low and middle latitudes inferred by all-sky meteor radar

Abstract. We have applied a modified composite day analysis to the Hocking (2005) technique to study gravity wave (GW) momentum fluxes in the mesosphere and lower thermosphere (MLT). Wind measurements from almost continuous meteor radar observations during June 2004–December 2008 over São João do Cariri (Cariri; 7° S, 36° W), April 1999–November 2008 over Cachoeira Paulista (CP; 23° S, 45° W), and February 2005–December 2009 over Santa Maria (SM; 30° S, 54° W) were used to estimate the GW momentum fluxes and variances in the MLT region. Our analysis can provide monthly mean altitude profiles of vertical fluxes of horizontal momentum for short-period (less than 2–3 h) GWs. The averages for each month throughout the entire data series have shown different behavior for the momentum fluxes depending on latitude and component. The meridional component has almost the same behavior at the three sites, being positive (northward), for most part of the year. On the other hand, the zonal component shows different behavior at each location: it is positive for almost half the year at Cariri and SM but predominantly negative over CP. Annual variation in the GW momentum fluxes is present at all sites in the zonal component and also in SM at 89 km in the meridional component. The seasonal analysis has also shown a 4-month oscillation at 92.5 km over SM in the zonal component and over CP at the same altitudes but for the meridional component.

The mean flow and long waves induced by two-dimensional internal gravity wavepackets

Through theory supported by numerical simulations, we examine the induced local and long range response flows resulting from the momentum flux divergence associated with with a two-dimensional Boussinesq internal gravity wavepacket in a uniformly stratified ambient. Our theoretical approach performs a perturbation analysis that takes advantage of the separation of scales between waves and the amplitude envelope of a quasi-monochromatic wavepacket. We first illustrate our approach by applying it to the well-studied case of deep water surface gravity waves, showing that the induced flow, UDF, resulting from the divergence of the horizontal momentum flux is equal to the Stokes drift. For a localized surface wavepacket, UDF is itself a divergent flow and so there is the well-known non-local response manifest in the form of a deep return flow beneath the wavepacket. For horizontally periodic and vertically localized internal wavepackets, the divergent-flux induced flow, uDF, is found from consideration of the vertical gradient of the vertical flux of horizontal momentum associated with the waves. Because uDF is itself a non-divergent flow field, this accounts entirely for the wave-induced flow; there is no response flow. Our focus is upon internal wavepackets that are localized in the horizontal and vertical. We derive a formula for the divergent-flux induced flow that, as in this case of surface wavepackets, is itself a divergent flow. We show that the response is a horizontally long internal wave that translates vertically with the wavepacket at its group velocity. Scaling relationships are used to estimate the wavenumber, horizontal extent, and amplitude of this induced long wave. At higher order in perturbation theory we derive an explicit integral formula for the induced long wave. Thus, we provide validation of Bretherton's analysis of flows induced by two-dimensional internal wavepackets [F. P. Bretherton, “On the mean motion induced by gravity waves,” J. Fluid Mech. 36, 785–803 (1969)] and we provide further analyses that give intuitive insights into the physics governing the properties of the induced long wave. In particular, consistent with momentum conservation, we show that the horizontally-integrated horizontal flow associated with the long wave is given exactly by the horizontal integral of uDF. However, qualitatively different from horizontally periodic internal waves, the vertical profile of the induced horizontal flow across the horizontally localized wavepacket is positive at the leading edge and negative at the trailing edge. These results are validated by the results of numerical simulations of a Gaussian wavepacket initialized in an otherwise stationary ambient.

On the application of Wentzel–Kramer–Brillouin theory for the simulation of the weakly nonlinear dynamics of gravity waves

The dynamics of internal gravity waves is modelled using Wentzel–Kramer–Brillouin (WKB) theory in position–wave number phase space. A transport equation for the phase‐space wave‐action density is derived for describing one‐dimensional wave fields in a background with height‐dependent stratification and height‐ and time‐dependent horizontal‐mean horizontal wind, where the mean wind is coupled to the waves through the divergence of the mean vertical flux of horizontal momentum associated with the waves. The phase‐space approach bypasses the caustics problem that occurs in WKB ray‐tracing models when the wave number becomes a multivalued function of position, such as in the case of a wave packet encountering a reflecting jet or in the presence of a time‐dependent background flow. Two numerical models were developed to solve the coupled equations for the wave‐action density and horizontal mean wind: an Eulerian model using a finite‐volume method and a Lagrangian ‘phase‐space ray tracer’ that transports wave‐action density along phase‐space paths determined by the classical WKB ray equations for position and wave number. The models are used to simulate the upward propagation of a Gaussian wave packet through a variable stratification, a wind jet and the mean flow induced by the waves. Results from the WKB models are in good agreement with simulations using a weakly nonlinear wave‐resolving model, as well as with a fully nonlinear large‐eddy‐simulation model. The work is a step toward more realistic parametrizations of atmospheric gravity waves in weather and climate models.

Finescale Dual-Doppler Analysis of Hurricane Boundary Layer Structures in Hurricane Frances (2004) at Landfall

Abstract Two Doppler on Wheels (DOW) mobile radars collected fine-spatial-scale dual-Doppler data in the right-front quadrant and eye of Hurricane Frances (2004) as it made landfall near Stuart, Florida. A 5.7-km dual-Doppler baseline established a dual-Doppler domain south and east of Fort Pierce, Florida, encompassing a 5.5 km × 5.5 km horizontal area, with a grid spacing of 20 m, allowing for the resolution of subkilometer-scale horizontal structures and associated kinematics. Three-dimensional vector wind analyses of the boundary layer revealed the presence of linear coherent structures with a characteristic wavelength of 400–500 m near the surface that increased in size and became more cellular in shape with increasing height. Average horizontal perturbation winds were proportional to average total horizontal winds. Within the eye of the hurricane, the features lost linear coherency despite a high mean wind speed, possibly due to changes in stability. A slight decrease in the characteristic wavelength of boundary layer structures was documented as the winds cross the barrier islands east of Fort Pierce. Vertical flux of horizontal momentum caused by individual vortical structures was substantially higher than values employed in turbulence parameterization schemes, but the domain-wide average flux was substantially lower than that in individual structures, likely due to the transient nature of the most intense portions of the structures. Analysis of the turbulent kinetic energy (TKE) yielded values comparable to those reported in previous observational studies over the open ocean. However, there was substantial variability in TKE within the dual-Doppler domain, emphasizing the challenge in obtaining representative samples using non-3D measurements such as dropsondes.

Numerical Buoyancy-Wave Model for Wave Stress and Drag Simulations in the Atmosphere

AbstractOrographic drag formation is investigated using a numerical wave model (NWM), based on the pressure-coordinate dynamics of non-hydrostatic HIRLAM. The surface drag, wave stress (vertical flux of horizontal momentum), and wave drag are split to the longitudinal and transverse components and presented as Fourier sums of their spectral amplitudes weighted with the power spectrum of relative orographic height. The NWM is accomplished, enabling a spectral investigation of the buoyancy wave stress, and drag generation by orography and is then applied to a cold front, characterised by low static stability of the upper troposphere, large vertical and directional wind variations, and intensive trapped wave generation downstream of obstacles. Resonances are discovered in the stress and drag spectra in the form of high narrow peaks. The stress conservation problem is revisited. Longitudinal stress conserves in unidirectional flow, 2D orography conditions, but becomes convergent for rotating wind or 3D orography. Even in the convergent case the vertical momentum flux from the troposphere to stratosphere remains substantial. The transverse stress never conserves. Disappearing at the surface and on the top, it realises the main momentum exchange between lower an upper parts of the troposphere. Existence of stationary stratospheric quasi-turbulence (SQT) is established above wind minimum in the stratosphere.

On the determination of gravity wave momentum flux from GPS radio occultation data

Abstract. Global Positioning System (GPS) radio occultation (RO) is a well-established technique for obtaining global gravity wave (GW) information. RO uses GPS signals received by low Earth-orbiting satellites for atmospheric limb sounding. Temperature profiles are derived with high vertical resolution and provide a global coverage under any weather conditions, offering the possibility of global monitoring of the vertical temperature structure and atmospheric wave parameters. The six-satellite constellation COSMIC/FORMOSAT-3 delivers approximately 2000 temperature profiles daily. In this study, we use a method to obtain global distributions of horizontal gravity wave wavelengths, to be applied in the determination of the vertical flux of horizontal momentum transported by gravity waves. Here, a method for the determination of the real horizontal wavelength from three vertical profiles is applied to the COSMIC data. The horizontal and vertical wavelength, the specific potential energy (Ep), and the vertical flux of horizontal momentum (MF) are calculated and their global distribution is discussed.

Short period gravity wave momentum fluxes observed in the tropical troposphere, stratosphere and mesosphere

Using long-term data (1998–2008) collected from mesosphere–stratosphere–troposphere (MST) radar and Rayleigh Lidar located at a tropical station, Gadanki (13.5°N, 79.2°E), India, vertical flux of the momentum from troposphere to mesosphere associated with the gravity waves of periods in the range 20min to 2h is investigated for the first time. The emphasis is on seasonal variability of mean zonal and meridional momentum fluxes in mesosphere and troposphere and vertical flux of horizontal momentum in the stratosphere. At tropospheric altitudes of 11–16km large enhancement in flux is noticed during equinoxes. In the lower mesosphere in the altitude region 58–62km the maximum values of flux (∼2.8m2/s2) observed are pragmatic in winter and spring. Interestingly, the vertical flux of horizontal momentum estimated from lidar is in the range of those estimated from radar data in the overlap altitude region, though the estimates are from two different techniques. In the mesosphere, large variations with altitude in zonal momentum flux are noticed with a magnitude ∼0–4m2/s2 in summer. In winter and summer the zonal wind direction is opposite to the momentum flux direction between 73 and 80km and in equinoxes zonal wind follows the momentum flux. The meridional fluxes in the mesosphere are higher in equinoxes (∼10–12m2/s2).