Clear sky shortwave solar radiation varies in response to altitude and elevation, surface gradient (slope) and orientation (aspect), as well as position relative to neighbouring surfaces While the

Modelling topographic variation in solar radiation in a GIS environment

We present a review of the radiative-convective models that have been used in studies pertaining to the earth's climate. After familiarizing the reader with the theoretical background, modeling methodology, and techniques for solving the radiative transfer equation the review focuses on the published model studies concerning global climate and global climate change. Radiative-convective models compute the globally and seasonally averaged surface and atmospheric temperatures. The computed temperatures are in good agreement with the observed temperatures. The models include the important climatic feedback mechanism between surface temperature and H2O amount in the atmosphere. The principal weakness of the current models is their inability to simulate the feedback mechanism between surface temperature and cloud cover. It is shown that the value of the critical lapse rate adopted in radiative-convective models for convective adjustment is significantly larger than the observed globally averaged tropospheric lapse rate. The review also summarizes radiative-convective model results for the sensitivity of surface temperature to perturbations in (1) the concentrations of the major and minor optically active trace constituents, (2) aerosols, and (3) cloud amount. A simple analytical model is presented to demonstrate how the surface temperature in a radiative-convective model responds to perturbations.

Climate modeling through radiative‐convective models

Turbulent flow over idealized water waves with varying wave slope ak and wave age c/u. is investigated using direct numerical simulations at a bulk Reynolds number Re = 8000. In the present idealization, the shape of the water wave and the associated orbital velocities are prescribed and do not evolve dynamically under the action of the wind. The results show that the imposed waves significantly influence the mean flow, vertical momentum fluxes, velocity variances, pressure, and form stress (drag). Compared to a stationary wave, slow (fast) moving waves increase (decrease) the form stress. At small c/u., waves act similarly to increasing surface roughness z o resulting in mean vertical velocity profiles with shorter buffer and longer logarithmic regions. With increasing wave age, z o decreases so that the wavy lower surface is nearly as smooth as a flat lower boundary. Vertical profiles of turbulence statistics show that the wave effects depend on wave age and wave slope but are confined to a region kz < 1 (where k is the wavenumber of the surface undulation and z is the vertical coordinate). The turbulent momentum flux can be altered by as much as 40% by the waves. A region of closed streamlines (or cat's-eye pattern) centred about the critical layer height was found to be dynamically important at low to moderate values of c/u. The wave-correlated velocity and flux fields are strongly dependent on the variation of the critical layer height and to a lesser extent the surface orbital velocities. Above the critical layer z cr the positions of the maximum and minimum wave-correlated vertical velocity w w occur upwind and downwind of the peak in z cr , like a stationary surface. The wave-correlated flux u w w w is positive (negative) above (below) the critical layer height.

Simulation of turbulent flow over idealized water waves

Conditions leading to the onset of air-flow separation over a mobile air-water interface are discussed. It is argued that, in a frame of reference in which the interfacial boundary assumes a steady shape, the occurrence of separation requires a stagnation point on the interface. In the case of air blowing over water waves, this corresponds to the onset of wave breaking. These arguments are strongly supported by flow visualization and pressure measurements carried out in a laboratory wind-wave flume. Furthermore, the pressure measurements show a greatly enhanced interfacial shear stress for a breaking wave compared with that over an unbroken wave of the same wavelength. The implications of these findings for wind-wave generation are discussed.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112076002905

On the separation of air flow over water waves

We investigate the changes to a fully developed turbulent boundary layer caused by the presence of a two-dimensional moving wave of wavelength L = 2π/k and amplitude a. Attention is focused on small slopes, ak, and small wave speeds, c, so that the linear perturbations are calculated as asymptotic sequences in the limit (u* + c)/UB(L) → 0 (u* is the unperturbed friction velocity and UB(L) is the approach-flow mean velocity at height L). The perturbations can then be described by an extension of the four-layer asymptotic structure developed by Hunt, Leibovich & Richards (1988) to calculate the changes to a boundary layer passing over a low hill.When (u* + c)/UB(L) is small, the matched height, zm (the height where UB equals c), lies within an inner surface layer, where the perturbation Reynolds shear stress varies only slowly. Solutions across the matched height are then constructed by considering an equation for the shear stress. The importance of the shear-stress perturbation at the matched height implies that the inviscid theory of Miles (1957) is inappropriate in this parameter range. The perturbations above the inner surface layer are not directly influenced by the matched height and the region of reversed flow below zm: they are similar to the perturbations due to a static undulation, but the ‘effective roughness length’ that determines the shape of the unperturbed velocity profile is modified to zm = z0 exp (kc/u*).The solutions for the perturbations to the boundary layer are used to calculate the growth rate of waves, which is determined at leading order by the asymmetric pressure perturbation induced by the thickening of the perturbed boundary layer on the leeside of the wave crest. At first order in (u* + c)/UB(L), however, there are three new effects which, numerically, contribute significantly to the growth rate, namely: the asymmetries in both the normal and shear Reynolds stresses associated with the leeside thickening of the boundary layer, and asymmetric perturbations induced by the varying surface velocity associated with the fluid motion in the wave; further asymmetries induced by the variation in the surface roughness along the wave may also be important.

Turbulent shear flow over slowly moving waves

Turbulent boundary layer interaction with wavy wall in wind tunnel, discussing wall pressure drag and surface waves interaction

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112070000617

The turbulent boundary layer over a wall with progressive surface waves

Two cavity-type radiometers have been developed, based on first principles, having the capability of measuring an irradiance with an indicated error 0.3%. The prerequisites for this accuracy are a measured aperture area, a measurement of electric voltages, and an effective absorptance of its blackbody cavity from 0.998 to 0.999 throughout the uv, visible, and ir spectral ranges. The first cavity-type radiometer is designed to operate only in a vacuum of <10−5 Torr and to measure intensities from 10 mW cm−1 to 300 mW cm−2. By using this radiometer in an evacuated cold chamber, an experimental determination of the Stefan-Boltzmann constant is obtained at a value that differs from the theoretical value by 0.3%, which indicates the degree of confidence that can be expected in measurements made with blackbody cavity radiometers. The second type of radiometer is designed to operate in either air or vacuum. Although its aperture opening is windowless, it is unaffected by wind. The range of intensities accurately measurable is from about 10 mW cm−2 to 800 mW cm−2; the indicated accuracy is also 0.3%.

Two blackbody radiometers of high accuracy.

Total solar irradiance was observed simultaneously outside the earth's atmosphere by three types of absolute cavity radiometers and duplicates of four of the Nimbus 6 Earth Radiation Budget (ERB) solar channels in a June 1976 sounding rocket experiment. The preliminary average solar constant result from the cavity radiometers is 1367 Wm (-2) with an uncertainty of less than + or - 0.5% in S.I. units. The duplicate ERB channel 3 on the rocket gave a value of 1389 Wm (-2) which agreed exactly with the Nimbus 6 ERB channel 3 measurement made simultaneously with the rocket flight.

/pdf/rocket-calibration-of-the-nimbus-6-solar-constant-s6df1lxtqz.pdf

Rocket calibration of the Nimbus 6 solar constant measurements.

Latest rocket measurements of the solar constant

The utility of stability theory in the prediction of transition at supersonic and hypersonic speeds has come to be widely accepted during the past few decades. The first compressible stability theory results to be obtained by direct numerical computation were produced during the late 1950s, and the work by Mack [1] and by others continues to evolve. Two principal results obtained early in the development were that for supersonic flow those waves (first mode) which are the counterpart of Tollmien-Schlichting waves in incompressible flow are more unstable when oblique than when two-dimensional, and that above a certain Mach number, there arises an acoustic mode (second mode) which can be highly amplified especially for a 2-D orientation. Supersonic and hypersonic stability experiments were reported by 1960 but were judged invalid for test of theory because the disturbance wave-fronts were of undetermined obliquity. The wave-front waxpage problem was subsequently overcome by use of an improved disturbance-generator and by operating the tunnel such as to avoid eddy Mach-wave radiation from the wall boundary layers [2].

J. M. Kendall

Papers

The turbulent boundary layer over a wall with progressive surface waves

Two blackbody radiometers of high accuracy.

Rocket calibration of the Nimbus 6 solar constant measurements.

Latest rocket measurements of the solar constant

Some comparisons of linear stability theory with experiment at supersonic and hypersonic speed