Katabatic flow along a differentially cooled sloping surface

2007 ◽  
Vol 571 ◽  
pp. 149-175 ◽  
Author(s):  
ALAN SHAPIRO ◽  
EVGENI FEDOROVICH
Keyword(s):  
Boundary Layer ◽  
Steady State ◽  
Vegetation Type ◽  
Lower Boundary ◽  
Terminal State ◽  
Asymptotic Solutions ◽  
Normal Velocity ◽  
Katabatic Flow ◽  
Prandtl Model ◽  
Surface Buoyancy

Buoyancy inhomogeneities on sloping surfaces arise in numerous situations, for example, from variations in snow/ice cover, cloud cover, topographic shading, soil moisture, vegetation type, and land use. In this paper, the classical Prandtl model for one-dimensional flow of a viscous stably stratified fluid along a uniformly cooled sloping planar surface is extended to include the simplest type of surface inhomogeneity – a surface buoyancy that varies linearly down the slope. The inhomogeneity gives rise to acceleration, vertical motions associated with low-level convergence, and horizontal and vertical advection of perturbation buoyancy. Such processes are not accounted for in the classical Prandtl model. A similarity hypothesis appropriate for this inhomogeneous flow removes the along-slope dependence from the problem, and, in the steady state, reduces the Boussinesq equations of motion and thermodynamic energy to a set of coupled nonlinear ordinary differential equations. Asymptotic solutions for the velocity and buoyancy variables in the steady state, valid for large values of the slope-normal coordinate, are obtained for a Prandtl number of unity for pure katabatic flow with no ambient wind or externally imposed pressure gradient. The undetermined parameters in these solutions are adjusted to conform to lower boundary conditions of no-slip, impermeability and specified buoyancy. These solutions yield formulae for the boundary-layer thickness and slope-normal velocity component at the top of the boundary layer, and provide an upper bound of the along-slope surface-buoyancy gradient beyond which steady-state solutions do not exist. Although strictly valid for flow above the boundary layer, the steady asymptotic solutions are found to be in very good agreement with the terminal state of the numerical solution of an initial-value problem (suddenly applied surface buoyancy) throughout the flow domain. The numerical results also show that solution non-existence is associated with self-excitation of growing low-frequency gravity waves.

An airfoil theory of bifurcating laminar separation from thin obstacles

1990 ◽  
Vol 216 ◽  
pp. 255-284 ◽  
Author(s):  
C. J. Lee ◽  
H. K. Cheng
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Steady State ◽  
Steady State Solution ◽  
Equation System ◽  
Branch Points ◽  
Laminar Separation ◽  
Kutta Condition ◽  
Numerical Studies ◽  
Steady State Solutions

Global interaction of the boundary layer separating from an obstacle with resulting open/closed wakes is studied for a thin airfoil in a steady flow. Replacing the Kutta condition of the classical theory is the breakaway criterion of the laminar triple-deck interaction (Sychev 1972; Smith 1977), which, together with the assumption of a uniform wake/eddy pressure, leads to a nonlinear equation system for the breakaway location and wake shape. The solutions depend on a Reynolds numberReand an airfoil thickness ratio or incidence τ and, in the domain$Re^{\frac{1}{16}}\tau = O(1)$considered, the separation locations are found to be far removed from the classical Brillouin–Villat point for the breakaway from a smooth shape. Bifurcations of the steady-state solution are found among examples of symmetrical and asymmetrical flows, allowing open and closed wakes, as well as symmetry breaking in an otherwise symmetrical flow. Accordingly, the influence of thickness and incidence, as well as Reynolds number is critical in the vicinity of branch points and cut-off points where steady-state solutions can/must change branches/types. The study suggests a correspondence of this bifurcation feature with the lift hysteresis and other aerodynamic anomalies observed from wind-tunnel and numerical studies in subcritical and high-subcriticalReflows.

Measurements in a Turbulent Boundary Layer Over a d-Type Surface Roughness

1975 ◽  
Vol 42 (3) ◽  
pp. 591-597 ◽  
Author(s):  
D. H. Wood ◽  
R. A. Antonia
Keyword(s):  
Boundary Layer ◽  
Surface Roughness ◽  
Turbulent Boundary Layer ◽  
Turbulent Energy ◽  
Shear Stresses ◽  
Normal Velocity ◽  
Mean Velocity ◽  
Outer Flow ◽  
Intensity Measurements ◽  
Normal And Shear Stresses

Mean velocity and turbulence intensity measurements have been made in a fully developed turbulent boundary layer over a d-type surface roughness. This roughness is characterised by regular two-dimensional elements of square cross section placed one element width apart, with the cavity flow between elements being essentially isolated from the outer flow. The measurements show that this boundary layer closely satisfies the requirement of exact self-preservation. Distribution across the layer of Reynolds normal and shear stresses are closely similar to those found over a smooth surface except for the region immediately above the grooves. This similarity extends to distributions of third and fourth-order moments of longitudinal and normal velocity fluctuations and also to the distribution of turbulent energy dissipation. The present results are compared with those obtained for a k-type or sand grained roughness.

Hydrodynamics and behaviour of Simuliidae larvae (Diptera)

1986 ◽  
Vol 64 (6) ◽  
pp. 1295-1309 ◽  
Author(s):  
M. M. Chance ◽  
D. A. Craig
Keyword(s):  
Boundary Layer ◽  
Lower Boundary ◽  
The Body ◽  
The Other ◽  
Avoidance Reaction ◽  
Larval Body ◽  
Video Recordings ◽  
Von Karman ◽  
Von Kármán ◽  
Lower Boundary Layer

Detailed water flow around larvae of Simulium vittatum Zett. (sibling IS-7) was investigated using flow tanks, aluminium flakes, pigment, still photography, cinematography, and video recordings. Angle of deflection of a larva from the vertical has a hyperbolic relationship to water velocity. Velocity profiles around larvae show that the body is in the boundary layer. Frontal area of the body decreases as velocity increases. Disturbed larvae exhibit "avoidance reaction" and pull the body into the lower boundary layer. Longitudinal twisting and yawing of the larval body places one labral fan closer to the substrate, the other near the top of the boundary layer. Models and live larvae were used to demonstrate the basic hydrodynamic phenomenon of downstream paired vortices. Body shape and feeding stance result in one of the vortices remaining in the lower boundary layer. The other rises up the downstream side of the body, passes through the lower fan, then forms a von Karman trail of detaching vortices. This vortex entrains particulate matter from the substrate, which larvae then filter. Discharge of water into this upper vortex remains constant at various velocities and only water between the substrate and top of the posterior abdomen is incorporated into it. The upper fan filters water only from the top of the boundary layer. Formation of vortices probably influences larval microdistribution and filter feeding. Larvae positioned side by side across the flow mutually influence flow between them, thus enhancing feeding. Larvae downstream of one another may use information from the von Karman trail of vortices to position themselves advantageously.

Contribution of vertical advection to supergradient wind in tropical cyclone boundary layer: A numerical study

2021 ◽  
Author(s):  
Rong Fei ◽  
Yuqing Wang ◽  
Yuanlong Li
Keyword(s):  
Boundary Layer ◽  
Steady State ◽  
Wind Speed ◽  
Tropical Cyclone ◽  
Vertical Structure ◽  
Numerical Study ◽  
Substantial Reduction ◽  
Vertical Advection ◽  
Physics Model ◽  
Tropical Cyclone Boundary Layer

AbstractThe existence of supergradient wind in the interior of the boundary layer is a distinct feature of a tropical cyclone (TC). Although the vertical advection is shown to enhance supergradient wind in TC boundary layer (TCBL), how and to what extent the strength and structure of supergradient wind are modulated by vertical advection are not well understood. In this study, both a TCBL model and an axisymmetric full-physics model are used to quantify the contribution of vertical advection process to the strength and vertical structure of supergradient wind in TCBL. Results from the TCBL model show that the removal of vertical advection of radial wind reduces both the strength and height of supergradient wind by slightly more than 50%. The removal of vertical advection of agradient wind reduces the height of the supergradient wind core by ~30% but increases the strength of supergradient wind by ~10%. Results from the full-physics model show that the removal of vertical advection of radial wind or agradient wind reduces both the strength and height of supergradient wind but the removal of that of radial wind produces a more substantial reduction (52%) than the removal of that of agradient wind (35%). However, both the intensification rate and final intensity of the simulated TCs in terms of maximum 10-m wind speed show little differences in experiments with and without the vertical advection of radial or agradient wind, suggesting that supergradient wind contributes little to either the intensification rate or the steady-state intensity of the simulated TC.

scholarly journals Sound propagation in a lined nozzle with shear and bias flows

2018 ◽  
Vol 18 (1) ◽  
pp. 3-48
Author(s):  
LMBC Campos ◽  
C Legendre
Keyword(s):  
Boundary Layer ◽  
Mach Number ◽  
Boundary Layers ◽  
Lower Boundary ◽  
Cross Flow ◽  
Core Flow ◽  
The Core ◽  
Wide Range ◽  
Bias Flow ◽  
Number Formula

In this study, the propagation of waves in a two-dimensional parallel-sided nozzle is considered allowing for the combination of: (a) distinct impedances of the upper and lower walls; (b) upper and lower boundary layers with different thicknesses with linear shear velocity profiles matched to a uniform core flow; and (c) a uniform cross-flow as a bias flow out of one and into the other porous acoustic liner. The model involves an “acoustic triple deck” consisting of third-order non-sinusoidal non-plane acoustic-shear waves in the upper and lower boundary layers coupled to convected plane sinusoidal acoustic waves in the uniform core flow. The acoustic modes are determined from a dispersion relation corresponding to the vanishing of an 8 × 8 matrix determinant, and the waveforms are combinations of two acoustic and two sets of three acoustic-shear waves. The eigenvalues are calculated and the waveforms are plotted for a wide range of values of the four parameters of the problem, namely: (i/ii) the core and bias flow Mach numbers; (iii) the impedances at the two walls; and (iv) the thicknesses of the two boundary layers relative to each other and the core flow. It is shown that all three main physical phenomena considered in this model can have a significant effect on the wave field: (c) a bias or cross-flow even with small Mach number [Formula: see text] relative to the mean flow Mach number [Formula: see text] can modify the waveforms; (b) the possibly dissimilar impedances of the lined walls can absorb (or amplify) waves more or less depending on the reactance and inductance; (a) the exchange of the wave energy with the shear flow is also important, since for the same stream velocity, a thin boundary layer has higher vorticity, and lower vorticity corresponds to a thicker boundary layer. The combination of all these three effects (a–c) leads to a large set of different waveforms in the duct that are plotted for a wide range of the parameters (i–iv) of the problem.

scholarly journals Evaluation of simulated aerosol properties with the aerosol-climate model ECHAM5-HAM using observations from the IMPACT field campaign

2010 ◽  
Vol 10 (16) ◽  
pp. 7709-7722 ◽  
Author(s):  
G.-J. Roelofs ◽  
H. ten Brink ◽  
A. Kiendler-Scharr ◽  
G. de Leeuw ◽  
A. Mensah ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Climate Model ◽  
Lower Boundary ◽  
Synoptic Scale ◽  
Concentration Gradients ◽  
Cloud Properties ◽  
Dry Conditions ◽  
Strong Exchange ◽  
The Impact ◽  
Lower Boundary Layer

Abstract. In May 2008, the measurement campaign IMPACT for observation of atmospheric aerosol and cloud properties was conducted in Cabauw, The Netherlands. With a nudged version of the coupled aerosol-climate model ECHAM5-HAM we simulate the size distribution and chemical composition of the aerosol and the associated aerosol optical thickness (AOT) for the campaign period. Synoptic scale meteorology is represented realistically through nudging of the vorticity, the divergence, the temperature and the surface pressure. Simulated concentrations of aerosol sulfate and organics at the surface are generally within a factor of two from observed values. The monthly averaged AOT from the model is 0.33, about 20% larger than observed. For selected periods of the month with relatively dry and moist conditions discrepancies are approximately −30% and +15%, respectively. Discrepancies during the dry period are partly caused by inaccurate representation of boundary layer (BL) dynamics by the model affecting the simulated AOT. The model simulates too strong exchange between the BL and the free troposphere, resulting in weaker concentration gradients at the BL top than observed for aerosol and humidity, while upward mixing from the surface layers into the BL appears to be underestimated. The results indicate that beside aerosol sulfate and organics also aerosol ammonium and nitrate significantly contribute to aerosol water uptake. The simulated day-to-day variability of AOT follows synoptic scale advection of humidity rather than particle concentration. Even for relatively dry conditions AOT appears to be strongly influenced by the diurnal cycle of RH in the lower boundary layer, further enhanced by uptake and release of nitric acid and ammonia by aerosol water.

Trailing-edge stall

1970 ◽  
Vol 42 (3) ◽  
pp. 561-584 ◽  
Author(s):  
S. N. Brown ◽  
K. Stewartson
Keyword(s):  
Boundary Layer ◽  
Complete Solution ◽  
Leading Edge ◽  
Asymptotic Solutions ◽  
Angle Of Incidence ◽  
Trailing Edge ◽  
Boundary Layer Equations ◽  
Order Of Magnitude ◽  
Stall Angle ◽  
Fundamental Equations

A study is made of the laminar flow in the neighbourhood of the trailing edge of an aerofoil at incidence. The aerofoil is replaced by a flat plate on the assumption that leading-edge stall has not taken place. It is shown that the critical order of magnitude of the angle of incidence α* for the occurrence of separation on one side of the plate is$\alpha^{*} = O(R^{\frac{1}{16}})$, whereRis a representative Reynolds number, for incompressible flow, and α* =O(R−¼) for supersonic flow. The structure of the flow is determined by the incompressible boundary-layer equations but with unconventional boundary conditions. The complete solution of these fundamental equations requires a numerical investigation of considerable complexity which has not been undertaken. The only solutions available are asymptotic solutions valid at distances from the trailing edge that are large in terms of the scaled variable of orderR−⅜, and a linearized solution for the boundary layer over the plate which gives the antisymmetric properties of the aerofoil at incidence. The value of α* for which separation occurs is the trailing-edge stall angle and an estimate is obtained from the asymptotic solutions. The linearized solution yields an estimate for the viscous correction to the circulation determined by the Kutta condition.

Sign in / Sign up

Export Citation Format

Share Document