Modeling Atmospheric Turbulence via Rapid Distortion Theory: Spectral Tensor of Velocity and Buoyancy

Research output: Contribution to journalJournal articleResearchpeer-review

431 Downloads (Pure)

Abstract

A spectral tensor model is presented for turbulent fluctuations of wind velocity components and temperature, assuming uniform vertical gradients in mean temperature and mean wind speed. The model is built upon rapid distortion theory (RDT) following studies by Mann and by Hanazaki and Hunt, using the eddy lifetime parameterization of Mann to make the model stationary. The buoyant spectral tensor model is driven via five parameters: the viscous dissipation rate epsilon, length scale of energy-containing eddies L, a turbulence anisotropy parameter Gamma, gradient Richardson number (Ri) representing the local atmospheric stability, and the rate of destruction of temperature variance eta(theta). Model output includes velocity and temperature spectra and associated cospectra, including those of longitudinal and vertical temperature fluxes. The model also produces two-point statistics, such as coherences and phases of velocity components and temperature. The statistics of uniformly sheared and stratified turbulence from the model are compared with atmospheric observations taken from the Horizontal Array Turbulence Study (HATS) field program, and model results fit observed one-dimensional spectra quite well. For highly unstable stratification, however, the model has deficiencies at low wavenumbers that limit its prediction of longitudinal velocity component spectra at scales on the order of 0.6 km. The model predicts coherences well for horizontal separations but overestimates vertical coherence with increasing separation. Finally, it is shown that the RDT output can deviate from Monin-Obukhov similarity theory.
Original languageEnglish
JournalJournal of the Atmospheric Sciences
Volume74
Issue number4
Pages (from-to)949-974
Number of pages26
ISSN0022-4928
DOIs
Publication statusPublished - 2017

Keywords

  • Atmospheric Science
  • Boundary layer
  • Buoyancy
  • Fluxes
  • Stability
  • Turbulence
  • Wind shear
  • Atmospheric thermodynamics
  • Atmospheric turbulence
  • Boundary layer flow
  • Boundary layers
  • Convergence of numerical methods
  • Tensors
  • Velocity
  • Wind
  • Atmospheric observations
  • Energy-containing eddies
  • Horizontal array turbulence study field programs
  • Monin-Obukhov similarity theory
  • Rapid distortion theory
  • Stratified turbulence
  • Viscous dissipation rate
  • Wind shears
  • Atmospheric temperature
  • METEOROLOGY
  • STABLY STRATIFIED TURBULENCE
  • SURFACE-LAYER TURBULENCE
  • SIMILARITY
  • SIMULATION
  • PROFILE
  • SCALE
  • FLOW

Cite this

@article{d2e00074a519432382b4187a881d17c6,
title = "Modeling Atmospheric Turbulence via Rapid Distortion Theory: Spectral Tensor of Velocity and Buoyancy",
abstract = "A spectral tensor model is presented for turbulent fluctuations of wind velocity components and temperature, assuming uniform vertical gradients in mean temperature and mean wind speed. The model is built upon rapid distortion theory (RDT) following studies by Mann and by Hanazaki and Hunt, using the eddy lifetime parameterization of Mann to make the model stationary. The buoyant spectral tensor model is driven via five parameters: the viscous dissipation rate epsilon, length scale of energy-containing eddies L, a turbulence anisotropy parameter Gamma, gradient Richardson number (Ri) representing the local atmospheric stability, and the rate of destruction of temperature variance eta(theta). Model output includes velocity and temperature spectra and associated cospectra, including those of longitudinal and vertical temperature fluxes. The model also produces two-point statistics, such as coherences and phases of velocity components and temperature. The statistics of uniformly sheared and stratified turbulence from the model are compared with atmospheric observations taken from the Horizontal Array Turbulence Study (HATS) field program, and model results fit observed one-dimensional spectra quite well. For highly unstable stratification, however, the model has deficiencies at low wavenumbers that limit its prediction of longitudinal velocity component spectra at scales on the order of 0.6 km. The model predicts coherences well for horizontal separations but overestimates vertical coherence with increasing separation. Finally, it is shown that the RDT output can deviate from Monin-Obukhov similarity theory.",
keywords = "Atmospheric Science, Boundary layer, Buoyancy, Fluxes, Stability, Turbulence, Wind shear, Atmospheric thermodynamics, Atmospheric turbulence, Boundary layer flow, Boundary layers, Convergence of numerical methods, Tensors, Velocity, Wind, Atmospheric observations, Energy-containing eddies, Horizontal array turbulence study field programs, Monin-Obukhov similarity theory, Rapid distortion theory, Stratified turbulence, Viscous dissipation rate, Wind shears, Atmospheric temperature, METEOROLOGY, STABLY STRATIFIED TURBULENCE, SURFACE-LAYER TURBULENCE, SIMILARITY, SIMULATION, PROFILE, SCALE, FLOW",
author = "Chougule, {Abhijit S.} and Jakob Mann and Kelly, {Mark C.} and Larsen, {Gunner Chr.}",
year = "2017",
doi = "10.1175/JAS-D-16-0215.1",
language = "English",
volume = "74",
pages = "949--974",
journal = "Journal of the Atmospheric Sciences",
issn = "0022-4928",
publisher = "American Meteorological Society",
number = "4",

}

Modeling Atmospheric Turbulence via Rapid Distortion Theory: Spectral Tensor of Velocity and Buoyancy. / Chougule, Abhijit S.; Mann, Jakob; Kelly, Mark C.; Larsen, Gunner Chr.

In: Journal of the Atmospheric Sciences, Vol. 74, No. 4, 2017, p. 949-974.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - Modeling Atmospheric Turbulence via Rapid Distortion Theory: Spectral Tensor of Velocity and Buoyancy

AU - Chougule, Abhijit S.

AU - Mann, Jakob

AU - Kelly, Mark C.

AU - Larsen, Gunner Chr.

PY - 2017

Y1 - 2017

N2 - A spectral tensor model is presented for turbulent fluctuations of wind velocity components and temperature, assuming uniform vertical gradients in mean temperature and mean wind speed. The model is built upon rapid distortion theory (RDT) following studies by Mann and by Hanazaki and Hunt, using the eddy lifetime parameterization of Mann to make the model stationary. The buoyant spectral tensor model is driven via five parameters: the viscous dissipation rate epsilon, length scale of energy-containing eddies L, a turbulence anisotropy parameter Gamma, gradient Richardson number (Ri) representing the local atmospheric stability, and the rate of destruction of temperature variance eta(theta). Model output includes velocity and temperature spectra and associated cospectra, including those of longitudinal and vertical temperature fluxes. The model also produces two-point statistics, such as coherences and phases of velocity components and temperature. The statistics of uniformly sheared and stratified turbulence from the model are compared with atmospheric observations taken from the Horizontal Array Turbulence Study (HATS) field program, and model results fit observed one-dimensional spectra quite well. For highly unstable stratification, however, the model has deficiencies at low wavenumbers that limit its prediction of longitudinal velocity component spectra at scales on the order of 0.6 km. The model predicts coherences well for horizontal separations but overestimates vertical coherence with increasing separation. Finally, it is shown that the RDT output can deviate from Monin-Obukhov similarity theory.

AB - A spectral tensor model is presented for turbulent fluctuations of wind velocity components and temperature, assuming uniform vertical gradients in mean temperature and mean wind speed. The model is built upon rapid distortion theory (RDT) following studies by Mann and by Hanazaki and Hunt, using the eddy lifetime parameterization of Mann to make the model stationary. The buoyant spectral tensor model is driven via five parameters: the viscous dissipation rate epsilon, length scale of energy-containing eddies L, a turbulence anisotropy parameter Gamma, gradient Richardson number (Ri) representing the local atmospheric stability, and the rate of destruction of temperature variance eta(theta). Model output includes velocity and temperature spectra and associated cospectra, including those of longitudinal and vertical temperature fluxes. The model also produces two-point statistics, such as coherences and phases of velocity components and temperature. The statistics of uniformly sheared and stratified turbulence from the model are compared with atmospheric observations taken from the Horizontal Array Turbulence Study (HATS) field program, and model results fit observed one-dimensional spectra quite well. For highly unstable stratification, however, the model has deficiencies at low wavenumbers that limit its prediction of longitudinal velocity component spectra at scales on the order of 0.6 km. The model predicts coherences well for horizontal separations but overestimates vertical coherence with increasing separation. Finally, it is shown that the RDT output can deviate from Monin-Obukhov similarity theory.

KW - Atmospheric Science

KW - Boundary layer

KW - Buoyancy

KW - Fluxes

KW - Stability

KW - Turbulence

KW - Wind shear

KW - Atmospheric thermodynamics

KW - Atmospheric turbulence

KW - Boundary layer flow

KW - Boundary layers

KW - Convergence of numerical methods

KW - Tensors

KW - Velocity

KW - Wind

KW - Atmospheric observations

KW - Energy-containing eddies

KW - Horizontal array turbulence study field programs

KW - Monin-Obukhov similarity theory

KW - Rapid distortion theory

KW - Stratified turbulence

KW - Viscous dissipation rate

KW - Wind shears

KW - Atmospheric temperature

KW - METEOROLOGY

KW - STABLY STRATIFIED TURBULENCE

KW - SURFACE-LAYER TURBULENCE

KW - SIMILARITY

KW - SIMULATION

KW - PROFILE

KW - SCALE

KW - FLOW

U2 - 10.1175/JAS-D-16-0215.1

DO - 10.1175/JAS-D-16-0215.1

M3 - Journal article

VL - 74

SP - 949

EP - 974

JO - Journal of the Atmospheric Sciences

JF - Journal of the Atmospheric Sciences

SN - 0022-4928

IS - 4

ER -