Search Results

You are looking at 1 - 10 of 63 items for

  • Author or Editor: L. Mahrt x
  • All content x
Clear All Modify Search
L. Mahrt

Abstract

Lagrangian equations for momentum and buoyancy are developed for idealized turbulent fluid elements. The resulting formulation of transport can he viewed as a generalization of mixing length and parcel theories of mixing for application to gridded Eulerian models. This formulation of transport recognizes the mean gradients on the scale of the main transporting eddies and avoids problems with existing methods due to parameterization of fluxes in terms of local gradients between adjacent grid levels.

The modeled fluid elements develop relative horizontal motions due to mean vertical shear. Shear-produced horizontal kinetic energy is converted to vertical kinetic energy through modeled pressure adjustments. The fluid element is decelerated through nonlinear pressure drag and small scale diffusion with the ambient fluid while vertical motions are constrained by stable stratification.

The linearized version of the equations reproduces classical shear instability governed by a critical Richardson number. With nonlinear pressure drag and small scale diffusion, the element motion adjusts to limit cycle conditions which transport heat and momentum. The limit cycle motion varies from a buoyancy oscillation for large Richardson number to a bimodal limit cycle for small Richardson number. Due to momentum transport by pressure fluctuations, the eddy Prandtl number for stable stratification is generally greater than 1 and increases with stability.

Full access
L. Mahrt

Abstract

No abstract available.

Full access
L. Mahrt

Abstract

Early afternoon environmental conditions preceding hail-producing thunderstorms are statistically compared with conditions for classes of less severe moist convection using only data from individual radiosonde releases collected during the National Hail Research Experiment in northeast Colorado. The ensuing analyses emphasize the thermodynamic characteristics of the mixed layer and immediate overlying free flow.

On days with hail-producing thunderstorms, the mixed layer tends to be particularly thin and moist. Energy required to initiate moist convection is found to be somewhat greater than normal, while energy required to further develop moist convection is substantially less than normal. Parcel energies are found to be quite sensitive to the level of parcel origin in the mixed layer.

Full access
L. Mahrt

Abstract

The structure of turbulence in a strongly stratified nocturnal boundary layer is studied using fast-response aircraft data collected under clear sky conditions with weak ambient flow. The principal source of turbulence is shear generation near the top of the surface inversion layer. This shear is induced by the development of surface flow which appears to be cold air drainage. The downward heat flux in the turbulent shear zone acts to warm the upper part of the inversion layer and is opposed by clear-air radiative cooling and advection of cold air.

The horizontal structure of the turbulence is studied using conditional means and other properties of the joint frequency distribution and analysis of the eigenvectors of the correlation matrix. Often, the turbulence exhibits statistical properties consistent with shear instability on horizontal scales near 300–400 m. Although modified by stratification, the main motions are turbulent-like with sharp horizontal boundaries and lead to net downward heat transport. The overturning also appears to lead to some buoyancy instability on somewhat smaller scales. The smaller scale turbulence is more three-dimensional but some influence of stratification is evident on horizontal scales even smaller than 100 m.

Full access
L. Mahrt

Abstract

Radiosonde data from the National Hail Research Experiment and the Wangara experiment are examined to study vertical gradients of moisture in heated boundary layers which are well-mixed in virtual potential temperature. The frequent occurrence of a significant decrease of moisture with height in the mixed layer over the high plains region of the United States seems to be related in part to rapid growth of the mixed layer into very dry air aloft and/or height variations of horizontal advection of moisture. However, the exact cause cannot be unambiguously determined from the data.

Full access
L. Mahrt

Abstract

The approximate equations for shallow motions are derived mainly by following the approach of Spiegel and Veronis and the subsequent development of Dutton and Fichtl. Other derivations are also briefly noted. While each derivation assumes shallow flow, the conditions on the time scale and auxiliary assumptions vary between derivations. In the present study, the shallow motion approximations are found to be valid for a wider range of conditions than included in earlier derivations.

The more restrictive Boussinesq or “shallow convection” approximations form a subclass motions. Existing derivations of the full Boussinesq approximations do not apply to near-neutral conditions even though they are often applied to such conditions. The conditions required for the validity of the Boussinesq approximations are reformulated into criteria that are easier to evaluate.

Finally; the use of the shallow motion approximations in concert with Reynolds averaging is examined in some detail. Additional necessary conditions resulting from Reynolds averaging appear to be violated only in rather special situations, at least for atmospheric flows.

Full access
L. Mahrt

Abstract

Various errors and influences leading to differences between tower- and aircraft-measured fluxes are surveyed. This survey is motivated by reports in the literature that aircraft fluxes are sometimes smaller than tower-measured fluxes. Both tower and aircraft flux errors are larger with surface heterogeneity due to several independent effects. Surface heterogeneity may cause tower flux errors to increase with decreasing wind speed.

Techniques to assess flux sampling errors are reviewed. Such error estimates suffer various degrees of inapplicability in real geophysical time series due to nonstationarity of tower time series (or inhomogeneity of aircraft data). A new measure for nonstationarity is developed that eliminates assumptions on the form of the nonstationarity inherent in previous methods. When this nonstationarity measure becomes large, the surface energy imbalance increases sharply. Finally, strategies for obtaining adequate flux sampling using repeated aircraft passes and grid patterns are outlined.

Full access
L. Mahrt

Abstract

Dimensionless structure functions such as kurtosis of the velocity gradients are computed from aircraft data for a variety of atmospheric situations in order to characterize the intermittency of the turbulence. It is necessary to distinguish between small scale intermittency of the velocity gradients organized by the individual main eddies and global intermittency associated with patchiness of turbulence on scales larger than the main eddies. Failure to make such a distinction can lead to ambiguity and inability to recognize contamination of statistics by sampling problems.

The sharp edges of the main eddies contribute to the small scale intermittency as measured by the kurtosis of the velocity gradients and other intermittency statistics. However, for some of the strongly stratified cases, global intermittency increases the kurtosis by a factor of 2 or 3 in which case the statistics reflect the global spatial variability of the turbulence (patchiness) more than the local characteristics of the turbulence itself. As a result, the kurtosis increases with record length as more of the larger scale spatial variability is incorporated. in such case record partitioning is employed to construct more useful estimates of the small scale intermittency.

The variation of the structure kurtosis with separation distance is normally found to obey the Kolmogorov similarity theory which has been modified to include the influence of small scale intermittency. However, the modified theory does not describe decaying turbulence nor turbulence with strong global intermittency.

The dimensionless structure function for artificial turbulence and mixtures of distributions are studied analytically. The usual dimensional structure function responds to the scale of the main building blocks (simulated eddies) while the structure kurtosis and other dimensionless moments respond to the spatial scale of the edges of the building blocks where gradients are particularly large and contribute to the tails of the frequency distribution. The dimensionless structure function of the artificial turbulence is also augmented by global intermittency posed in terms of mixtures of frequency distributions. This analytical analysis appears to explain the observed enhancement of the dimensionless structure kurtosis by the sharp edges of the main eddies and by the global intermittency of those records with strong thermal stratification.

Full access
L. Mahrt

Abstract

Statistical measures are developed to study the influence of mean shear on the asymmetry of eddy updrafts as observed from low-level aircraft flights in HAPEX, FIFE, and SESAME. This asymmetry involves formation of microfronts between updrafts with slow horizontal motion and downdrafts with faster horizontal motion. The variance of the Haar-wavelet transform (step-function basis) is found to be a superior indicator of the dominant scales of such eddies compared to the structure function. For those analyses where scale dependence is not of interest, the simpler structure function is applied. The coherent structures at the dominant scale are examined by computing eigenvectors of the lagged correlation matrix based on conditionally sampled events.

With strong mean shear and weak surface heating, the horizontal motion field of the main coherent eddies is more in phase with the vertical motion which corresponds to efficient vertical transport of horizontal momentum. With stronger heating and weaker mean shear, the horizontal convergence beginning at the microfront extends inward across the updraft. Consequently, the decorrelation between fluctuations of horizontal and vertical velocity components in the heated boundary layer results from a systematic phase difference rather than randomness of the horizontal velocity fluctuations as proposed in previous studies. This phase difference leads to decreasing Prandtl number with increasing convective instability. This conceptual model of the main eddies is used to interpret the variation of other statistics of fluctuating gradients between different types of atmospheric turbulence.

Full access
L. Mahrt

Abstract

This study analyzes measurements from a network of sonic anemometers over gentle topography to investigate the possibility of nocturnal lee-generated turbulence. Although the valley side slopes are less than 6° and extend only about 12 m above the floor of the valley, the turbulence can be enhanced in the lee of one of the slopes. Significant lee turbulence develops downwind from an abrupt slope transition between a miniplateau and the modest valley side slope. Lee-generated turbulence is not observed on the opposite slope, where the slope magnitude gradually decreases with height. With intermediate 1-m wind speeds of roughly 2–4 m s−1, the cold pool is advected up the downwind slope. This downwind displacement of the cold pool and warming by lee-generated turbulence, when it occurs, leads to significant horizontal asymmetry of the temperature across the valley. For stronger winds, the cold pool is eliminated by mixing. For weak winds, a more traditional cold pool forms centered on the valley floor with limited or no lee-generated turbulence. While the impact of the gentle topography is modest compared to more dramatic terrain, less organized gentle topography covers a large fraction of Earth’s surface. However, with gentle topography, various relationships show substantial scatter, and the generalization of results from an individual network is probably not possible.

Full access