scholarly journals A Unifying Perspective on Transfer Function Solutions to the Unsteady Ekman Problem

Fluids ◽  
2021 ◽  
Vol 6 (2) ◽  
pp. 85
Author(s):  
Jonathan M. Lilly ◽  
Shane Elipot
Keyword(s):  
Transfer Function ◽  
Impulse Response Function ◽  
Lower Boundary ◽  
Finite Depth ◽  
Systematic Investigation ◽  
Numerical Code ◽  
Uniform Motion ◽  
Lower Boundary Condition ◽  
Near Surface ◽  
The Fourier Transform

The unsteady Ekman problem involves finding the response of the near-surface currents to wind stress forcing under linear dynamics. Its solution can be conveniently framed in the frequency domain in terms of a quantity that is known as the transfer function, the Fourier transform of the impulse response function. In this paper, a theoretical investigation of a fairly general transfer function form is undertaken with the goal of paving the way for future observational studies. Building on earlier work, we consider in detail the transfer function arising from a linearly-varying profile of the vertical eddy viscosity, subject to a no-slip lower boundary condition at a finite depth. The horizontal momentum equations, rendered linear by the assumption of horizontally uniform motion, are shown to transform to a modified Bessel’s equation for the transfer function. Two self-similarities, or rescalings that each effectively eliminate one independent variable, are identified, enabling the dependence of the transfer function on its parameters to be more readily assessed. A systematic investigation of asymptotic behaviors of the transfer function is then undertaken, yielding expressions appropriate for eighteen different regimes, and unifying the results from numerous earlier studies. A solution to a numerical overflow problem that arises in the computation of the transfer function is also found. All numerical code associated with this paper is distributed freely for use by the community.

scholarly journals A Unifying Perspective on Transfer Function Solutions to the Unsteady Ekman Problem

2020 ◽  
Author(s):  
Jonathan M. Lilly ◽  
Shane Elipot
Keyword(s):  
Transfer Function ◽  
Impulse Response Function ◽  
Lower Boundary ◽  
Finite Depth ◽  
Systematic Investigation ◽  
Numerical Code ◽  
Lower Boundary Condition ◽  
Near Surface ◽  
Independent Variable ◽  
The Fourier Transform

The unsteady Ekman problem involves finding the response of the near-surface currents to wind stress forcing under linearized dynamics. Its solution can be conveniently framed in the frequency domain in terms of a quantity that is known as the transfer function, the Fourier transform of the impulse response function. In this paper, a theoretical investigation of a fairly general transfer function form is undertaken with the goal of paving the way for future observational studies. Building on earlier work, we consider in detail the transfer function arising from a linearly-varying profile of the vertical eddy viscosity, subject to a no-slip lower boundary condition at a finite depth. The linearized horizontal momentum equations are shown to transform to a modified Bessel’s equation for the transfer function. Two self-similarities, or rescalings that each effectively eliminate one independent variable, are identified, enabling the dependence of the transfer function on its parameters to be more readily assessed. A systematic investigation of asymptotic behaviors of the transfer function is then undertaken, yielding expressions appropriate for eighteen different regimes, and unifying the results from numerous earlier studies. A solution to a numerical overflow problem that arises in the computation of the transfer function is also found. All numerical code associated with this paper is distributed freely for use by the community.

scholarly journals Interannual Variability of Deep-Layer Hydrologic Memory and Mechanisms of Its Influence on Surface Energy Fluxes

2005 ◽  
Vol 18 (23) ◽  
pp. 5024-5045 ◽  
Author(s):  
Geremew G. Amenu ◽  
Praveen Kumar ◽  
Xin-Zhong Liang
Keyword(s):  
Soil Moisture ◽  
Soil Temperature ◽  
Annual Cycle ◽  
Temporal Variability ◽  
Deep Layer ◽  
Lower Boundary ◽  
Surface Fluxes ◽  
Heat Fluxes ◽  
Lower Boundary Condition ◽  
Near Surface

Abstract The characteristics of deep-layer terrestrial memory are explored using observed soil moisture data and simulated soil temperature from the Illinois Climate Network stations. Both soil moisture and soil temperature are characterized by exponential decay in amplitude, linear lag in phase, and increasing persistence with depth. Using spectral analysis, four dominant low-frequency modes are identified in the soil moisture variability. These signals have periods of about 12, 17, 34, and 60 months, which correspond to annual cycle, (4/3) ENSO, quasi-biennial (QB) ENSO, and quasi-quadrennial (QQ) ENSO signals, respectively. For deep layers, the interannual modes are dominant over the annual cycle, and vice versa for the near-surface layer. There are inherently two mechanisms by which deep-layer moisture impacts the surface fluxes. First, its temporal variability sets the lower boundary condition for the transfer of moisture and heat fluxes from the surface. Second, this temporal variability influences the uptake of moisture by plant roots, resulting in the variability of the transpiration and, therefore, the entire energy balance. Initial results suggest that this second mechanism may be more predominant.

scholarly journals LES of Laminar Flow in the PBL: A Potential Problem for Convective Storm Simulations

2016 ◽  
Vol 144 (5) ◽  
pp. 1841-1850 ◽  
Author(s):  
Paul M. Markowski ◽  
George H. Bryan
Keyword(s):  
Lower Boundary ◽  
Vertical Wind Shear ◽  
Surface Friction ◽  
Vertical Wind ◽  
Lower Boundary Condition ◽  
Near Surface ◽  
Severe Storms ◽  
Turbulent Eddies ◽  
Wind Profiles ◽  
Tornadic Storms

In idealized simulations of convective storms, which are almost always run as large-eddy simulations (LES), the planetary boundary layers (PBLs) are typically laminar (i.e., they lack turbulent eddies). When compared with turbulent simulations, theory, or simulations with PBL schemes, the typically laminar LES used in the severe-storms community produce unrealistic near-surface vertical wind profiles containing excessive vertical wind shear when the lower boundary condition is nonfree slip. Such simulations are potentially problematic given the recent interest within the severe storms community in the influence of friction on vorticity generation within tornadic storms. Simulations run as LES that include surface friction but lack well-resolved turbulent eddies thus probably overestimate friction’s effects on storms.

scholarly journals Significance of a Midlatitude SST Frontal Zone in the Formation of a Storm Track and an Eddy-Driven Westerly Jet*

2010 ◽  
Vol 23 (7) ◽  
pp. 1793-1814 ◽  
Author(s):  
Takeaki Sampe ◽  
Hisashi Nakamura ◽  
Atsushi Goto ◽  
Wataru Ohfuchi
Keyword(s):  
General Circulation ◽  
Frontal Zone ◽  
Sensible Heat Flux ◽  
Lower Boundary ◽  
Storm Track ◽  
Lower Boundary Condition ◽  
Near Surface ◽  
Low Level ◽  
Sst Front ◽  
Sst Gradient

Abstract In a set of idealized “aquaplanet” experiments with an atmospheric general circulation model to which zonally uniform sea surface temperature (SST) is prescribed globally as the lower boundary condition, an assessment is made of the potential influence of the frontal SST gradient upon the formation of a storm track and an eddy-driven midlatitude polar front jet (PFJ), and on its robustness against changes in the intensity of a subtropical jet (STJ). In experiments with the frontal midlatitude SST gradient as that observed in the southwestern Indian Ocean, transient eddy activity in each of the winter and summer hemispheres is organized into a deep storm track along the SST front with an enhanced low-level baroclinic growth of eddies. In the winter hemisphere, another storm track forms just below the intense STJ core, but it is confined to the upper troposphere with no significant baroclinic eddy growth underneath. The near-surface westerlies are strongest near the midlatitude SST front as observed, consistent with westerly momentum transport associated with baroclinic eddy growth. The sharp poleward decline in the surface sensible heat flux across the SST frontal zone sustains strong near-surface baroclinicity against the relaxing effect by vigorous poleward eddy heat transport. Elimination of the midlatitude frontal SST gradient yields marked decreases in the activity of eddies and their transport of angular momentum into midlatitudes, in association with equatorward shifts of the PFJ-associated low-level westerlies and a subtropical high pressure belt, especially in the summer hemisphere. These impacts of the midlatitude frontal SST gradient are found to be robust against modest changes in the STJ intensity as observed in its interannual variability, suggesting the potential importance of midlatitude atmosphere–ocean interaction in shaping the tropospheric general circulation.

Observations of Near-Surface Vertical Wind Profiles and Vertical Momentum Fluxes from VORTEX-SE 2017: Comparisons to Monin–Obukhov Similarity Theory

2019 ◽  
Vol 147 (10) ◽  
pp. 3811-3824 ◽  
Author(s):  
Paul M. Markowski ◽  
Nathan T. Lis ◽  
David D. Turner ◽  
Temple R. Lee ◽  
Michael S. Buban
Keyword(s):  
Boundary Condition ◽  
Similarity Theory ◽  
Lower Boundary ◽  
Vertical Wind Shear ◽  
Vertical Wind ◽  
Lower Boundary Condition ◽  
Near Surface ◽  
Convective Storms ◽  
Momentum Fluxes ◽  
Wind Profiles

Abstract Observations of near-surface vertical wind profiles and vertical momentum fluxes obtained from a Doppler lidar and instrumented towers deployed during VORTEX-SE in the spring of 2017 are analyzed. In particular, departures from the predictions of Monin–Obukhov similarity theory (MOST) are documented on thunderstorm days, both in the warm air masses ahead of storms and within the cool outflow of storms, where MOST assumptions (e.g., horizontal homogeneity and a steady state) are least credible. In these regions, it is found that the nondimensional vertical wind shear near the surface commonly exceeds predictions by MOST. The departures from MOST have implications for the specification of the lower boundary condition in numerical simulations of convective storms. Documenting departures from MOST is a necessary first-step toward improving the lower boundary condition and parameterization of near-surface turbulence (“wall models”) in storm simulations.

scholarly journals An Idealized Numerical Simulation Investigation of the Effects of Surface Drag on the Development of Near-Surface Vertical Vorticity in Supercell Thunderstorms

2016 ◽  
Vol 73 (11) ◽  
pp. 4349-4385 ◽  
Author(s):  
Paul M. Markowski
Keyword(s):  
Lower Boundary ◽  
Cold Pool ◽  
Surface Drag ◽  
Lower Boundary Condition ◽  
Near Surface ◽  
Vertical Vorticity ◽  
Supercell Storms ◽  
Scale Turbulence ◽  
Barotropic Vorticity ◽  
Pool Formation

Abstract Idealized simulations are used to investigate the contributions of frictionally generated horizontal vorticity to the development of near-surface vertical vorticity in supercell storms. Of interest is the relative importance of barotropic vorticity (vorticity present in the prestorm environment), baroclinic vorticity (vorticity that is principally generated by horizontal buoyancy gradients), and viscous vorticity (vorticity that originates from the subgrid-scale turbulence parameterization, wherein the effects of surface drag reside), all of which can be advected, tilted, and stretched. Equations for the three partial vorticities are integrated in parallel with the model. The partial vorticity calculations are complemented by analyses of circulation following material circuits, which are often able to be carried out further in time because they are less susceptible to explosive error growth. Near-surface mesocyclones that develop prior to cold-pool formation (this only happens when the environmental vorticity is crosswise near the surface) are dominated by only barotropic vertical vorticity when the lower boundary is free slip, but both barotropic and viscous vertical vorticity when surface drag is included. Baroclinic vertical vorticity grows large once a cold pool is established, regardless of the lower boundary condition and, in fact, dominates at the time the vortices are most intense in all but one simulation (a simulation dominated early by a barotropic mode of vortex genesis that may not be relevant to real convective storms).

scholarly journals The Effect of Soil and Vegetation Parameters in the ECMWF Land Surface Scheme

2004 ◽  
Vol 5 (6) ◽  
pp. 1131-1146 ◽  
Author(s):  
H. Richter ◽  
A. W. Western ◽  
F. H. S. Chiew
Keyword(s):  
Soil Moisture ◽  
Land Surface ◽  
Weather Prediction ◽  
Lower Boundary ◽  
Soil Parameters ◽  
Model Parameters ◽  
Lower Boundary Condition ◽  
Land Surface Scheme ◽  
Vegetation Parameters ◽  
Surface Scheme

Abstract Numerical Weather Prediction (NWP) and climate models are sensitive to evapotranspiration at the land surface. This sensitivity requires the prediction of realistic surface moisture and heat fluxes by land surface models that provide the lower boundary condition for the atmospheric models. This paper compares simulations of a stand-alone version of the European Centre for Medium-Range Weather Forecasts (ECMWF) land surface scheme, or the Viterbo and Beljaars scheme (VB95), with various soil and vegetation parameter sets against soil moisture observations across the Murrumbidgee River catchment in southeast Australia. The study is, in part, motivated by the adoption of VB95 as the operational land surface scheme by the Australian Bureau of Meteorology in 1999. VB95 can model the temporal fluctuations in soil moisture, and therefore the moisture fluxes, fairly realistically. The monthly model latent heat flux is also fairly insensitive to soil or vegetation parameters. The VB95 soil moisture is sensitive to the soil and, to a lesser degree, the vegetation parameters. The model exhibits a significant (generally wet) bias in the absolute soil moisture that varies spatially. The use of the best Australia-wide available soils and vegetation information did not improve VB95 simulations consistently, compared with the original model parameters. Comparisons of model and observed soil moistures revealed that more realistic soil parameters are needed to reduce the model soil moisture bias. Given currently available continent-wide soils parameters, any initialization of soil moisture with observed values would likely result in significant flux errors. The soil moisture bias could be largely eliminated by using soil parameters that were derived directly from the actual soil moisture observations. Such parameters, however, are only available at very few point locations.

Modified electromyography-assisted optimization approach for predicting lumbar spine loading while walking with backpack loads

2020 ◽  
Vol 234 (5) ◽  
pp. 527-533
Author(s):  
Simon SW Li ◽  
Daniel HK Chow
Keyword(s):  
Boundary Condition ◽  
Lumbar Spine ◽  
Maximal Voluntary Contraction ◽  
Lower Boundary ◽  
Voluntary Contraction ◽  
Optimization Approach ◽  
Compression Force ◽  
Lower Boundary Condition ◽  
Force Profile ◽  
Mean Square Difference

This study modified an electromyography-assisted optimization approach for predicting lumbar spine loading while walking with backpack loads. The modified-electromyography-assisted optimization approach eliminated the electromyography measurement at maximal voluntary contraction and adopted a linear electromyography–force relationship. Moreover, an optimal lower boundary condition for muscle gain was introduced to constrain the trunk muscle co-activation. Anthropometric information of 10 healthy young men as well as their kinematic, kinetic, and electromyography data obtained while walking with backpack loads were used as inputs in this study. A computational algorithm was used to find and analyse the sensitivity of the optimal lower boundary condition for achieving minimum deviation of the modified-electromyography-assisted optimization approach from the electromyography-assisted optimization approach for predicting lumbosacral joint compression force. Results validated that the modified-electromyography-assisted optimization approach (at optimal lower boundary condition of 0.92) predicted on average, a non-significant deviation in peak lumbosacral joint compression force of −18 N, a standard error of 9 N, and a root mean square difference in force profile of 73.8 N. The modified-electromyography-assisted optimization approach simplified the experimental process by eliminating the electromyography measurement at maximal voluntary contraction and provided comparable estimations for lumbosacral joint compression force that is also applicable to patients or individuals having difficulty in performing the maximal voluntary contraction activity.

scholarly journals Turbulent Flow over Steep Steady and Unsteady Waves under Strong Wind Forcing

2018 ◽  
Vol 48 (1) ◽  
pp. 3-27 ◽  
Author(s):  
Peter P. Sullivan ◽  
Michael L. Banner ◽  
Russel P. Morison ◽  
William L. Peirson
Keyword(s):  
Turbulent Flow ◽  
Lower Boundary ◽  
Breaking Waves ◽  
Wave Crest ◽  
Strong Wind ◽  
Wave Group ◽  
Wave Surface ◽  
Form Drag ◽  
Lower Boundary Condition ◽  
Wave Slope

AbstractTurbulent flow over strongly forced steep steady and unsteady waves is simulated using large-eddy simulation (LES) with time t and space x varying wave height h(x, t) imposed as a lower boundary condition. With steady waves, h(x, t) is based on measurements of incipient and active breaking waves collected in a wind-wave flume, while a numerical wave code is used to generate an unsteady evolving wave packet (group). Highly intermittent airflow separation is found in the simulations, and the results suggest separation near a wave crest occurs prior to the onset of wave breaking. The form (pressure) drag is most sensitive to the wave slope, and the form drag can contribute as much as 74% to the total stress. Wind and scalar profiles from the LES display log-linear variations above the wave surface; the LES wind profiles are in good agreement with the measurements. The momentum roughness increases as the water surface changes from wind ripples to incipient breaking to active breaking. However, the scalar roughness decreases as the wave surface becomes rougher. This highlights major differences in momentum and scalar transport over a rough wavy surface. For a rapidly evolving, strongly forced wave group, the form drag is highly correlated with the wave slope, and intermittent separation is found early in the packet evolution when the local wave slope −∂h/∂x(x, t) ≥ 0.22. The packet root-mean-square wave slope is 0.084, but the form drag fraction is 2.4 times larger than a comparably forced steady wave. Thus, a passing wave group can induce unsteadiness in the wind stress.

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