Momentum transport by gravity waves in a perfectly conducting shear flow

1972 ◽  
Vol 54 (2) ◽  
pp. 217-240 ◽  
Author(s):  
N. Rudraiah ◽  
M. Venkatachalappa
Keyword(s):  
Magnetic Field ◽  
Gravity Waves ◽  
Critical Level ◽  
Critical Levels ◽  
Mean Flow ◽  
Critical Layers ◽  
The Mean ◽  
Pass Through ◽  
The Waves ◽  
Aligned Magnetic Field

Alfvén-gravitational waves propagating in a Boussinesq, inviscid, adiabatic, perfectly conducting fluid in the presence of a uniform aligned magnetic field in which the mean horizontal velocityU(z)depends on heightzonly are considered. The governing wave equation has three singularities, at the Doppler-shifted frequencies Ωd= 0, ± ΩA, where ΩAis the Alfvén frequency. Hence the effect of the Lorentz force is to introduce two more critical levels, called hydromagnetic critical levels, in addition to the hydrodynamic critical level. To study the influence of magnetic field on the attenuation of waves two situations, one concerning waves far away from the critical levels (i.e. Ωd[Gt ] ΩA) and the other waves at moderate distances from the critical levels (i.e. Ωd> ΩA), are investigated. In the former case, if the hydrodynamic Richardson numberJHexceeds one quarter the waves are attenuated by a factor exp{−2π(JH−¼)½} as they pass through the hydromagnetic critical levels, at which Ωd= ± ΩA, and momentum is transferred to the mean flow there. Whereas in the case of waves at moderate distances from the critical levels the ratio of momentum fluxes on either side of the hydromagnetic critical levels differ by a factor exp {−2π(J−¼)½}, whereJ(> ¼) is the algebraic sum of hydrodynamic and hydromagnetic Richardson numbers. Thus the solutions to the hydromagnetic system approach asymptotically those of the hydrodynamic system sufficiently far on either side of the magnetic critical layers, though their behaviour in the vicinity of such levels is quite dissimilar. There is no attenuation and momentum transfer to the mean flow across the hydrodynamic critical level, at which Ωd= 0. The general theory is applied to a particular problem of flow over a sinusoidal corrugation. This is significant in considering the propagation of Alfvén-gravity waves, in the presence of a geomagnetic field, from troposphere to ionosphere.

The critical layer for internal gravity waves in a shear flow

1967 ◽  
Vol 27 (3) ◽  
pp. 513-539 ◽  
Author(s):  
John R. Booker ◽  
Francis P. Bretherton
Keyword(s):  
Gravity Waves ◽  
Phase Speed ◽  
Deep Ocean ◽  
Internal Gravity Waves ◽  
Mean Flow ◽  
Lee Waves ◽  
The Mean ◽  
Horizontal Momentum ◽  
Pass Through ◽  
The Waves

Internal gravity waves of small amplitude propagate in a Boussinesq inviscid, adiabatic liquid in which the mean horizontal velocity U(z) depends on height z only. If the Richardson number R is everywhere larger than 1/4, the waves are attenuated by a factor $\exp\{-2\pi(R - \frac{1}{4})^{\frac{1}{2}}\}$ as they pass through a critical level at which U is equal to the horizontal phase speed, and momentum is transferred to the mean flow there. This effect is considered in relation to lee waves in the airflow over a mountain, and in relation to transient localized disturbances. It is significant in considering the propagation of gravity waves from the troposphere to the ionosphere, and possibly in transferring horizontal momentum into the deep ocean without substantial mixing.

Nonlinear internal gravity waves in a rotating fluid

1975 ◽  
Vol 71 (3) ◽  
pp. 497-512 ◽  
Author(s):  
R. Grimshaw
Keyword(s):  
Gravity Waves ◽  
Wave Structure ◽  
Internal Gravity Waves ◽  
Mean Flow ◽  
Mean Velocity ◽  
Main Effect ◽  
Local Wave ◽  
The Mean ◽  
The Waves ◽  
Circulation Theorem

The interaction between internal gravity waves in a rotating frame and the mean flow is discussed for the case when the properties of the mean flow vary slowly on a scale determined by the local wave structure. The principle of conservation of wave action is established. It is shown that the main effect of the waves on the Lagrangian mean velocity is due to an appropriate ‘radiation stress’ tensor. A circulation theorem and a potential-vorticity equation are derived for the mean velocity.

Effect of ohmic dissipation on internal Alfvén-gravity waves in a conducting shear flow

1974 ◽  
Vol 62 (4) ◽  
pp. 705-726 ◽  
Author(s):  
N. Rudraiah ◽  
M. Venkatachalappa
Keyword(s):  
Magnetic Field ◽  
Wave Equation ◽  
Gravity Waves ◽  
Momentum Flux ◽  
Critical Level ◽  
Transverse Magnetic ◽  
Asymptotic Solutions ◽  
Ohmic Dissipation ◽  
Propagation Of Waves ◽  
The Waves

Internal Alfvén-gravity waves of small amplitude propagating in a Boussinesq, inviscid, adiabatic, finitely conducting fluid in the presence of a uniform transverse magnetic field in which the mean horizontal velocityU(z) depends on heightzonly are considered. We find that the governing wave equation is singular only at the Doppler-shifted frequency Ωd= 0 and not at the magnetic singularities Ωd= ± ΩA, where ΩAis the Alfvén frequency. Hence the effect of ohmic dissipation is to prevent the resulting wave equation from having magnetic singularities. Asymptotic solutions of the wave equation, which is a fourth-order differential equation, are obtained. They show the presence of the magnetic Stokes points Ωd= ± ΩA. The interpretation of upward and downward propagation of waves is also discussed.To study the combined effect of electrical conductivity and the magnetic field on waves at the critical level, we have used the group-velocity approach and found that the waves are transmitted across the magnetic Stokes points but are completely absorbed at the hydrodynamic critical level Ωd= 0. The general expression for the momentum flux is mathematically complicated but will be simplified under the assumption\[ \frac{\partial^2h}{\partial x^2}+\frac{\partial^2h}{\partial y^2}\gg \frac{\partial^2h}{\partial z^2}, \]wherehis the perturbation magnetic field. In this approximation we find that the momentum flux is not conserved and the waves are completely absorbed at Ωd= 0.The general theory is applied to a particular problem of flow over a sinusoidal corrugation and asymptotic solutions are obtained by applying the Laplace transformation and using the method of steepest descent.

Propagation of internal gravity waves in perfectly conducting fluids with shear flow, rotation and transverse magnetic field

1972 ◽  
Vol 52 (1) ◽  
pp. 193-206 ◽  
Author(s):  
N. Rudraiah ◽  
M. Venkatachalappa
Keyword(s):  
Magnetic Field ◽  
Angular Momentum ◽  
Shear Flow ◽  
Gravitational Waves ◽  
Transverse Magnetic Field ◽  
Internal Gravity Waves ◽  
Transverse Magnetic ◽  
Critical Levels ◽  
Mean Flow ◽  
The Waves

The propagation of internal Alfvén-inertio-gravitational waves in a Boussinesq inviscid adiabatic perfectly conducting shear flow with rotation is investigated in the presence of a transverse magnetic field. It is shown that the effect of the rotational nature of electromagnetic force and Coriolis force is that linear momentum is not conserved anywhere in the fluid even at critical levels, whereas the angular momentum flux is conserved everywhere in the fluid except at the critical levels at which the Doppler-shifted frequency Ωd = 0, + ΩA or ± Ω ± (Ω2 + Ω2A)½, where ΩA is the Alfvén frequency and Ω is the Coriolis frequency, and the angular momentum is transferred to the mean flow there by Alfvén-inertio-gravitational waves. Asymptotic solutions to the wave equation are obtained near the critical levels and it is shown that the effect of the Lorentz force on the waves at the critical levels is to increase the process of critical layer absorption. The condition for neglection of rotation for higher frequency waves is also obtained and is found to be the same in both hydrodynamic and hydro-magnetic flows.

Oblique wind waves generated by the instability of wind blowing over water

1996 ◽  
Vol 316 ◽  
pp. 163-172 ◽  
Author(s):  
L. C. Morland
Keyword(s):  
Gravity Waves ◽  
Wind Waves ◽  
Maximum Growth ◽  
Maximum Growth Rate ◽  
Mean Flow ◽  
Oblique Angle ◽  
Wind Speeds ◽  
The Mean ◽  
Directional Distributions ◽  
The Waves

The growth rates of gravity waves are computed from linear, inviscid stability theory for wind velocity profiles that are representative of the mean flow in a turbulent boundary layer. The energy transfer to the waves is largely concentrated in an angle (to the wind) interval that broadens with increasing wind speed and narrows with increasing wavelength. At sufficiently high wind speeds and sufficiently short wavelengths, the waves of maximum growth rate propagate at an oblique angle to the wind. The connection with bimodal directional distributions of observed spectra is discussed.

Internal gravity waves: critical layer absorption in a rotating fluid

1975 ◽  
Vol 70 (2) ◽  
pp. 287-304 ◽  
Author(s):  
R. Grimshaw
Keyword(s):  
Gravity Waves ◽  
Critical Level ◽  
Vertical Component ◽  
Internal Gravity Waves ◽  
Wave Action ◽  
Rotating Fluid ◽  
Mean Flow ◽  
Coriolis Parameter ◽  
Shear Rates ◽  
The Mean

The propagation of internal gravity waves in a shear flow in a rotating fluid is examined for the case when the rotation vector is inclined to the vertical. It is shown that internal gravity waves approaching a critical level, where ω*, the Doppler-shifted frequency, equals 2ΩV, the vertical component of the Coriolis parameter, will be either transmitted or absorbed according as \[ W_g\omega^{*}2\Omega_V\{m(U_z + 2\Omega_H)-lV_z\}\lessgtr 0; \] here Wg is the vertical group velocity, 2ΩH is the horizontal component of the Coriolis parameter, l and m are the easterly and northerly wavenumber components, and Uz and Vz are the shear rates of the easterly and northerly components of the mean flow. Between critical levels, wave action flux is conserved. However, for a wave absorbed at a critical level, the wave action flux is attenuated by a factor exp { − 2π|m(Uz + 2ΩH) − lVz]/(lUz + mVz)|}. The phenomenon is also analysed using a WKBJ approximation.

On internal gravity waves in an accelerating shear flow

1978 ◽  
Vol 88 (4) ◽  
pp. 623-639 ◽  
Author(s):  
S. A. Thorpe
Keyword(s):  
Gravity Waves ◽  
Phase Distribution ◽  
Phase Speed ◽  
Internal Gravity Waves ◽  
Initial Energy ◽  
Constant Density ◽  
Mean Flow ◽  
Mean Velocity ◽  
The Mean ◽  
The Waves

The investigation of the effects which a changing mean flow has on a uniform train of internal gravity waves (Thorpe 1978a) is continued by considering waves in a uniformly accelerating stratified plane Couette flow with constant density gradient. Experiments reveal a change in the mode structure and phase distribution of the waves, and their eventual breaking near the boundary where the mean flow is greatest, the phase speed of the waves being positive. A linear numerical model is devised which accurately describes the waves up to the onset of their breaking, and this is used to investigate their energetics. The working of the Reynolds stress against the mean velocity gradient results in a very rapid transfer of energy from the waves to the mean flow, so that by the time breaking occurs only a small fraction of their initial energy remains for possible transfer into potential energy of the fluid.The consequences have important applications in oceanography and meteorology, to flow stability and flow generation, and explain some earlier laboratory observations.

scholarly journals Generation of Reverse Meniscus Flow by Applying An Electromagnetic Brake

2021 ◽  
Author(s):  
Alexander Vakhrushev ◽  
Abdellah Kharicha ◽  
Ebrahim Karimi-Sibaki ◽  
Menghuai Wu ◽  
Andreas Ludwig ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Lorentz Force ◽  
Applied Magnetic Field ◽  
Numerical Study ◽  
Flow Direction ◽  
Experimental Studies ◽  
Submerged Entry Nozzle ◽  
Mean Flow ◽  
Slab Caster ◽  
The Mean

AbstractA numerical study is presented that deals with the flow in the mold of a continuous slab caster under the influence of a DC magnetic field (electromagnetic brakes (EMBrs)). The arrangement and geometry investigated here is based on a series of previous experimental studies carried out at the mini-LIMMCAST facility at the Helmholtz-Zentrum Dresden-Rossendorf (HZDR). The magnetic field models a ruler-type EMBr and is installed in the region of the ports of the submerged entry nozzle (SEN). The current article considers magnet field strengths up to 441 mT, corresponding to a Hartmann number of about 600, and takes the electrical conductivity of the solidified shell into account. The numerical model of the turbulent flow under the applied magnetic field is implemented using the open-source CFD package OpenFOAM®. Our numerical results reveal that a growing magnitude of the applied magnetic field may cause a reversal of the flow direction at the meniscus surface, which is related the formation of a “multiroll” flow pattern in the mold. This phenomenon can be explained as a classical magnetohydrodynamics (MHD) effect: (1) the closure of the induced electric current results not primarily in a braking Lorentz force inside the jet but in an acceleration in regions of previously weak velocities, which initiates the formation of an opposite vortex (OV) close to the mean jet; (2) this vortex develops in size at the expense of the main vortex until it reaches the meniscus surface, where it becomes clearly visible. We also show that an acceleration of the meniscus flow must be expected when the applied magnetic field is smaller than a critical value. This acceleration is due to the transfer of kinetic energy from smaller turbulent structures into the mean flow. A further increase in the EMBr intensity leads to the expected damping of the mean flow and, consequently, to a reduction in the size of the upper roll. These investigations show that the Lorentz force cannot be reduced to a simple damping effect; depending on the field strength, its action is found to be topologically complex.

scholarly journals Influence of the Monsoon Trough on Westward-Propagating Tropical Waves over the Western North Pacific. Part II: Energetics and Numerical Experiments

2015 ◽  
Vol 28 (23) ◽  
pp. 9332-9349 ◽  
Author(s):  
Liang Wu ◽  
Zhiping Wen ◽  
Renguang Wu
Keyword(s):  
North Pacific ◽  
Numerical Experiments ◽  
Western North Pacific ◽  
Monsoon Trough ◽  
Water Model ◽  
Mean Flow ◽  
Horizontal Structure ◽  
Rotational Flows ◽  
The Mean ◽  
The Waves

Abstract Part I of this study examined the modulation of the monsoon trough (MT) on tropical depression (TD)-type–mixed Rossby–gravity (MRG) and equatorial Rossby (ER) waves over the western North Pacific based on observations. This part investigates the interaction of these waves with the MT through a diagnostics of energy conversion that separates the effect of the MT on TD–MRG and ER waves. It is found that the barotropic conversion associated with the MT is the most important mechanism for the growth of eddy energy in both TD–MRG and ER waves. The large rotational flows help to maintain the rapid growth and tilted horizontal structure of the lower-tropospheric waves through a positive feedback between the wave growth and horizontal structure. The baroclinic conversion process associated with the MT contributes a smaller part for TD–MRG waves, but is of importance comparable to barotropic conversion for ER waves as it can produce the tilted vertical structure. The growth rates of the waves are much larger during strong MT years than during weak MT years. Numerical experiments are conducted for an idealized MRG or ER wave using a linear shallow-water model. The results confirm that the monsoon background flow can lead to an MRG-to-TD transition and the ER wave amplifies along the axis of the MT and is more active in the strong MT state. Those results are consistent with the findings in Part I. This indicates that the mean flow of the MT provides a favorable background condition for the development of the waves and acts as a key energy source.

scholarly journals On strongly nonlinear gravity waves in a vertically sheared atmosphere

2020 ◽  
Vol 6 (1) ◽  
pp. 63-74
Author(s):  
Mark Schlutow ◽  
Georg S. Voelker
Keyword(s):  
Gravity Waves ◽  
Lower Layer ◽  
Vertical Shear ◽  
Horizontal Wind ◽  
Necessary Condition ◽  
Mean Flow ◽  
Individual Layer ◽  
Strongly Nonlinear ◽  
The Mean ◽  
The Stability

Abstract We investigate strongly nonlinear stationary gravity waves which experience refraction due to a thin vertical shear layer of horizontal background wind. The velocity amplitude of the waves is of the same order of magnitude as the background flow and hence the self-induced mean flow alters the modulation properties to leading order. In this theoretical study, we show that the stability of such a refracted wave depends on the classical modulation stability criterion for each individual layer, above and below the shearing. Additionally, the stability is conditioned by novel instability criteria providing bounds on the mean-flow horizontal wind and the amplitude of the wave. A necessary condition for instability is that the mean-flow horizontal wind in the upper layer is stronger than the wind in the lower layer.

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