scholarly journals Interacting Mountain Waves and Boundary Layers

2007 ◽  
Vol 64 (2) ◽  
pp. 594-607 ◽  
Author(s):  
Ronald B. Smith
Keyword(s):  
Boundary Layer ◽  
Relaxation Times ◽  
Wave Theory ◽  
Mountain Wave ◽  
Mountain Waves ◽  
Thickness Change ◽  
Pressure Drag ◽  
Wind Response ◽  
Flow Splitting ◽  
And Shifts

Abstract Linear hydrostatic 3D mountain wave theory is extended to include a thin frictional boundary layer (BL), parameterized using two characteristic relaxation times for wind adjustment. The character of the BL is described using a “compliance coefficient,” defined as the ratio of BL thickness change to imposed pressure. In this formulation the simplest model that captures the two-way interaction between mountain waves and the boundary layer is sought. The slower BL wind speed amplifies the wind response and shifts it upstream so that the wind maxima occur in regions of favorable pressure gradient, not at points of minimum pressure. Variations in BL thickness reduce the mountain wave amplitude. The BL effect is sensitive to the wind profile convexity. The boundary layer improves the linear theory description of windy peaks. Low-level flow splitting is enhanced and wave breaking aloft is reduced. The BL also decreases the amount of upslope orographic precipitation. The wave momentum flux reduction by the BL is greater than the pressure drag reduction, indicating that part of the pressure drag is taken from BL momentum.

scholarly journals Limitations of One-Dimensional Mesoscale PBL Parameterizations in Reproducing Mountain-Wave Flows

2016 ◽  
Vol 73 (7) ◽  
pp. 2603-2614 ◽  
Author(s):  
Domingo Muñoz-Esparza ◽  
Jeremy A. Sauer ◽  
Rodman R. Linn ◽  
Branko Kosović
Keyword(s):  
Boundary Layer ◽  
Atmospheric Boundary Layer ◽  
General Circulation ◽  
Wavelength Shift ◽  
Mountain Wave ◽  
Vertical Wavelength ◽  
Mountain Waves ◽  
Mesoscale Models ◽  
One Dimensional ◽  
Wave Flows

Abstract Mesoscale models are considered to be the state of the art in modeling mountain-wave flows. Herein, the authors investigate the role and accuracy of planetary boundary layer (PBL) parameterizations in handling the interaction between large-scale mountain waves and the atmospheric boundary layer. To that end, recent large-eddy simulation (LES) results of mountain waves over a symmetric two-dimensional bell-shaped hill are used and compared to four commonly used PBL schemes. It is found that one-dimensional PBL parameterizations produce reasonable agreement with the LES results in terms of vertical wavelength, amplitude of velocity, and turbulent kinetic energy distribution in the downhill shooting-flow region. However, the assumption of horizontal homogeneity in PBL parameterizations does not hold in the context of these complex flow configurations. This inappropriate modeling assumption results in a vertical wavelength shift, producing errors of approximately 10 m s−1 at downstream locations because of the presence of a coherent trapped lee wave that does not mix with the atmospheric boundary layer. In contrast, horizontally integrated momentum flux derived from these PBL schemes displays a realistic pattern. Therefore, results from mesoscale models using ensembles of one-dimensional PBL schemes can still potentially be used to parameterize drag effects in general circulation models. Nonetheless, three-dimensional PBL schemes must be developed in order for mesoscale models to accurately represent complex terrain and other types of flows where one-dimensional PBL assumptions are violated.

scholarly journals Diurnal variation of mountain waves

2006 ◽  
Vol 24 (11) ◽  
pp. 2891-2900 ◽  
Author(s):  
R. M. Worthington
Keyword(s):  
Boundary Layer ◽  
Seasonal Variation ◽  
Diurnal Variation ◽  
Case Studies ◽  
Wave Amplitude ◽  
Mountain Wave ◽  
Vhf Radar ◽  
Mountain Waves ◽  
Radar Measurements ◽  
Convective Rolls

Abstract. Mountain waves could be modified as the boundary layer varies between stable and convective. However case studies show mountain waves day and night, and above e.g. convective rolls with precipitation lines over mountains. VHF radar measurements of vertical wind (1990–2006) confirm a seasonal variation of mountain-wave amplitude, yet there is little diurnal variation of amplitude. Mountain-wave azimuth shows possible diurnal variation compared to wind rotation across the boundary layer.

scholarly journals Mountain Waves Produced by a Stratified Boundary Layer Flow. Part I: Hydrostatic Case

2020 ◽  
Vol 77 (5) ◽  
pp. 1683-1697
Author(s):  
François Lott ◽  
Bruno Deremble ◽  
Clément Soufflet
Keyword(s):  
Boundary Layer ◽  
Static Stability ◽  
Wave Drag ◽  
Mountain Waves ◽  
Pressure Drag ◽  
Downslope Winds ◽  
Vertical Scale ◽  
Flow Part ◽  
Layer Flow ◽  
Upper Level

Abstract A hydrostatic theory for mountain waves with a boundary layer of constant eddy viscosity is presented. It predicts that dissipation impacts the dynamics over an inner layer whose depth is controlled by the inner-layer scale δ of viscous critical-level theory. The theory applies when the mountain height is smaller or near δ and is validated with a fully nonlinear model. In this case the pressure drag and the wave Reynolds stress can be predicted by inviscid theory, if one takes for the incident wind its value around the inner-layer scale. In contrast with the inviscid theory and for small mountains the wave drag is compensated by an acceleration of the flow in the inner layer rather than of the solid earth. Still for small mountains and when stability increases, the emitted waves have smaller vertical scale and are more dissipated when traveling through the inner layer: a fraction of the wave drag is deposited around the top of the inner layer before reaching the outer regions. When the mountain height becomes comparable to the inner-layer scale, nonseparated upstream blocking and downslope winds develop. Theory and the model show that (i) the downslope winds penetrate well into the inner layer and (ii) upstream blocking and downslope winds are favored when the static stability is strong and (iii) are not associated with upper-level wave breaking.

scholarly journals Mountain waves can impact wind power generation

2021 ◽  
Vol 6 (1) ◽  
pp. 45-60
Author(s):  
Caroline Draxl ◽  
Rochelle P. Worsnop ◽  
Geng Xia ◽  
Yelena Pichugina ◽  
Duli Chand ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Power Output ◽  
Wind Farm ◽  
Wrf Model ◽  
Wind Farms ◽  
The United States ◽  
Mountain Wave ◽  
Mountain Waves ◽  
Improvement Project ◽  
Wind Speeds

Abstract. Mountains can modify the weather downstream of the terrain. In particular, when stably stratified air ascends a mountain barrier, buoyancy perturbations develop. These perturbations can trigger mountain waves downstream of the mountains that can reach deep into the atmospheric boundary layer where wind turbines operate. Several such cases of mountain waves occurred during the Second Wind Forecast Improvement Project (WFIP2) in the Columbia River basin in the lee of the Cascade Range bounding the states of Washington and Oregon in the Pacific Northwest of the United States. Signals from the mountain waves appear in boundary layer sodar and lidar observations as well as in nacelle wind speeds and power observations from wind plants. Weather Research and Forecasting (WRF) model simulations also produce mountain waves and are compared to satellite, lidar, and sodar observations. Simulated mountain wave wavelengths and wave propagation speeds (group velocities) are analyzed using the fast Fourier transform. We found that not all mountain waves exhibit the same speed and conclude that the speed of propagation, magnitudes of wind speeds, or wavelengths are important parameters for forecasters to recognize the risk for mountain waves and associated large drops or surges in power. When analyzing wind farm power output and nacelle wind speeds, we found that even small oscillations in wind speed caused by mountain waves can induce oscillations between full-rated power of a wind farm and half of the power output, depending on the position of the mountain wave's crests and troughs. For the wind plant analyzed in this paper, mountain-wave-induced fluctuations translate to approximately 11 % of the total wind farm output being influenced by mountain waves. Oscillations in measured wind speeds agree well with WRF simulations in timing and magnitude. We conclude that mountain waves can impact wind turbine and wind farm power output and, therefore, should be considered in complex terrain when designing, building, and forecasting for wind farms.

scholarly journals Theoretical Effect of Temperature on Threshold in the Hodgkin-Huxley Nerve Model

1966 ◽  
Vol 49 (5) ◽  
pp. 989-1005 ◽  
Author(s):  
Richard Fitzhugh
Keyword(s):  
Relaxation Time ◽  
Relaxation Times ◽  
Giant Axon ◽  
Temperature Curve ◽  
Effect Of Temperature ◽  
Threshold Temperature ◽  
Ionic Conductances ◽  
And Shifts ◽  
The Right ◽  
Increasing Temperature

In the squid giant axon, Sjodin and Mullins (1958), using 1 msec duration pulses, found a decrease of threshold with increasing temperature, while Guttman (1962), using 100 msec pulses, found an increase. Both results are qualitatively predicted by the Hodgkin-Huxley model. The threshold vs. temperature curve varies so much with the assumptions made regarding the temperature-dependence of the membrane ionic conductances that quantitative comparison between theory and experiment is not yet possible. For very short pulses, increasing temperature has two effects. (1) At lower temperatures the decrease of relaxation time of Na activation (m) relative to the electrical (RC) relaxation time favors excitation and decreases threshold. (2) For higher temperatures, effect (1) saturates, but the decreasing relaxation times of Na inactivation (h) and K activation (n) factor accommodation and increased threshold. The result is a U-shaped threshold temperature curve. R. Guttman has obtained such U-shaped curves for 50 µsec pulses. Assuming higher ionic conductances decreases the electrical relaxation time and shifts the curve to the right along the temperature axis. Making the conductances increase with temperature flattens the curve. Using very long pulses favors effect (2) over (1) and makes threshold increase monotonically with temperature.

Modeling the Atmospheric Boundary Layer Wind Response to Mesoscale Sea Surface Temperature Perturbations

2014 ◽  
Vol 142 (11) ◽  
pp. 4284-4307 ◽  
Author(s):  
Natalie Perlin ◽  
Simon P. de Szoeke ◽  
Dudley B. Chelton ◽  
Roger M. Samelson ◽  
Eric D. Skyllingstad ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Wind Speed ◽  
Surface Temperature ◽  
Sea Surface Temperature ◽  
Coupling Coefficient ◽  
Eddy Viscosity ◽  
Sea Surface ◽  
Coupling Coefficients ◽  
Wind Response ◽  
Speed Response

Abstract The wind speed response to mesoscale SST variability is investigated over the Agulhas Return Current region of the Southern Ocean using the Weather Research and Forecasting (WRF) Model and the U.S. Navy Coupled Ocean–Atmosphere Mesoscale Prediction System (COAMPS) atmospheric model. The SST-induced wind response is assessed from eight simulations with different subgrid-scale vertical mixing parameterizations, validated using Quick Scatterometer (QuikSCAT) winds and satellite-based sea surface temperature (SST) observations on 0.25° grids. The satellite data produce a coupling coefficient of sU = 0.42 m s−1 °C−1 for wind to mesoscale SST perturbations. The eight model configurations produce coupling coefficients varying from 0.31 to 0.56 m s−1 °C−1. Most closely matching QuikSCAT are a WRF simulation with the Grenier–Bretherton–McCaa (GBM) boundary layer mixing scheme (sU = 0.40 m s−1 °C−1), and a COAMPS simulation with a form of Mellor–Yamada parameterization (sU = 0.38 m s−1 °C−1). Model rankings based on coupling coefficients for wind stress, or for curl and divergence of vector winds and wind stress, are similar to that based on sU. In all simulations, the atmospheric potential temperature response to local SST variations decreases gradually with height throughout the boundary layer (0–1.5 km). In contrast, the wind speed response to local SST perturbations decreases rapidly with height to near zero at 150–300 m. The simulated wind speed coupling coefficient is found to correlate well with the height-averaged turbulent eddy viscosity coefficient. The details of the vertical structure of the eddy viscosity depend on both the absolute magnitude of local SST perturbations, and the orientation of the surface wind to the SST gradient.

scholarly journals Nondissipative and Dissipative Momentum Deposition by Mountain Wave Events in Sheared Environments

2018 ◽  
Vol 75 (8) ◽  
pp. 2721-2740 ◽  
Author(s):  
Christopher G. Kruse ◽  
Ronald B. Smith
Keyword(s):  
Broad Spectrum ◽  
Numerical Models ◽  
Wrf Model ◽  
Vertical Wind Shear ◽  
Mountain Wave ◽  
Subsequent Evolution ◽  
Event Duration ◽  
Mountain Waves ◽  
Vertical Dispersion ◽  
Nonlinear Transient

AbstractMountain waves (MWs) are generated during episodic cross-barrier flow over broad-spectrum terrain. However, most MW drag parameterizations neglect transient, broad-spectrum dynamics. Here, the influences of these dynamics on both nondissipative and dissipative momentum deposition by MW events are quantified in a 2D, horizontally periodic idealized framework. The influences of the MW spectrum, vertical wind shear, and forcing duration are investigated. MW events are studied using three numerical models—the nonlinear, transient WRF Model; a linear, quasi-transient Fourier-ray model; and an optimally tuned Lindzen-type saturation parameterization—allowing quantification of total, nondissipative, and dissipative MW-induced decelerations, respectively. Additionally, a pseudomomentum diagnostic is used to estimate nondissipative decelerations within the WRF solutions. For broad-spectrum MWs, vertical dispersion controls spectrum evolution aloft. Short MWs propagate upward quickly and break first at the highest altitudes. Subsequently, the arrival of additional longer MWs allows breaking at lower altitudes because of their greater contribution to u variance. As a result, minimum breaking levels descend with time and event duration. In zero- and positive-shear environments, this descent is not smooth but proceeds downward in steps as a result of vertically recurring steepening levels. Nondissipative decelerations are nonnegligible and influence an MW’s approach to breaking, but breaking and dissipative decelerations quickly develop and dominate the subsequent evolution. Comparison of the three model solutions suggests that the conventional instant propagation and monochromatic parameterization assumptions lead to too much MW drag at too low an altitude.

scholarly journals Numerical Study of Viscoelastic Micropolar Heat Transfer from a Vertical Cone for Thermal Polymer Coating

2019 ◽  
Vol 8 (1) ◽  
pp. 449-460 ◽  
Author(s):  
K. Madhavi ◽  
V. Ramachandra Prasad ◽  
A. Subba Rao ◽  
O. Anwar Bég ◽  
A. Kadir
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Angular Velocity ◽  
Numerical Study ◽  
Relaxation Times ◽  
Viscoelastic Model ◽  
Deborah Number ◽  
Convection Boundary Layer ◽  
Density Parameter ◽  
R Ratio

Abstract A mathematical model is developed to study laminar, nonlinear, non-isothermal, steady-state free convection boundary layer flow and heat transfer of a micropolar viscoelastic fluid from a vertical isothermal cone. The Eringen model and Jeffery’s viscoelastic model are combined to simulate the non-Newtonian characteristics of polymers, which constitutes a novelty of the present work. The transformed conservation equations for linear momentum, angular momentum and energy are solved numerically under physically viable boundary conditions using a finite difference scheme (Keller Box method). The effects of Deborah number (De), Eringen vortex viscosity parameter (R), ratio of relaxation to retardation times (λ), micro-inertia density parameter (B), Prandtl number (Pr) and dimensionless stream wise coordinate (ξ) on velocity, surface temperature and angular velocity in the boundary layer regime are evaluated. The computations show that with greater ratio of retardation to relaxation times, the linear and angular velocity are enhanced whereas temperature (and also thermal boundary layer thickness) is reduced. Greater values of the Eringen parameter decelerate both the linear velocity and micro-rotation values and enhance temperatures. Increasing Deborah number decelerates the linear flow and Nusselt number whereas it increases temperatures and boosts micro-rotation magnitudes. The study is relevant to non-Newtonian polymeric thermal coating processes.

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