472 research outputs found
First passage time statistics of Brownian motion with purely time dependent drift and diffusion
Systems where resource availability approaches a critical threshold are
common to many engineering and scientific applications and often necessitate
the estimation of first passage time statistics of a Brownian motion (Bm)
driven by time-dependent drift and diffusion coefficients. Modeling such
systems requires solving the associated Fokker-Planck equation subject to an
absorbing barrier. Transitional probabilities are derived via the method of
images, whose applicability to time dependent problems is shown to be limited
to state-independent drift and diffusion coefficients that only depend on time
and are proportional to each other. First passage time statistics, such as the
survival probabilities and first passage time densities are obtained
analytically. The analysis includes the study of different functional forms of
the time dependent drift and diffusion, including power-law time dependence and
different periodic drivers. As a case study of these theoretical results, a
stochastic model for water availability from surface runoff in snowmelt
dominated regions is presented, where both temperature effects and
snow-precipitation input are incorporated
A note on aerosol sized particle deposition onto dense and tall canopies situated on gentle cosine hills
Micrometeorological measurements of aerosol sized dry particle deposition velocity ( V d ) onto forested canopies have significantly advanced over the past two decades and now include bothâairborne and stationary platforms. However, the interpretation of theseâ V d measurements still relies on stationary and planar homogeneous flow assumptions only appropriate to flat-terrain conditions. Simplified model calculations were used to examine how variations in hill height ( H ) introduce biases inâ V d when assumptions appropriate to flat terrain are applied to periodic and gentle 2-D cosine topography covered with tall and dense forested canopies. It was shown that increasingâ H reduced the variability inâ V d for all aerosol sized particle diameters ( d p ) inside the canopy when the hill slope ( H / L ) remained constant (=0.1), whereâ L is the cosine hill half-length. At the landscape scale, as may be monitored from airborne platforms, assumptions appropriate to flat-terrain appear accurate with increasingâ H for a constant and gentleâH/ L (= 0.1). Inside the canopy, variability inâ V d tends to be larger than above the canopy for allâ H values andâ d p classes. DOI: 10.1111/j.1600-0889.2011.00528.
Delay-induced rebounds in CO_{2} emissions and critical time-scales to meet global warming targets
While climate science debates are focused on the attainment of peak anthropogenic CO2 emissions and policy tools to reduce peak temperatures, the humanâenergyâclimate system can hold âreboundâ surprises beyond this peak. Following the second industrial revolution, global per capita CO_{2} emissions (c_{c}) experienced a punctuated growth of about 100% every 60âyears, mainly attributable to technological development and its global spread. A model of the humanâenergyâclimate system capable of reproducing past punctuated dynamics shows that rebounds in global CO_{2} emissions emerge due to delays intrinsic to the diffusion of innovations. Such intrinsic delays in the adoption and spread of lowâcarbon emitting technologies, together with projected population growth, upset the warming target set by the Paris Agreement. To avoid rebounds and their negative climate effects, model calculations show that the diffusion of climateâfriendly technologies must occur with lags oneâorder of magnitude shorter (i.e., âŒ6âyears) than the characteristic timescale of past punctuated growth in c_{c}. Radically new strategies to globally implement the technological advances at unprecedented rates are needed if the current emission goals are to be achieved
Relation between the spectral properties of wall turbulence and the scaling of the Darcy-Weisbach friction factor
Empirical formulas describing the Darcy-Weisbach friction factor remain indispensable for applications in sciences and engineering dealing with turbulent flows. Despite their practical significance, these formulas have remained without theoretical interpretation for many decades. To close this knowledge gap, much research has been devoted to the development of the so-called "spectral link"introduced in the early 2000s. Such a theory is entirely based on elegant phenomenological arguments that make no contact with equations describing turbulent wall flows. The spectral link spawned alternative approaches, now labeled "cospectral budget"(or CSB) models, that describe how turbulent eddies contribute to wall stresses. The CSB overcomes some of the shortcomings of the phenomenological approach and is here employed to provide a thorough clarification of the link between spectral properties of velocity fluctuations and the scaling of friction factors in turbulent pipe flows in the hydraulically smooth and fully rough regimes
Inverse Cascade Evidenced by Information Entropy of Passive Scalars in Submerged Canopy Flows
Turbulent mixing of scalars within canopies is investigated using a flume experiment with canopy-like rods of height h mounted to the channel bed. The data comprised a time sequence of high-resolution images of a dye recorded in a plane parallel to the bed at z/h= 0.2. Image processing shows that von KĂĄrmĂĄn wakes shed by canopy drag and downward turbulent transport from upper canopy layers impose distinct scaling regimes on the scalar spectrum. Measures from information theory are then used to explore the dominant directionality of the interaction between small and large scales underlying these two spectral regimes, showing that the arrival of sweeps from aloft establishes an inertial-range spectrum with forward âinformationâ cascade. In contrast, wake growth with downstream distance leads to persistent upscale transfer (inverse cascade) of scalar variance, which hints at their nondiffusive character and the significance of the stem diameter as an active length scale in canopy turbulence
Closure Schemes for Stably Stratified Atmospheric Flows without Turbulence Cutoff
Two recently proposed turbulence closure schemes are compared against the conventional Mellor-Yamada (MY) model for stably stratified atmospheric flows. The Energy and Flux-Budget (EFB) approach solves the budgets of turbulent momentum and heat fluxes and turbulent kinetic and potential energies. The Cospectral Budget (CSB) approach is formulated in wavenumber space and integrated across all turbulent scales to obtain flow variables in physical space. Unlike the MY model, which is subject to a "critical gradient Richardson number," both EFB and CSB models allow turbulence to exist at any gradient Richardson number R-t and predict a saturation of flux Richardson number (R-f -> R-fm) at sufficiently large R-i. The CSB approach further predicts the value of Rim and reveals a unique expression linking the Rotta and von Karman constants. Hence, all constants in the CSB model are nontunable and stability independent. All models agree that the dimensionless sensible heat flux decays with increasing R-i. However, the decay rate and subsequent cutoff in the MY model appear abrupt. The MY model further exhibits an abrupt cutoff in the turbulent stress normalized by vertical velocity variance, while the CSB and EFB models display increasing trends. The EFB model produces a rapid increase in the ratio of turbulent potential energy and vertical velocity variance as Rim is approached, suggesting a strong self-preservation mechanism. Vertical anisotropy in the turbulent kinetic energy is parameterized in different ways in MY and EFB, but this consideration is not required in CSB. Differences between EFB and CSB model predictions originate from how the vertical anisotropy is specified in the EFB model.Peer reviewe
Estimation of bare soil evaporation using skin temperature measurements
A simple model based on the Monin-Obukhov surface layer similarity theory of heat and momentum transport can be used to predict the latent heat flux for a variety of atmospheric and soil moisture conditions. Experiments were carried out on the Campbell Tract at the University of California, Davis, from 14 September to 23 November 1990. The latent heat flux was measured precisely with a large weighing lysimeter and the surface temperature by a thermal IR transducer. The evaporation predictions and lysimeter measurements overall were in good agreement (R2 = 0.86), including cases of dry surface conditions. Even low daily evaporation of the order of 1 mm could be modeled with the procedure studied
The spatial structure of turbulence at production wave-numbers using orthonormal wavelet
Orthonormal wavelet expansions are applied to surface-layer measurements of vertical wind speed under various atmospheric stability conditions. The orthonormal wavelet transform allows for the unfolding of these measurements into space and scale simultaneously to reveal the large intermittent behavior in space for the turbulent production wavenumbers. Both Fourier and wavelet power spectra indicated the existence of a -1 power law for the vertical velocity measurements at the production wavenumbers. The -1 power law in the turbulent production range was derived from surface-layer similarity theory. A dimensionless skewness structure function is applied to the wavelet decomposed vertical velocity field to trace the destruction of the shear- or buoyancy-induced anisotropy under various stability conditions. The structure skewness function revealed shear- or buoyancy-induced eddy asymmetry dependence on stability at each scale within the -1 power-law wavenumber range with more isotropy during propagation from smaller to larger wavenumbers. The asymmetry of these events at the turbulent production wavenumbers appeared very localized in space, as well as in scale, and could be described with a simple eddy-overturning model. It is demonstrated that the wavelet transform is suitable for such analysis
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