A theoretical model analysis of the sudden narrow temperature-layer formation observed in the ALOHA-93 Campaign

2002 ◽  
Vol 80 (12) ◽  
pp. 1543-1558 ◽  
Author(s):  
H Hur ◽  
T Y Huang ◽  
Z Zhao ◽  
P Karunanayaka ◽  
T F Tuan
Keyword(s):  
Energy Dissipation ◽  
Gravity Wave ◽  
Temperature Rise ◽  
Critical Level ◽  
Inversion Layer ◽  
Phase Speed ◽  
Temperature Inversion ◽  
Critical Layer ◽  
Mean Flow ◽  
Wind Profiles

The behavior of temperature and wind profiles observed on 21 October 1993 in the ALOHA-93 Campaign is theoretically and numerically analyzed. A sudden temperature rise took place in a very narrow vertical region (3–4 km) at about 87 km. Simultaneously observed radar wind profiles and mesospheric airglow wave structures that show a horizontal phase speed of 35 m/s and a period of about half an hour strongly suggest that a critical level may occur in the proximity of that altitude and that the energy dissipation due to the interaction of the gravity wave with the critical level causes the temperature rise. The numerical model used is a solution to the gravity wave – mean-flow interaction in the critical layer, including a simple cooling mechanism and a wave-energy dissipation simulated by the "optical model" technique. The solutions for the temperature variations so obtained show good agreement with the observed temperature profiles at different times, providing a quantitative explanation for the temperature inversion layer as a phenomenon of gravity wave – critical layer interaction. PACS Nos.: 91.10V, 94.10D

Laboratory Observations of Gravity Wave, Critical Layer Flows Using Single and Double Wave Forcing

1994 ◽  
Vol 47 (6S) ◽  
pp. S113-S117
Author(s):  
Donald P. Delisi ◽  
Timothy J. Dunkerton
Keyword(s):  
Gravity Wave ◽  
Wave Breaking ◽  
Critical Level ◽  
Phase Speed ◽  
Vertical Shear ◽  
Critical Layer ◽  
Small Scale ◽  
Mean Flow ◽  
Wave Forcing ◽  
Internal Mixing

Laboratory measurements of gravity wave, critical layer flows are presented. The measurements are obtained in a salt-stratified annular tank, with a vertical shear profile. Internal gravity waves are generated at the floor of the tank and propagate vertically upward into the fluid. At a depth where the phase speed of the wave equals the mean flow speed, defined as a critical level, the waves break down, under the right forcing conditions, generating small scale turbulence. Two cases are presented. In the first case, the wave forcing is a single, monochromatic wave. In this case, the early wave breaking is characterized as Kelvin-Helmholtz breaking at depths below the critical level. Later wave breaking is characterized by weak overturning in the upper part of the tank and regular, internal mixing regions in the lower part of the tank. In the second case, the wave forcing is two monochromatic waves, each propagating with a different phase speed. In this case, the early wave breaking is again Kelvin-Helmholtz in nature, but later wave breaking is characterized by sustained overturning in the upper part of the tank with internal mixing regions in the lower part of the tank. Mean velocity profiles are obtained both before and during the experiments.

Critical-level behaviour and wave amplification of a gravity wave incident upon a shear layer

1975 ◽  
Vol 72 (4) ◽  
pp. 661-671 ◽  
Author(s):  
I. A. Eltayeb ◽  
J. F. McKenzie
Keyword(s):  
Shear Layer ◽  
Gravity Wave ◽  
Critical Level ◽  
Phase Speed ◽  
Flow Speed ◽  
Wave Incident ◽  
Mean Flow ◽  
Wave Amplification ◽  
The Mean ◽  
Streaming Motion

The properties of reflexion, refraction and absorption of a gravity wave incident upon a shear layer are investigated. It is shown that one must expect these properties to be very different depending upon the parameters (such as the Richardson number Ri, the wavelength normalized by the length scale of the shear and the ratio of the flow speed to the phase speed of the wave) characterizing the interaction of a gravity wave with a shear layer. In particular, it is shown that for all Richardson numbers there is a discontinuity in the net wave-action flux across the critical level, i.e. at a height where the flow speed matches the horizontal phase speed of the wave. When Ri > ¼, this is accompanied by absorption of part of the energy of the incident wave into the mean flow. In addition it is shown that the phenomenon of wave amplification (over-reflexion) can arise provided that the ultimate shear flow speed exceeds the horizontal phase speed of the wave and Ri is less than a certain critical value Ric ≃ 0·1129, in which case the reflected wave extracts energy from the streaming motion. It is also pointed out that wave amplification can lead to instability if the boundary conditions are altered in such a way that the system can behave like an ‘amplifier’.

scholarly journals Long-term Lidar Observations of the Gravity Wave Activity near the Mesopause at Arecibo

2018 ◽  
Author(s):  
Xianchang Yue ◽  
Jonathan S. Friedman ◽  
Qihou Zhou ◽  
Xiongbin Wu ◽  
Jens Lautenbach
Keyword(s):  
Potential Energy ◽  
Gravity Wave ◽  
Inversion Layer ◽  
Lower Thermosphere ◽  
Temperature Inversion ◽  
Temperature Structure ◽  
Mean Temperature ◽  
The Mean ◽  
Highly Correlated ◽  
Lidar Observations

Abstract. 11-years long K Doppler lidar observations of temperature profiles in the mesosphere and lower thermosphere (MLT) between 85 and 100 km, conducted at the Arecibo Observatory, Puerto Rico (18.35° N, 66.75° W), are used to estimate seasonal variations of the mean temperature, the squared Brunt-Väisälä frequency, and the gravity wave potential energy in a composite year. The following unique features are obtained: (1) The mean temperature structure shows similar characteristics as a prior report based on a smaller dataset: (2) The profiles of the squared Brunt-Väisälä frequency usually reach the maxima at or just below the temperature inversion layer when that layer is present. The first complete range-resolved climatology of potential energy of temperature fluctuations in the tropical MLT exhibits an altitude dependent combination of annual oscillation (AO) and semiannual oscillation (SAO). Between 88 to 96 km altitude, the amplitudes of AO and SAO are comparable, and their phases are almost the same and quite close to day of year (DOY) 100. Below 88 km, the SAO amplitude is significantly larger than AO and the AO phase shifts to DOY 200 and after. At 97 to 98 km altitude, the amplitudes of AO and SAO reach their minima, and both phases shift significantly. Above that, the AO amplitude becomes greater. The annual mean potential energy profile reaches the minimum at 91 to 92 km altitude. The altitude-dependent SAO of the potential energy is found to be highly correlated with the satellite observed mean zonal winds reported in the literature.

The Reflection of a Stationary Gravity Wave by a Viscous Boundary Layer

2007 ◽  
Vol 64 (9) ◽  
pp. 3363-3371 ◽  
Author(s):  
François Lott
Keyword(s):  
Boundary Layer ◽  
Gravity Wave ◽  
Richardson Number ◽  
Critical Level ◽  
Inviscid Limit ◽  
Mean Flow ◽  
Viscous Boundary Layer ◽  
Lee Waves ◽  
The Mean ◽  
Viscous Boundary

Abstract The backward reflection of a stationary gravity wave (GW) propagating toward the ground is examined in the linear viscous case and for large Reynolds numbers (Re). In this case, the stationary GW presents a critical level at the ground because the mean wind is null there. When the mean flow Richardson number at the surface (J) is below 0.25, the GW reflection by the viscous boundary layer is total in the inviscid limit Re → ∞. The GW is a little absorbed when Re is finite, and the reflection decreases when both the dissipation and J increase. When J > 0.25, the GW is absorbed for all values of the Reynolds number, with a general tendency for the GW reflection to decrease when J increases. As a large ground reflection favors the downstream development of a trapped lee wave, the fact that it decreases when J increases explains why the more unstable boundary layers favor the onset of mountain lee waves. It is also shown that the GW reflection when J > 0.25 is substantially larger than that predicted by the conventional inviscid critical level theory and larger than that predicted when the dissipations are represented by Rayleigh friction and Newtonian cooling. The fact that the GW reflection depends strongly on the Richardson number indicates that there is some correspondence between the dynamics of trapped lee waves and the dynamics of Kelvin–Helmholtz instabilities. Accordingly, and in one classical example, it is shown that some among the neutral modes for Kelvin–Helmholtz instabilities that exist in an unbounded flow when J < 0.25 can also be stationary trapped-wave solutions when there is a ground and in the inviscid limit Re → ∞. When Re is finite, these solutions are affected by the dissipation in the boundary layer and decay in the downstream direction. Interestingly, their decay rate increases when both the dissipation and J increase, as does the GW absorption by the viscous boundary layer.

scholarly journals Sudden narrow temperature-inversion-layer formation in ALOHA-93 as a critical-layer-interaction phenomenon

1998 ◽  
Vol 103 (D6) ◽  
pp. 6323-6332 ◽  
Author(s):  
T. Y. Huang ◽  
H. Hur ◽  
T. F. Tuan ◽  
X. Li ◽  
E. M. Dewan ◽  
...  
Keyword(s):  
Inversion Layer ◽  
Temperature Inversion ◽  
Critical Layer ◽  
Layer Formation ◽  
Layer Interaction ◽  
Interaction Phenomenon

scholarly journals Mean flow induced by the viscous critical layer in a stratified fluid

1988 ◽  
Vol 29 (3) ◽  
pp. 352-373 ◽  
Author(s):  
Noel Smyth
Keyword(s):  
Reynolds Number ◽  
Steady State ◽  
Critical Level ◽  
Reynolds Numbers ◽  
Stratified Fluid ◽  
Critical Layer ◽  
Mean Flow ◽  
Incoming Wave ◽  
Outer Flow

AbstractThe evolution of the critical layer in a viscous, stratified fluid is examined in the limit of large Richardson and Reynolds numbers. A source far above the critical layer and of amplitude ɛ is turned on at t = 0 and the behaviour of both the steady state and transients is found. Viscosity dominates over nonlinearity in the critical layer for , Re being an appropriately defined Reynolds number. Wave amplitudes are found to grow as the critical layer is approached, then decay rapidly due to the action of viscosity in a critical layer of O((Re)−1/3) around the critical level. The critical layer acts as a source of vorticity, which diffuses into the outer flow, resulting in an induced mean flow of . This induced mean flow causes the critical level to move towards the incoming wave.

scholarly journals Physics of tidal dissipation in early-type stars and white dwarfs: hydrodynamical simulations of internal gravity wave breaking in stellar envelopes

2020 ◽  
Vol 495 (1) ◽  
pp. 1239-1251 ◽  
Author(s):  
Yubo Su ◽  
Daniel Lecoanet ◽  
Dong Lai
Keyword(s):  
Wave Breaking ◽  
White Dwarfs ◽  
Phase Speed ◽  
Critical Layer ◽  
Linear Wave ◽  
Early Type ◽  
Mean Flow ◽  
Layer Width ◽  
Early Type Stars ◽  
Hydrodynamical Simulations

ABSTRACT In binaries composed of either early-type stars or white dwarfs, the dominant tidal process involves the excitation of internal gravity waves (IGWs), which propagate towards the stellar surface, and their dissipation via non-linear wave breaking. We perform 2D hydrodynamical simulations of this wave breaking process in a stratified, isothermal atmosphere. We find that, after an initial transient phase, the dissipation of the IGWs naturally generates a sharp critical layer, separating the lower stationary region (with no mean flow) and the upper ‘synchronized’ region (with the mean flow velocity equal to the horizontal wave phase speed). While the critical layer is steepened by absorption of these waves, it is simultaneously broadened by Kelvin–Helmholtz instabilities such that, in steady state, the critical layer width is determined by the Richardson criterion. We study the absorption and reflection of incident waves off the critical layer and provide analytical formulae describing its long-term evolution. The result of this study is important for characterizing the evolution of tidally heated white dwarfs and other binary stars.

The critical layer in linear-shear boundary layers over acoustic linings

2012 ◽  
Vol 710 ◽  
pp. 545-568 ◽  
Author(s):  
E. J. Brambley ◽  
M. Darau ◽  
S. W. Rienstra
Keyword(s):  
Boundary Layers ◽  
Phase Speed ◽  
Sound Field ◽  
Critical Layer ◽  
Uniform Density ◽  
Mean Flow ◽  
Linearized Euler Equations ◽  
Sheared Flow ◽  
Linear Shear ◽  
Critical Layers

AbstractAcoustics within mean flows are governed by the linearized Euler equations, which possess a singularity wherever the local mean flow velocity is equal to the phase speed of the disturbance. Such locations are termed critical layers, and are usually ignored when estimating the sound field, with their contribution assumed to be negligible. This paper studies fully both numerically and analytically a simple yet typical sheared ducted flow in order to investigate the influence of the critical layer, and shows that the neglect of critical layers is sometimes, but certainly not always, justified. The model is that of a linear-then-constant velocity profile with uniform density in a cylindrical duct, allowing exact Green’s function solutions in terms of Bessel functions and Frobenius expansions. For sources outside the sheared flow, the contribution of the critical layer is found to decay algebraically along the duct as $O(1/ {x}^{4} )$, where $x$ is the distance downstream of the source. For sources within the sheared flow, the contribution from the critical layer is found to consist of a non-modal disturbance of constant amplitude and a disturbance decaying algebraically as $O(1/ {x}^{3} )$. For thin boundary layers, these disturbances trigger the inherent convective instability of the flow. Extra care is required for high frequencies as the critical layer can be neglected only in combination with a particular downstream pole. The advantages of Frobenius expansions over direct numerical calculation are also demonstrated, especially with regard to spurious modes around the critical layer.

Quantifying Residual, Eddy, and Mean Flow Effects on Mixing in an Idealized Circumpolar Current

2017 ◽  
Vol 47 (8) ◽  
pp. 1897-1920 ◽  
Author(s):  
Phillip J. Wolfram ◽  
Todd D. Ringler
Keyword(s):  
High Performance ◽  
Phase Speed ◽  
Critical Layer ◽  
Linear Wave ◽  
Mean Flow ◽  
Wave Regime ◽  
Linear Waves ◽  
Parameter Ratio ◽  
Low Pass ◽  
Circumpolar Current

AbstractMeridional diffusivity is assessed for a baroclinically unstable jet in a high-latitude idealized circumpolar current (ICC) using the Model for Prediction across Scales Ocean (MPAS-O) and the online Lagrangian in Situ Global High-Performance Particle Tracking (LIGHT) diagnostic via space–time dispersion of particle clusters over 120 monthly realizations of O(106) particles on 11 potential density surfaces. Diffusivity in the jet reaches values of O(6000) m2 s−1 and is largest near the critical layer supporting mixing suppression and critical layer theory. Values in the vicinity of the shelf break are suppressed to O(100) m2 s−1 because of the presence of westward slope front currents. Diffusivity attenuates less rapidly with depth in the jet than both eddy velocity and kinetic energy scalings would suggest. Removal of the mean flow via high-pass filtering shifts the nonlinear parameter (ratio of the eddy velocity to eddy phase speed) into the linear wave regime by increasing the eddy phase speed via the depth-mean flow. Low-pass filtering, in contrast, quantifies the effect of mean shear. Diffusivity is decomposed into mean flow shear, linear waves, and the residual nonhomogeneous turbulence components, where turbulence dominates and eddy-produced filamentation strained by background mean shear enhances mixing, accounting for ≥80% of the total diffusivity relative to mean shear [O(100) m2 s−1], linear waves [O(1000) m2 s−1], and undecomposed full diffusivity [O(6000) m2 s−1]. Diffusivity parameterizations accounting for both the nonhomogeneous turbulence residual and depth variability are needed.

Troposphere-Stratosphere Coupling and the Role of Critical Layer Nonlinearity

2020 ◽  
Author(s):  
Imogen Dell
Keyword(s):  
Rossby Waves ◽  
Phase Speed ◽  
Nonlinear Effects ◽  
Critical Layer ◽  
Coupling Mechanism ◽  
Mathematical Framework ◽  
Mean Flow ◽  
Weather And Climate ◽  
Dynamical Coupling

<p>There exists a coupling mechanism between the troposphere and the stratosphere, which plays a fundamental role in weather and climate. The coupling is highly complex and rests upon radiative and chemical feedbacks, as well as dynamical coupling by Rossby waves. The troposphere acts as a source of Rossby waves which propagate upwards in to the stratosphere, affecting the zonal mean flow. Rossby waves are also likely to play a significant role in downward communication of information via reflection from the stratosphere in to the troposphere. A mechanism for this reflection could be from a so-called critical layer. A shear flow exhibits a critical layer where the phase speed equals the flow velocity, where viscous and nonlinear effects become important. A wave incident upon a critical layer may be absorbed, reflected or overreflected, whereby the amplitude of the reflected wave is larger than that of the incident wave. In the case of troposphere-stratosphere coupling, the concept of critical layer overreflection is key to understanding atmospheric instability.</p><p>Motivated by this, a mathematical framework for understanding the coupling will be presented together with an investigation in to the role of nonlinearity versus viscosity inside the critical layer.</p>

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