scholarly journals Incidence and reflection of internal waves and wave-induced currents at a jump in buoyancy frequency

2015 ◽  
Vol 22 (3) ◽  
pp. 259-274 ◽  
Author(s):  
J. P. McHugh
Keyword(s):  
Wave Packet ◽  
Internal Gravity Waves ◽  
Buoyancy Frequency ◽  
Mean Flow ◽  
Weakly Nonlinear ◽  
Transmitted Waves ◽  
The Mean ◽  
Induced Currents ◽  
Wave Induced ◽  
The Waves

Abstract. Weakly nonlinear internal gravity waves are treated in a two-layer fluid with a set of nonlinear Schrodinger equations. The layers have a sharp interface with a jump in buoyancy frequency approximately modeling the tropopause. The waves are periodic in the horizontal but modulated in the vertical and Boussinesq flow is assumed. The equation governing the incident wave packet is directly coupled to the equation for the reflected packet, while the equation governing transmitted waves is only coupled at the interface. Solutions are obtained numerically. The results indicate that the waves create a mean flow that is strong near and underneath the interface, and discontinuous at the interface. Furthermore, the mean flow has an oscillatory component that can contaminate the wave envelope and has a vertical wavelength that decreases as the wave packet interacts with the interface.

scholarly journals Incidence and reflection of internal waves and wave-induced currents at a jump in buoyancy frequency

2014 ◽  
Vol 1 (1) ◽  
pp. 269-315
Author(s):  
J. P. McHugh
Keyword(s):  
Wave Packet ◽  
Internal Gravity Waves ◽  
Buoyancy Frequency ◽  
Mean Flow ◽  
Weakly Nonlinear ◽  
Transmitted Waves ◽  
The Mean ◽  
Induced Currents ◽  
Wave Induced ◽  
The Waves

Abstract. Weakly nonlinear internal gravity waves are treated in a two-layer fluid with a set of nonlinear Schrodinger equations. The layers have a sharp interface with a jump in buoyance frequency approximately modelling the tropopause. The waves are periodic in the horizontal but modulated in the vertical and Boussinesq flow is assumed. The equation governing the incident wave packet is directly coupled to the equation for the reflected packet, while the equation governing transmitted waves is only coupled at the interface. Solutions are obtained numerically. The results indicate that the waves create a mean flow that is strong near and underneath the interface, and discontinuous at the interface. Furthermore, the mean flow has an oscillatory component with a vertical wavelength that decreases as the wave packet interacts with the interface.

The generation of internal waves by flow over the rough topography of a continental slope

1992 ◽  
Vol 439 (1905) ◽  
pp. 115-130 ◽  
Keyword(s):  
Internal Gravity Waves ◽  
Sea Surface ◽  
Small Scale ◽  
Buoyancy Frequency ◽  
Mean Flow ◽  
Sea Bed ◽  
Lee Waves ◽  
Inclined Slope ◽  
The Mean ◽  
The Waves

Internal gravity waves generated as standing lee waves by the flow, V , of a uniformly stratified fluid over small-scale topography on an inclined slope are examined in the particular case in which the flow is parallel to the mean slope isobaths. Attention is given to the magnitude and direction of the energy flux and to its dependence on Vl / N , α and β , where l is the wavenumber of the topography, N is the buoyancy frequency of the fluid, α is the mean slope and β defines the orientation of the two-dimensional topography on the slope. In general there is a greater probability of energy transfer towards shallow water, but in particular regions the direction of the flux depends on the orientation of the topography on the slope. For a given scale of topography and for fixed longslope current, V , and stratification, N , the drag associated with the lee waves is greatest when β = 0 (when the topography is oriented normal to the mean slope isobaths) and it can be as large as the turbulent stress on the sea bed. The lee waves may induce large variations in the currents on the sea surface. It is found that although stationary lee waves may be formed over sloping topography, the waves reflected at the sea surface may subsequently be scattered from the topography to produce waves that propagate in the mean flow.

Topographic Form Drag on Tides and Low-Frequency Flow: Observations of Nonlinear Lee Waves over a Tall Submarine Ridge near Palau

2020 ◽  
Vol 50 (5) ◽  
pp. 1489-1507 ◽  
Author(s):  
Gunnar Voet ◽  
Matthew H. Alford ◽  
Jennifer A. MacKinnon ◽  
Jonathan D. Nash
Keyword(s):  
Ocean Circulation ◽  
Neap Tide ◽  
Spring Tide ◽  
Tidal Flow ◽  
Low Frequency ◽  
Buoyancy Frequency ◽  
Mean Flow ◽  
Submarine Ridge ◽  
The Mean ◽  
The Waves

AbstractTowed shipboard and moored observations show internal gravity waves over a tall, supercritical submarine ridge that reaches to 1000 m below the ocean surface in the tropical western Pacific north of Palau. The lee-wave or topographic Froude number, Nh0/U0 (where N is the buoyancy frequency, h0 the ridge height, and U0 the farfield velocity), ranged between 25 and 140. The waves were generated by a superposition of tidal and low-frequency flows and thus had two distinct energy sources with combined amplitudes of up to 0.2 m s−1. Local breaking of the waves led to enhanced rates of dissipation of turbulent kinetic energy reaching above 10−6 W kg−1 in the lee of the ridge near topography. Turbulence observations showed a stark contrast between conditions at spring and neap tide. During spring tide, when the tidal flow dominated, turbulence was approximately equally distributed around both sides of the ridge. During neap tide, when the mean flow dominated over tidal oscillations, turbulence was mostly observed on the downstream side of the ridge relative to the mean flow. The drag exerted by the ridge on the flow, estimated to for individual ridge crossings, and the associated power loss, thus provide an energy sink both for the low-frequency ocean circulation and the tidal flow.

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.

On strongly nonlinear gravity waves in a vertically sheared atmosphere

2021 ◽  
Author(s):  
Georg Sebastian Voelker ◽  
Mark Schlutow
Keyword(s):  
Gravity Wave ◽  
Gravity Waves ◽  
Internal Gravity Wave ◽  
Internal Gravity Waves ◽  
Wave Drag ◽  
Mean Flow ◽  
Flow Strength ◽  
Weakly Nonlinear ◽  
Strongly Nonlinear ◽  
The Mean

<p>Internal gravity waves are a well-known mechanism of energy redistribution in stratified fluids such as the atmosphere. They may propagate from their generation region, typically in the Troposphere, up to high altitudes. During their lifetime internal waves couple to the atmospheric background through various processes. Among the most important interactions are the exertion of wave drag on the horizontal mean-flow, the heat generation upon wave breaking, or the mixing of atmospheric tracers such as aerosols or greenhouse gases.</p><p>Many of the known internal gravity wave properties and interactions are covered by linear or weakly nonlinear theories. However, for the consideration of some of the crucial effects, like a reciprocal wave-mean-flow interaction including the exertion of wave drag on the mean-flow, strongly nonlinear systems are required. That is, there is no assumption on the wave amplitude relative to the mean-flow strength such that they may be of the same order.</p><p>Here, we exploit a strongly nonlinear Boussinesq theory to analyze the stability of a stationary internal gravity wave which is refracted at the vertical edge of a horizontal jet. Thereby we assume that the incident wave is horizontally periodic, non-hydrostatic, and vertically modulated. Performing a linear stability analysis in the vicinity of the jet edge we find necessary and sufficient criteria for instabilities to grow. In particular, the refracted wave becomes unstable if its incident amplitude is large enough and both mean-flow horizontal winds, below and above the edge of the jet, do not exceed particular upper bounds.</p>

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.

Drift and deformation of oil slicks due to surface waves

2009 ◽  
Vol 620 ◽  
pp. 313-332 ◽  
Author(s):  
K. H. CHRISTENSEN ◽  
E. TERRILE
Keyword(s):  
Remote Sensing ◽  
Theoretical Model ◽  
Remote Sensing Data ◽  
Mean Flow ◽  
Horizontal Deformation ◽  
Oil Slick ◽  
Damping Rate ◽  
The Mean ◽  
Wave Induced ◽  
The Waves

We present a theoretical model for the wave-induced drift and horizontal deformation of an oil slick. The waves and the mean flow are coupled through the influence of the mean flow on the concentration of slick material, which in turn determines the damping rate of the waves and hence the transfer of momentum from the waves to the mean flow. We also briefly discuss a simplified version of the model that can be used when remote sensing data are available. With this simpler model the wave-induced forcing of the mean flow is obtained directly from observations of the wave field, hence knowledge of any specific slick properties is not required.

Mean motions and impulse of a guided internal gravity wave packet

1973 ◽  
Vol 60 (4) ◽  
pp. 801-811 ◽  
Author(s):  
Michael E. Mcintyre
Keyword(s):  
Wave Packet ◽  
Gravity Wave ◽  
Electromagnetic Waves ◽  
Internal Gravity Wave ◽  
Single Frequency ◽  
Buoyancy Frequency ◽  
Mean Fields ◽  
The Mean ◽  
Boussinesq Fluid ◽  
The Waves

Second-order mean fields of motion and density are calculated for the two-dimensional problem of an internal gravity wave packet (the waves are predominantly of a single frequency o and wavenumberk) propagating as a wave-guide mode in an inviscid, diffusionless Boussinesq fluid of constant buoyancy frequencyN, confined between horizontal boundaries. (The same mathematical analysis applies to the formally identical problem for inertia waves in a homogeneous rotating fluid.)To leading order the mean motions turn out to be zero outside the wave packet, which consequently possesses a well-defined fluid impulse [Iscr ]. This is directed horizontally, and is given in magnitude and sense by\[ {\cal I} = \alpha{\cal M};\quad\alpha = \frac{2c_{\rm g}(c-c_{\rm g})(c+2c_{\rm g})}{c^3-4c^3_{\rm g}}. \]Here [Mscr ] is the so-called ‘wave momentum’, defined as wave energy divided by horizontal phase velocity c ≡ ω/k, andcg=c(N2–ω2)/N2, the group velocity.If the wave packet is supposed generated by a horizontally towed obstacle, [Mscr ] appears as the total fluid impulse, but of this a portion [Mscr ]-[Iscr ] in general propagates independently away from the wave packet in the form of long waves. When the wave packet itself is totally reflected by a vertical barrier immersed in the fluid, the time-integrated horizontal force on the barrier equals 2 [Iscr ] (and not 2 [Mscr ] as might have been expected from a naive analogy with the radiation pressure of electromagnetic waves.)

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.

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.

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