Excitation of internal waves in a stably-stratified atmosphere with considerable wind-shear

1968 ◽  
Vol 32 (1) ◽  
pp. 145-171 ◽  
Author(s):  
A. A. Townsend
Keyword(s):  
Boundary Layer ◽  
Internal Waves ◽  
Wind Shear ◽  
Wave Packets ◽  
Normal Modes ◽  
Wave Number ◽  
Spectral Energy ◽  
Air Turbulence ◽  
Wave Numbers ◽  
Horizontal Wave

The rate of generation of internal waves by a thin turbulent boundary layer was calculated in a previous paper for a stably-stratified atmosphere with no significant wind-shear outside the boundary layer by considering the excitation of normal modes of wave propagation. By using the concept of wave-packets propagating upwards from the boundary layer, the effects of wind-shear can be included. Conditions for the validity of the approximation are given. In general, the spectral distribution of wave-energy at a particular height takes large values in two bands of horizontal wave-number, one band deriving from wave-packets undergoing internal reflexion near that height and the other from wave-packets of very small local frequency that accumulate there. The ‘reflexion’ wave-numbers are dominant if the wind increases with height and the ‘accumulation’ wave-numbers if the wind initially decreases with height. The spectral energy distributions and intensities of the wave-motion are discussed in more detail for an atmosphere of uniform stability and unidirectional wind-shear. The accumulation process may lead to instability or overturning of the waves, and estimates are made of the probable scale and intensity of the ‘clear-air’ turbulence produced. An interesting point is that the rate of energy loss from the boundary layer by radiation of internal waves turns out to be comparable with the rate of production in the outer nine-tenths of the layer, both for atmospheric boundary layers and for the surface layer of the ocean. It seems likely that radiation limits the layer thickness to some extent.

scholarly journals A new paradigm for intensity modification of tropical cyclones: thermodynamic impact of vertical wind shear on the inflow layer

2010 ◽  
Vol 10 (7) ◽  
pp. 3163-3188 ◽  
Author(s):  
M. Riemer ◽  
M. T. Montgomery ◽  
M. E. Nicholls
Keyword(s):  
Boundary Layer ◽  
Tropical Cyclones ◽  
Wind Shear ◽  
Vertical Wind Shear ◽  
Vertical Shear ◽  
Wave Number ◽  
Carnot Cycle ◽  
Storm Intensity ◽  
Azimuthal Wave Number ◽  
Intensity Evolution

Abstract. An important roadblock to improved intensity forecasts for tropical cyclones (TCs) is our incomplete understanding of the interaction of a TC with the environmental flow. In this paper we re-visit the canonical problem of a TC in vertical wind shear on an f-plane. A suite of numerical experiments is performed with intense TCs in moderate to strong vertical shear. We employ a set of simplified model physics – a simple bulk aerodynamic boundary layer scheme and "warm rain" microphysics – to foster better understanding of the dynamics and thermodynamics that govern the modification of TC intensity. In all experiments the TC is resilient to shear but significant differences in the intensity evolution occur. The ventilation of the TC core with dry environmental air at mid-levels and the dilution of the upper-level warm core are two prevailing hypotheses for the adverse effect of vertical shear on storm intensity. Here we propose an alternative and arguably more effective mechanism how cooler and drier (lower θe) air – "anti-fuel" for the TC power machine – can enter the core region of the TC. Strong and persistent, shear-induced downdrafts flux low θe air into the boundary layer from above, significantly depressing the θe values in the storm's inflow layer. Air with lower θe values enters the eyewall updrafts, considerably reducing eyewall θe values in the azimuthal mean. When viewed from the perspective of an idealised Carnot-cycle heat engine a decrease of storm intensity can thus be expected. Although the Carnot cycle model is – if at all – only valid for stationary and axisymmetric TCs, a close association of the downward transport of low θe into the boundary layer and the intensity evolution offers further evidence in support of our hypothesis. The downdrafts that flush the boundary layer with low θe air are tied to a quasi-stationary, azimuthal wave number 1 convective asymmetry outside of the eyewall. This convective asymmetry and the associated downdraft pattern extends outwards to approximately 150 km. Downdrafts occur on the vortex scale and form when precipitation falls out from sloping updrafts and evaporates in the unsaturated air below. It is argued that, to zero order, the formation of the convective asymmetry is forced by frictional convergence associated with the azimuthal wave number 1 vortex Rossby wave structure of the outer-vortex tilt. This work points to an important connection between the thermodynamic impact in the near-core boundary layer and the asymmetric balanced dynamics governing the TC vortex evolution.

PARAMETER SENSITIVITIES IN TWO-LAYER ISOSPEED MODELS OF SHALLOW WATER CHANNELS

1993 ◽  
Vol 01 (04) ◽  
pp. 469-486 ◽  
Author(s):  
R. J. CEDERBERG ◽  
W. L. SIEGMANN ◽  
M. J. JACOBSON ◽  
W. M. CAREY
Keyword(s):  
Shallow Water ◽  
Low Frequency ◽  
Propagation Model ◽  
Wave Number ◽  
Parameter Uncertainties ◽  
Rates Of Change ◽  
Wave Numbers ◽  
Analytic Expressions ◽  
Horizontal Wave ◽  
Order Of Magnitude

Sensitivities of relative intensity, interference wavelength, and horizontal wave number predictions to input parameters in two-layer isospeed models of shallow-water, low-frequency (less than 100 Hz) acoustic propagation problems are examined. The investigation is directed toward environmental parameter values corresponding generally to those near the site of a recent New Jersey shelf experiment. Typical parameter uncertainties in the environment of the experiment site are used to determine effects of parameter sensitivities on the accuracy of propagation model predictions. Also, analytic expressions for rates of change of wave numbers with respect to parameters are used to compute wave number and interference wavelength changes caused by parameter variations corresponding to the uncertainties. It is found that channel depth variations cause the largest change in intensity, while water sound speed variations have the greatest effect on wave numbers. Variabilities of the parameter sensitivities in regions about the base parameter sets are also examined, with the rates of change generally staying of the same order of magnitude throughout the regions considered. However, wave numbers which are close to cutoff can produce rates of change which vary by as much as three orders of magnitude.

Internal Waves: Measurements of the Two-Dimensional Spectrum in Vertical-Horizontal Wave Number Space

Science ◽  
1975 ◽  
Vol 189 (4203) ◽  
pp. 632-634 ◽  
Author(s):  
T. H. Bell ◽  
J. M. Bergin ◽  
J. P. Dugan ◽  
Z. C. B. Hamilton ◽  
W. D. Morris ◽  
...  
Keyword(s):  
Internal Waves ◽  
Wave Number ◽  
Two Dimensional ◽  
Dimensional Spectrum ◽  
Horizontal Wave

On Howard's upper bound for heat transport by turbulent convection

1969 ◽  
Vol 37 (3) ◽  
pp. 457-477 ◽  
Author(s):  
F. H. Busse
Keyword(s):  
Boundary Layer ◽  
Rayleigh Number ◽  
Heat Transport ◽  
Upper Bound ◽  
Layer Structure ◽  
Limited Range ◽  
Turbulent Convection ◽  
Wave Number ◽  
New Class ◽  
Horizontal Wave

The variational problem introduced by Howard (1963) for the derivation of an upper bound on heat transport by convection in a layer heated from below is analyzed for the case in which the equation of continuity is added as constraint for the velocity field. Howard's conjecture that the maximizing solution of the Euler equations is characterized by a single horizontal wave-number is shown to be true only for a limited range of the Rayleigh number, Ra. A new class of solutions with a multiple boundary-layer structure is derived. The upper bound for the Nusselt number, Nu, given by these solutions is Nu ≤ (Ra/1035)½ in the limit when the Rayleigh number tends to infinity. The comparison of the maximizing solution with experimental observations by Malkus (1954a) and Deardorff & Willis (1967) emphasizes the similarity pointed out by Howard.

Measurements of intermittency of turbulent motion in a boundary layer

1959 ◽  
Vol 6 (2) ◽  
pp. 221-240 ◽  
Author(s):  
V. A. Sandborn
Keyword(s):  
Boundary Layer ◽  
Turbulent Energy ◽  
Turbulent Motion ◽  
Wave Number ◽  
Separation Region ◽  
High Wave Number ◽  
Large Wave ◽  
High Wave ◽  
Wave Numbers ◽  
Longitudinal Distance

Previous observations of turbulent motion at large wave-numbers have revealed the existence of an uneven distribution of turbulent energy. The spotty distribution of the turbulent motion at high wave-numbers is here studied experimentally for the turbulent boundary layer. The high wave-number intermittency is observed at all locations through and along the boundary layer from near transition to near separation.The flatness factors for the longitudinal turbulent component at different wave-numbers are measured to give a quantitative value for the intermittency at particular wave-numbers. Upstream of the separation region the flatness factors are found to depend on wave-number and longitudinal distance, but not on the distance from the wall. It appears that the intermittency develops in the transition region and does not diminish very rapidly with distance downstream. Near separation the flatness factors change radically in distribution near the wall, and are there no longer independent of distance from the wall.

Infrared spectra and substituent effects in 2-(3-, and 4-substituted phenylmethylene)-1,3-cycloheptanediones

1983 ◽  
Vol 48 (2) ◽  
pp. 586-595 ◽  
Author(s):  
Alexander Perjéssy ◽  
Pavol Hrnčiar ◽  
Ján Šraga
Keyword(s):  
Substituent Effects ◽  
Phenyl Group ◽  
Wave Number ◽  
Vibrational Coupling ◽  
Wave Numbers ◽  
Stretching Vibration ◽  
Stretching Vibrations ◽  
The Relationship ◽  
Derivatives Of ◽  
Effect Of Structure

The wave numbers of the fundamental C=O and C=C stretching vibrations, as well as that of the first overtone of C=O stretching vibration of 2-(3-, and 4-substituted phenylmethylene)-1,3-cycloheptanediones and 1,3-cycloheptanedione were measured in tetrachloromethane and chloroform. The spectral data were correlated with σ+ constants of substituents attached to phenyl group and with wave number shifts of the C=O stretching vibration of substituted acetophenones. The slope of the linear dependence ν vs ν+ of the C=C stretching vibration of the ethylenic group was found to be more than two times higher than that of the analogous correlation of the C=O stretching vibration. Positive values of anharmonicity for asymmetric C=O stretching vibration can be considered as an evidence of the vibrational coupling in a cyclic 1,3-dicarbonyl system similarly, as with derivatives of 1,3-indanedione. The relationship between the wave numbers of the symmetric and asymmetric C=O stretching vibrations indicates that the effect of structure upon both vibrations is symmetric. The vibrational coupling in 1,3-cycloheptanediones and the application of Seth-Paul-Van-Duyse equation is discussed in relation to analogous results obtained for other cyclic 1,3-dicarbonyl compounds.

‘Inactive’ motion and pressure fluctuations in turbulent boundary layers

1967 ◽  
Vol 30 (2) ◽  
pp. 241-258 ◽  
Author(s):  
P. Bradshaw
Keyword(s):  
Boundary Layer ◽  
Outer Layer ◽  
Pressure Fluctuations ◽  
Turbulent Energy ◽  
Viscous Sublayer ◽  
Wave Number ◽  
Noticeable Effect ◽  
Frequency Spectra ◽  
Active Motion ◽  
Order Of Magnitude

Townsend's (1961) hypothesis that the turbulent motion in the inner region of a boundary layer consists of (i) an ‘active’ part which produces the shear stress τ and whose statistical properties are universal functions of τ and y, and (ii) an ‘inactive’ and effectively irrotational part determined by the turbulence in the outer layer, is supported in the present paper by measurements of frequency spectra in a strongly retarded boundary layer, in which the ‘inactive’ motion is particularly intense. The only noticeable effect of the inactive motion is an increased dissipation of kinetic energy into heat in the viscous sublayer, supplied by turbulent energy diffusion from the outer layer towards the surface. The required diffusion is of the right order of magnitude to explain the non-universal values of the triple products measured near the surface, which can therefore be reconciled with universality of the ‘active’ motion.Dimensional analysis shows that the contribution of the ‘active’ inner layer motion to the one-dimensional wave-number spectrum of the surface pressure fluctuations varies as τ2w/k1 up to a wave-number inversely proportional to the thickness of the viscous sublayer. This result is strongly supported by the recent measurements of Hodgson (1967), made with a much smaller ratio of microphone diameter to boundary-layer thickness than has been achieved previously. The disagreement of the result with most other measurements is attributed to inadequate transducer resolution in the other experiments.

Global three-dimensional optimal disturbances in the Blasius boundary-layer flow using time-steppers

2010 ◽  
Vol 650 ◽  
pp. 181-214 ◽  
Author(s):  
ANTONIOS MONOKROUSOS ◽  
ESPEN ÅKERVIK ◽  
LUCA BRANDT ◽  
DAN S. HENNINGSON
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Flow ◽  
Wave Packets ◽  
Three Dimensional ◽  
Computational Domain ◽  
Initial Condition ◽  
Oblique Wave ◽  
Layer Flow ◽  
Optimal Disturbances ◽  
Matrix Free

The global linear stability of the flat-plate boundary-layer flow to three-dimensional disturbances is studied by means of an optimization technique. We consider both the optimal initial condition leading to the largest growth at finite times and the optimal time-periodic forcing leading to the largest asymptotic response. Both optimization problems are solved using a Lagrange multiplier technique, where the objective function is the kinetic energy of the flow perturbations and the constraints involve the linearized Navier–Stokes equations. The approach proposed here is particularly suited to examine convectively unstable flows, where single global eigenmodes of the system do not capture the downstream growth of the disturbances. In addition, the use of matrix-free methods enables us to extend the present framework to any geometrical configuration. The optimal initial condition for spanwise wavelengths of the order of the boundary-layer thickness are finite-length streamwise vortices exploiting the lift-up mechanism to create streaks. For long spanwise wavelengths, it is the Orr mechanism combined with the amplification of oblique wave packets that is responsible for the disturbance growth. This mechanism is dominant for the long computational domain and thus for the relatively high Reynolds number considered here. Three-dimensional localized optimal initial conditions are also computed and the corresponding wave packets examined. For short optimization times, the optimal disturbances consist of streaky structures propagating and elongating in the downstream direction without significant spreading in the lateral direction. For long optimization times, we find the optimal disturbances with the largest energy amplification. These are wave packets of Tollmien–Schlichting waves with low streamwise propagation speed and faster spreading in the spanwise direction. The pseudo-spectrum of the system for real frequencies is also computed with matrix-free methods. The spatial structure of the optimal forcing is similar to that of the optimal initial condition, and the largest response to forcing is also associated with the Orr/oblique wave mechanism, however less so than in the case of the optimal initial condition. The lift-up mechanism is most efficient at zero frequency and degrades slowly for increasing frequencies. The response to localized upstream forcing is also discussed.

Assessing the influence of complex terrain on severe convective environments in northeastern Alabama

2021 ◽  
Author(s):  
Branden Katona ◽  
Paul Markowski
Keyword(s):  
Boundary Layer ◽  
Complex Terrain ◽  
Wind Shear ◽  
Vertical Wind Shear ◽  
Vertical Wind ◽  
Spatial Distributions ◽  
Convective Storm ◽  
Self Organizing Maps ◽  
Low Level ◽  
Wind Regimes

AbstractStorms crossing complex terrain can potentially encounter rapidly changing convective environments. However, our understanding of terrain-induced variability in convective stormenvironments remains limited. HRRR data are used to create climatologies of popular convective storm forecasting parameters for different wind regimes. Self-organizing maps (SOMs) are used to generate six different low-level wind regimes, characterized by different wind directions, for which popular instability and vertical wind shear parameters are averaged. The climatologies show that both instability and vertical wind shear are highly variable in regions of complex terrain, and that the spatial distributions of perturbations relative to the terrain are dependent on the low-level wind direction. Idealized simulations are used to investigate the origins of some of the perturbations seen in the SOM climatologies. The idealized simulations replicate many of the features in the SOM climatologies, which facilitates analysis of their dynamical origins. Terrain influences are greatest when winds are approximately perpendicular to the terrain. In such cases, a standing wave can develop in the lee, leading to an increase in low-level wind speed and a reduction in vertical wind shear with the valley lee of the plateau. Additionally, CAPE tends to be decreased and LCL heights are increased in the lee of the terrain where relative humidity within the boundary layer is locally decreased.

scholarly journals The band spectrum of hydrogen

1924 ◽  
Vol 106 (735) ◽  
pp. 69-82 ◽  
Keyword(s):  
Molecular Hydrogen ◽  
Hydrogen Molecule ◽  
Spectral Lines ◽  
Wave Number ◽  
Band Spectrum ◽  
Wave Numbers ◽  
Experimental Side ◽  
The Subject ◽  
The Moment ◽  
Theoretical Side

Many attempts have been made to detect regularities amongst the numerous lines which constitute the secondary or many-lined spectrum of hydrogen. The extreme complexity of the spectrum may be realised from the fact that in the Bakerian Lecture of 1922 Merton and Barratt record some 750 lines in the interval between Hα (wave-number v = 5233.216) and Hβ ( v = 20564.793). Three methods of investigation may be employed in the search for regularities. (1) The lines may be classified according to their physical characteristics, such as intensity or mode of excitation, as in the tables of Merton and Barrat ( loc. cit .). (2) Lines may be grouped together by the discovery of relations between their wave-lengths or wave-numbers, as in the important groups of lines which have been arranged in bands by Fulcher. (3) Lastly, the question may be attacked from the theoretical side, and a model of the hydrogen molecule may be imagined, which will give rise to the emission of certain characteristic spectral lines. Thus Sutherland, working on the foundation of the classical mechanical laws, more than twenty years ago, came to the conclusion that spectral series must arise from kinematical considera­tions, and explained them by considering the nodal sub-divisions of a circle. At the present time we may expect more successful results to follow from the application of the quantum theory, and in this paper an endeavour will be made to examine the secondary spectrum of hydrogen, and more particularly the Fulcher bands, from this standpoint. I may add that my interest in the subject was aroused when attempting to construct a model of the hydrogen molecule, for it seemed that the most likely method of obtaining reliable information from the experimental side as to the moment of inertia of the molecule would be from a study of the spectrum of molecular hydrogen.

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