Forced Flexural Gravity Wave Motion in Two-Layer Fluid

2015 ◽  
Vol 137 (3) ◽  
Author(s):  
R. Mondal ◽  
J. Bhattacharjee ◽  
T. Sahoo
Keyword(s):  
Gravity Wave ◽  
Wave Motion ◽  
Wave Reflection ◽  
Ice Sheet ◽  
Elastic Beam ◽  
Wave Theory ◽  
Free Edge ◽  
Physical Parameters ◽  
Flexural Gravity Wave ◽  
Water Depths

Generation of flexural gravity waves in a two-layer fluid due to the forced motion of a vertical rigid wavemaker is studied in both finite and infinite water depths. The two-dimensional (2D) fluid domain having an interface is covered by a semi-infinite ice sheet, which is modeled as an elastic beam. As an application of the wavemaker problem, flexural gravity wave reflection by a vertical cliff is analyzed. Under the assumptions of small amplitude water wave theory and structural response, the mathematical models are solved using a recently developed expansion formulae and the associated orthogonal mode-coupling relations as appropriate for finite and infinite water depths. Effect of three types of edges such as free edge, simply supported edge, and built-in edge on the wave reflection by the vertical cliff is analyzed whilst, for the wavemaker, the floating ice sheet is assumed to have free edge. Effect of various physical parameters on the wave motion is studied by analyzing the reflection coefficients, deflection of the ice sheet, interface elevation, strain and shear force on the floating ice sheet.

Flexural gravity wave motion over poroelastic bed

Wave Motion ◽  
2016 ◽  
Vol 63 ◽  
pp. 135-148 ◽  
Author(s):  
S. Das ◽  
H. Behera ◽  
T. Sahoo
Keyword(s):  
Gravity Wave ◽  
Wave Motion ◽  
Flexural Gravity Wave

Flexural-gravity wave dynamics in two-layer fluid: blocking and dead water analogue

2018 ◽  
Vol 854 ◽  
pp. 121-145 ◽  
Author(s):  
S. Das ◽  
T. Sahoo ◽  
M. H. Meylan
Keyword(s):  
Internal Wave ◽  
Gravity Wave ◽  
Water Depth ◽  
Phase Speed ◽  
Compressive Force ◽  
Wave Theory ◽  
High Amplitude ◽  
The Dead ◽  
Flexural Gravity Wave ◽  
Dead Water

Flexural-gravity wave characteristics are analysed, in the presence of a compressive force and a two-layer fluid, under the assumption of linearized water wave theory and small amplitude structural response. The occurrence of blocking for flexural-gravity waves is demonstrated in both the surface and internal modes. Within the threshold of the blocking and the buckling limit, the dispersion relation possesses four positive roots (for fixed wavenumber). It is shown that, under certain conditions, the phase and group velocities coalesce. Moreover, a wavenumber range for certain critical values of compression and depth is provided within which the internal wave energy moves faster than that of the surface wave. It is also demonstrated that, for shallow water, the wave frequencies in the surface and internal modes will never coalesce. It is established that the phase speed in the surface and internal modes attains a minimum and maximum, respectively, when the interface is located approximately in the middle of the water depth. An analogue of the dead water phenomenon, the occurrence of a high amplitude internal wave with a low amplitude at the surface, is established, irrespective of water depth, when the densities of the two fluids are close to each other. When the interface becomes close to the seabed, the dead water effect ceases to exist. The theory developed in the frequency domain is extended to the time domain and examples of negative energy waves and blocking are presented.

Dromions of flexural-gravity waves

2013 ◽  
Vol 719 ◽  
pp. 1-13 ◽  
Author(s):  
Mohammad-Reza Alam
Keyword(s):  
Gravity Wave ◽  
Multiple Scales ◽  
Three Dimensional ◽  
The Arctic ◽  
Computational Techniques ◽  
Illustrative Case ◽  
Mean Flow ◽  
Weakly Nonlinear ◽  
Flexural Gravity Wave ◽  
Water Depths

AbstractHere we show that weakly nonlinear flexural-gravity wave packets, such as those propagating on the surface of ice-covered waters, admit three-dimensional fully localized solutions that travel with a constant speed without dispersion or dissipation. These solutions, that are formed at the intersection of line-soliton mean-flow tracks, have exponentially decaying tails in all directions and are called dromions in contrast to lumps that decay only algebraically. We derive, by asymptotic expansion and assuming multiple scales for spatial and temporal variations, the three-dimensional weakly nonlinear governing equations that describe the coupled motion of the wavepacket envelope and the underlying mean current. We show that in the limit of long waves and strong flexural rigidity these equations reduce to a system of nonlinear elliptic–hyperbolic partial differential equations similar to the Davey–Stewartson I (DSI) equation, but with major differences in the coefficients. Specifically, and contrary to DSI equations, the elliptic and hyperbolic operators in the flexural-gravity equations are not canonical resulting in complications in analytical considerations. Furthermore, standard computational techniques encounter difficulties in obtaining the dromion solution to these equations owing to the presence of a spatial hyperbolic operator whose solution does not decay at infinity. Here, we present a direct (iterative) numerical scheme that uses pseudo-spectral expansion and pseudo-time integration to find the dromion solution to the flexural-gravity wave equation. Details of this direct simulation technique are discussed and properties of the solution are elaborated through an illustrative case study. Dromions may play an important role in transporting energy over the ice cover in the Arctic, resulting in the ice breaking far away from the ice edge, and also posing danger to icebreaker ships. In fact we found that, contrary to DSI dromions that only exist in water depths of less than 5 mm, flexural-gravity dromions exist for a broad range of ice thicknesses and water depths including values that may be realized in polar oceans.

Flexural-gravity wave motion in the presence of shear current: Wave blocking and negative energy waves

2018 ◽  
Vol 30 (10) ◽  
pp. 106606 ◽  
Author(s):  
Santu Das ◽  
Prakash Kar ◽  
Trilochan Sahoo ◽  
Michael H. Meylan
Keyword(s):  
Gravity Wave ◽  
Wave Motion ◽  
Negative Energy ◽  
Current Wave ◽  
Shear Current ◽  
Wave Blocking ◽  
Flexural Gravity Wave

Self-Acceleration in the Parameterization of Orographic Gravity Wave Drag

2010 ◽  
Vol 67 (8) ◽  
pp. 2537-2546 ◽  
Author(s):  
John F. Scinocca ◽  
Bruce R. Sutherland
Keyword(s):  
Gravity Wave ◽  
Middle Atmosphere ◽  
Wave Train ◽  
Leading Edge ◽  
Wave Theory ◽  
Wave Drag ◽  
Tuning Parameter ◽  
Mean Flow ◽  
Propagating Waves ◽  
The Impact

Abstract A new effect related to the evaluation of momentum deposition in conventional parameterizations of orographic gravity wave drag (GWD) is considered. The effect takes the form of an adjustment to the basic-state wind about which steady-state wave solutions are constructed. The adjustment is conservative and follows from wave–mean flow theory associated with wave transience at the leading edge of the wave train, which sets up the steady solution assumed in such parameterizations. This has been referred to as “self-acceleration” and it is shown to induce a systematic lowering of the elevation of momentum deposition, which depends quadratically on the amplitude of the wave. An expression for the leading-order impact of self-acceleration is derived in terms of a reduction of the critical inverse Froude number Fc, which determines the onset of wave breaking for upwardly propagating waves in orographic GWD schemes. In such schemes Fc is a central tuning parameter and typical values are generally smaller than anticipated from conventional wave theory. Here it is suggested that self-acceleration may provide some of the explanation for why such small values of Fc are required. The impact of Fc on present-day climate is illustrated by simulations of the Canadian Middle Atmosphere Model.

scholarly journals The nonlinear effects on the characteristics of gravity wave packets: dispersion and polarization relations

2000 ◽  
Vol 18 (10) ◽  
pp. 1316-1324 ◽  
Author(s):  
S.-D. Zhang ◽  
F. Yi ◽  
J.-F. Wang
Keyword(s):  
Gravity Wave ◽  
Gravity Waves ◽  
Middle Atmosphere ◽  
Wave Packets ◽  
Nonlinear Effects ◽  
Wave Theory ◽  
Nonlinear Propagation ◽  
Waves And Tides ◽  
Time Variations ◽  
Isothermal Atmosphere

Abstract. By analyzing the results of the numerical simulations of nonlinear propagation of three Gaussian gravity-wave packets in isothermal atmosphere individually, the nonlinear effects on the characteristics of gravity waves are studied quantitatively. The analyses show that during the nonlinear propagation of gravity wave packets the mean flows are accelerated and the vertical wavelengths show clear reduction due to nonlinearity. On the other hand, though nonlinear effects exist, the time variations of the frequencies of gravity wave packets are close to those derived from the dispersion relation and the amplitude and phase relations of wave-associated disturbance components are consistent with the predictions of the polarization relation of gravity waves. This indicates that the dispersion and polarization relations based on the linear gravity wave theory can be applied extensively in the nonlinear region.Key words: Meteorology and atmospheric dynamics (middle atmosphere dynamics; waves and tides)

scholarly journals Automatic weather stations for basic and applied glaciological research

1969 ◽  
pp. 69-72 ◽  
Author(s):  
Michele Citterio ◽  
Dirk Van As ◽  
Andreas P. Ahlstrøm ◽  
Morten L. Andersen ◽  
Signe B. Andersen ◽  
...  
Keyword(s):  
Climate Models ◽  
Ice Sheet ◽  
Greenland Ice Sheet ◽  
Feasibility Studies ◽  
Lessons Learned ◽  
Physical Parameters ◽  
Ice Caps ◽  
Technological Advances ◽  
Weather Stations ◽  
The Impact

Since the early 1980s, the Geological Survey of Denmark and Greenland (GEUS) glaciology group has developed automatic weather stations (AWSs) and operated them on the Greenland ice sheet and on local glaciers to support glaciological research and monitoring projects (e.g. Olesen & Braithwaite 1989; Ahlstrøm et al. 2008). GEUS has also operated AWSs in connection with consultancy services in relation to mining and hydropower pre-feasibility studies (Colgan et al. 2015). Over the years, the design of the AWS has evolved, partly due to technological advances and partly due to lessons learned in the fi eld. At the same time, we have kept the initial goal in focus: long-term, year-round accurate recording of ice ablation, snow depth and the physical parameters that determine the energy budget of glacierised surfaces. GEUS has an extensive record operating AWSs in the harsh Arctic environment of the diverse ablation areas of the Greenland ice sheet, glaciers and ice caps (Fig. 1). Th e current GEUS-type AWS (Fig. 2) records meteorological, surface and sub-surface variables, including accumulation and ablation, as well as for example ice velocity. A large part of the data is transmitted by satellite near real-time to support ongoing applications, fi eld activities and the planning of maintenance visits. Th e data have been essential for assessing the impact of climate change on land ice. Th e data are also crucial for calibration and validation of satellite-based observations and climate models (van As et al. 2014).

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