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

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.

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

Applied Mechanics Reviews ◽

10.1115/1.3124384 ◽

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.

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

Journal of Physical Oceanography ◽

10.1175/jpo-d-16-0101.1 ◽

2017 ◽

Vol 47 (8) ◽

pp. 1897-1920 ◽

Cited By ~ 7

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.

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

Journal of Fluid Mechanics ◽

10.1017/jfm.2012.376 ◽

2012 ◽

Vol 710 ◽

pp. 545-568 ◽

Cited By ~ 36

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.

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

Canadian Journal of Physics ◽

10.1139/p02-056 ◽

2002 ◽

Vol 80 (12) ◽

pp. 1543-1558 ◽

Cited By ~ 1

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 (34 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

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Troposphere-Stratosphere Coupling and the Role of Critical Layer Nonlinearity

10.5194/egusphere-egu2020-11841 ◽

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

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.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.

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Planetary (Rossby), Inertia-Gravity (Poincaré) and Kelvin waves on the f-plane and β-plane in the presence of a uniform zonal flow

10.5194/egusphere-egu21-13427 ◽

2021 ◽

Author(s):

Yair De-Leon ◽

Chaim I. Garfinkel ◽

Nathan Paldor

Keyword(s):

Numerical Solutions ◽

Bottom Topography ◽

Phase Speed ◽

Zonal Flow ◽

Dispersion Curves ◽

Kelvin Waves ◽

Linear Wave ◽

Hermite Function ◽

Mean Flow ◽

Zonal Wavenumber

A linear wave theory of the Rotating Shallow Water Equations (RSWE) is developed in a channel on either the mid-latitude f-plane/&#946;-plane or on the equatorial &#946;-plane in the presence of a uniform mean zonal flow that is balanced geostrophically by a meridional gradient of the fluid surface height. We show that this surface height gradient is a potential vorticity (PV) source that generates Rossby waves even on the f-plane similar to the generation of these waves by PV sources such as the &#946;&#8211;effect, shear of the mean flow and bottom topography. Numerical solutions of the RSWE show that the resulting planetary (Rossby), Inertia-Gravity (Poincar&#233;) and Kelvin-like waves differ from their counterparts without mean flow in both their phase speeds and meridional structures. Doppler shifting of the &#8220;no mean-flow&#8221; phase speeds does not account for the difference in phase speeds, and the meridional structure does not often oscillate across the channel but is trapped near one the channel's boundaries in mid latitudes or behaves as Hermite function in the case of an equatorial channel. The phase speed of Kelvin-like waves is modified by the presence of a mean flow compared to the classical gravity wave speed but their meridional velocity does not vanish. The gaps between the dispersion curves of adjacent Poincar&#233; modes are not uniform but change with the zonal wavenumber, and the convexity of the dispersion curves also changes with the zonal wavenumber. In some cases, the Kelvin-like dispersion curve crosses those of Poincar&#233; modes, but it is not an evidence for the existence of instability since the Kelvin waves are not part of the solutions of an eigenvalue problem.&#160;

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Selfconsistent Models of Winds from Rotating Early-Type Stars – Application to B[e] star winds

International Astronomical Union Colloquium ◽

10.1017/s0252921100056669 ◽

2000 ◽

Vol 175 ◽

pp. 626-631

Author(s):

P. Petrenz ◽

J. Puls

Keyword(s):

Spatial Variation ◽

Radiation Temperature ◽

Rotating Stars ◽

Early Type ◽

Disk Formation ◽

Early Type Stars ◽

Hydrodynamical Simulations ◽

Rapidly Rotating Stars ◽

First Time

AbstractWe present results of 2.5-D radiation hydrodynamical simulations of winds from rapidly rotating stars. For the first time, we consider the dependence of the line statistics on local density and radiation temperature implying a spatial variation of the force-multiplier parameters k, α and δ which control the dynamics of the flow.We apply our models to the problem of disk formation in B[e]-star winds.

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High-field magnetic white dwarfs as the progeny of early-type stars?

Monthly Notices of the Royal Astronomical Society Letters ◽

10.1093/mnrasl/sls005 ◽

2012 ◽

Vol 428 (1) ◽

pp. L16-L20 ◽

Cited By ~ 9

Author(s):

P. D. Dobbie ◽

B. Kulebi ◽

S. L. Casewell ◽

M. R. Burleigh ◽

Q. A. Parker ◽

...

Keyword(s):

High Field ◽

White Dwarfs ◽

Early Type ◽

Early Type Stars

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Some results of the Barbier-Chalonge-Divan system of stellar classification

Symposium - International Astronomical Union ◽

10.1017/s0074180900053250 ◽

1966 ◽

Vol 24 ◽

pp. 77-90 ◽

Cited By ~ 1

Author(s):

D. Chalonge

Keyword(s):

Early Type ◽

Parameter System ◽

Early Type Stars ◽

Two Parameter

Several years ago a three-parameter system of stellar classification has been proposed (1, 2), for the early-type stars (O-G): it was an improvement on the two-parameter system described by Barbier and Chalonge (3).

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