Dependence of Turbulent and Mesoscale Velocity Variances on Scale and Stability

L. Mahrt College of Oceanic and Atmospheric Sciences, Oregon State University, Corvallis, Oregon

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Erin Moore College of Oceanic and Atmospheric Sciences, Oregon State University, Corvallis, Oregon

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Dean Vickers College of Oceanic and Atmospheric Sciences, Oregon State University, Corvallis, Oregon

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N. O. Jensen Meteorology and Wind Energy Department, Risø National Laboratory, Roskilde, Denmark

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Abstract

The scale dependence of velocity variances is studied using data collected from a grassland site, a heather site, and four forested sites. The dependence of velocity variances on averaging time, used to define the fluctuation quantities, is modeled. The crosswind velocity variance is emphasized, because it is more difficult to model than the other two components and is crucial input for applications such as dispersion modeling. The distinction between turbulence and mesoscale variances is examined in detail. Because mesoscale and turbulence motions are governed by different physics, meaningful study of the behavior of velocity variances requires adequate separation of turbulence and mesoscale motions from data. For stable conditions, the horizontal velocity variances near the surface exhibit a spectral gap, here corresponding to a very slow or nonexistent increase of variance with increasing averaging time. This “gap region,” when it occurs, allows separation of mesoscale and turbulence motions; however, the averaging times corresponding to this gap vary substantially with stability. A choice of typical averaging times for defining turbulent perturbations, such as 5 or 10 min, leads to the capture of significant mesoscale motions for very stable conditions and contributes to the disagreement with turbulence similarity theory. For unstable motions, the gap region for the horizontal velocity variances shrinks or becomes poorly defined, because large convective eddies tend to “fill in” the gap between turbulence and mesoscale motions. The formulation developed here allows turbulence and mesoscale motions to overlap into the same intermediate timescales. The mesoscale variances are less predictable, because a wide variety of physical processes contribute to mesoscale motions. Their magnitude and range of timescales vary substantially among sites. The variation of the behavior of turbulence variances among sites is significant but substantially less than that for the mesoscale motions.

Corresponding author address: Larry Mahrt, College of Oceanic and Atmospheric Sciences, Oregon State University, Corvallis, OR 97331.

mahrt@oce.orst.edu

Abstract

The scale dependence of velocity variances is studied using data collected from a grassland site, a heather site, and four forested sites. The dependence of velocity variances on averaging time, used to define the fluctuation quantities, is modeled. The crosswind velocity variance is emphasized, because it is more difficult to model than the other two components and is crucial input for applications such as dispersion modeling. The distinction between turbulence and mesoscale variances is examined in detail. Because mesoscale and turbulence motions are governed by different physics, meaningful study of the behavior of velocity variances requires adequate separation of turbulence and mesoscale motions from data. For stable conditions, the horizontal velocity variances near the surface exhibit a spectral gap, here corresponding to a very slow or nonexistent increase of variance with increasing averaging time. This “gap region,” when it occurs, allows separation of mesoscale and turbulence motions; however, the averaging times corresponding to this gap vary substantially with stability. A choice of typical averaging times for defining turbulent perturbations, such as 5 or 10 min, leads to the capture of significant mesoscale motions for very stable conditions and contributes to the disagreement with turbulence similarity theory. For unstable motions, the gap region for the horizontal velocity variances shrinks or becomes poorly defined, because large convective eddies tend to “fill in” the gap between turbulence and mesoscale motions. The formulation developed here allows turbulence and mesoscale motions to overlap into the same intermediate timescales. The mesoscale variances are less predictable, because a wide variety of physical processes contribute to mesoscale motions. Their magnitude and range of timescales vary substantially among sites. The variation of the behavior of turbulence variances among sites is significant but substantially less than that for the mesoscale motions.

Corresponding author address: Larry Mahrt, College of Oceanic and Atmospheric Sciences, Oregon State University, Corvallis, OR 97331.

mahrt@oce.orst.edu

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