17 research outputs found
Energy- and flux-budget (EFB) turbulence closure model for the stably stratified flows. Part I: Steady-state, homogeneous regimes
We propose a new turbulence closure model based on the budget equations for
the key second moments: turbulent kinetic and potential energies: TKE and TPE
(comprising the turbulent total energy: TTE = TKE + TPE) and vertical turbulent
fluxes of momentum and buoyancy (proportional to potential temperature).
Besides the concept of TTE, we take into account the non-gradient correction to
the traditional buoyancy flux formulation. The proposed model grants the
existence of turbulence at any gradient Richardson number, Ri. Instead of its
critical value separating - as usually assumed - the turbulent and the laminar
regimes, it reveals a transition interval, 0.1< Ri <1, which separates two
regimes of essentially different nature but both turbulent: strong turbulence
at Ri<<1; and weak turbulence, capable of transporting momentum but much less
efficient in transporting heat, at Ri>1. Predictions from this model are
consistent with available data from atmospheric and lab experiments, direct
numerical simulation (DNS) and large-eddy simulation (LES).Comment: 40 pages, 6 figures, Boundary-layer Meteorology, resubmitted, revised
versio
Energy- and flux-budget turbulence closure model for stably stratified flows. Part II: the role of internal gravity waves
We advance our prior energy- and flux-budget turbulence closure model
(Zilitinkevich et al., 2007, 2008) for the stably stratified atmospheric flows
and extend it accounting for additional vertical flux of momentum and
additional productions of turbulent kinetic energy, turbulent potential energy
(TPE) and turbulent flux of potential temperature due to large-scale internal
gravity waves (IGW). Main effects of IGW are following: the maximal value of
the flux Richardson number (universal constant 0.2-0.25 in the no-IGW regime)
becomes strongly variable. In the vertically homogeneous stratification, it
increases with increasing wave energy and can even exceed 1. In the
heterogeneous stratification, when IGW propagate towards stronger
stratification, the maximal flux Richardson number decreases with increasing
wave energy, reaches zero and then becomes negative. In other words, the
vertical flux of potential temperature becomes counter-gradient. IGW also
reduce anisotropy of turbulence and increase the share of TPE in the turbulent
total energy. Depending on the direction (downward or upward), IGW either
strengthen or weaken the total vertical flux of momentum. Predictions from the
proposed model are consistent with available data from atmospheric and
laboratory experiments, direct numerical simulations and large-eddy
simulations.Comment: 37 pages, 5 figures, revised versio
A neighborhood statistics model for predicting stream pathogen indicator levels
Because elevated levels of water-borne Escherichia coli in streams are a leading cause of water quality impairments in the U.S., water-quality managers need tools for predicting aqueous E. coli levels. Presently, E. coli levels may be predicted using complex mechanistic models that have a high degree of unchecked uncertainty or simpler statistical models. To assess spatio-temporal patterns of instream E. coli levels, herein we measured E. coli, a pathogen indicator, at 16 sites (at four different times) within the Squaw Creek watershed, Iowa, and subsequently, the Markov Random Field model was exploited to develop a neighborhood statistics model for predicting instream E. coli levels. Two observed covariates, local water temperature (degrees Celsius) and mean cross-sectional depth (meters), were used as inputs to the model. Predictions of E. coli levels in the water column were compared with independent observational data collected from 16 in-stream locations. The results revealed that spatio-temporal averages of predicted and observed E. coli levels were extremely close. Approximately 66 % of individual predicted E. coli concentrations were within a factor of 2 of the observed values. In only one event, the difference between prediction and observation was beyond one order of magnitude. The mean of all predicted values at 16 locations was approximately 1 % higher than the mean of the observed values. The approach presented here will be useful while assessing instream contaminations such as pathogen/pathogen indicator levels at the watershed scale