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.

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.

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 Eddy Phase Speeds in a Two-Layer Model of Quasigeostrophic Baroclinic Turbulence with Applications to Ocean Observations

2016 ◽  
Vol 46 (6) ◽  
pp. 1963-1985 ◽  
Author(s):  
Lei Wang ◽  
Malte Jansen ◽  
Ryan Abernathey
Keyword(s):  
Practical Importance ◽  
Phase Speed ◽  
Wave Theory ◽  
Inverse Cascade ◽  
Barotropic Mode ◽  
Eddy Fluxes ◽  
Circumpolar Current ◽  
The Antarctic ◽  
Ocean Observations ◽  
Shed Light

AbstractThe phase speed spectrum of ocean mesoscale eddies is fundamental to understanding turbulent baroclinic flows. Since eddy phase propagation has been shown to modulate eddy fluxes, an understanding of eddy phase speeds is also of practical importance for the development of improved eddy parameterizations for coarse resolution ocean models. However, it is not totally clear whether and how linear Rossby wave theory can be used to explain the phase speed spectra in various weakly turbulent flow regimes. Using linear analysis, theoretical constraints are identified that control the eddy phase speed in a two-layer quasigeostrophic (QG) model. These constraints are then verified in a series of nonlinear two-layer QG simulations, spanning a range of parameters with potential relevance to the ocean. In the two-layer QG model, the strength of the inverse cascade exerts an important control on the eddy phase speed. If the inverse cascade is weak, the phase speed spectrum is reasonably well approximated by the phase speed of the linearly most unstable mode. A significant inverse cascade instead leads to barotropization, which in turn leads to mean phase speeds closer to those of barotropic-mode Rossby waves. The two-layer QG results are qualitatively consistent with the observed eddy phase speed spectra in the Antarctic Circumpolar Current and may also shed light on the interpretation of phase speed spectra observed in other regions.

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 TSUNAMI PHASE SPEED REDUCTION DUE TO WATER COMPRESSIBILTY

2018 ◽  
pp. 9
Author(s):  
Ali Abdolali ◽  
James T. Kirby
Keyword(s):  
Arrival Time ◽  
Phase Speed ◽  
Propagation Speed ◽  
Frequency Dispersion ◽  
Wave Theory ◽  
Polar Coordinates ◽  
Ocean Bottom ◽  
Tsunami Propagation ◽  
Boussinesq Model ◽  
Tsunami Waves

Most existing tsunami propagation models consider the ocean to be an incompressible, homogenous medium. Recently, it has been shown that a number of physical features can slow the propagation speed of tsunami waves, including wave frequency dispersion, ocean bottom elasticity, water compressibility and thermal or salinity stratification. These physical effects are secondary to the leading order, shallow water or long wave behavior, but still play a quantifiable role in tsunami arrival time, especially at far distant locations. In this work, we have performed analytical and numerical investigations and have shown that consideration of those effects can actually improve the prediction of arrival time at distant stations, compared to incompressible forms of wave equations. We derive a modified Mild Slope Equation for Weakly Compressible fluid following the method proposed by Sammarco et al. (2013) and Abdolali et al. (2015) using linearized wave theory, and then describe comparable extensions to the Boussinesq model of Kirby et al. (2013). Both models account for water compressibility and compression of static water column to simulate tsunami waves. The mild slope model is formulated in plane Cartesian coordinates and is thus limited to medium propagation distances, while the Boussinesq model is formulated in spherical polar coordinates and is suitable for ocean scale simulations.

scholarly journals Advanced hodograph-based analysis technique to derive gravity-wave parameters from lidar observations

2020 ◽  
Vol 13 (2) ◽  
pp. 479-499
Author(s):  
Irina Strelnikova ◽  
Gerd Baumgarten ◽  
Franz-Josef Lübken
Keyword(s):  
Gravity Wave ◽  
Wave Theory ◽  
Linear Wave ◽  
Data Set ◽  
Background Removal ◽  
Analysis Technique ◽  
Lidar Measurements ◽  
Meridional Winds ◽  
Linear Fit ◽  
Removal Technique

Abstract. An advanced hodograph-based analysis technique to derive gravity-wave (GW) parameters from observations of temperature and winds is developed and presented as a step-by-step recipe with justification for every step in such an analysis. As the most adequate background removal technique the 2-D FFT is suggested. For an unbiased analysis of fluctuation whose amplitude grows with height exponentially, we propose applying a scaling function of the form exp (z∕(ςH)), where H is scale height, z is altitude, and the constant ς can be derived by a linear fit to the fluctuation profile and should be in the range 1–10. The most essential part of the proposed analysis technique consists of fitting cosine waves to simultaneously measured profiles of zonal and meridional winds and temperature and subsequent hodograph analysis of these fitted waves. The linear wave theory applied in this analysis is extended by introducing a wave packet envelope term exp⁡(-(z-z0)2/2σ2) that accounts for limited extent of GWs in the observational data set. The novelty of our approach is that its robustness ultimately allows for automation of the hodograph analysis and resolves many more GWs than can be inferred by the manually applied hodograph technique. This technique allows us to unambiguously identify upward- and downward-propagating GWs and their parameters. This technique is applied to unique lidar measurements of temperature and horizontal winds measured in an altitude range of 30 to 70 km.

A Methodology to Characterize Internal Solitons in the Ocean

2018 ◽  
Author(s):  
Henrique Coelho ◽  
Zhong Peng ◽  
Dave Sproson ◽  
Jill Bradon
Keyword(s):  
Internal Waves ◽  
Large Scale ◽  
Numerical Models ◽  
Phase Speed ◽  
Selection Procedure ◽  
Wave Theory ◽  
Tidal Energy ◽  
Internal Tides ◽  
Linear Wave ◽  
Soliton Generation

Internal waves in the ocean occur in stably stratified fluids when a water parcel is vertically displaced by some external forcing and is restored by buoyancy forces. A specific case of such internal waves is internal tides and their associated currents. These currents can be significant in areas where internal waves degenerate into nonlinear solitary waves, known as solitons. Solitons are potentially hazardous for offshore engineering constructions, such as oil/gas pipelines and floating platforms. The most efficient mechanism of soliton generation is the tidal energy conversion from barotropic to baroclinic component over large-scale oceanic bottom obstructions (shelf breaks, seamounts, canyons and ridges). In this paper, a methodology is provided to compute diagnostics and prognostics for soliton generation and propagation, including the associated currents. The methodology comprises a diagnostic tool which, through the use of a set of theoretical and empirical formulations, selects areas where solitons are likely to occur. These theoretical and empirical formulations include the computation of the integral body force (1), the linear wave theory to compute the phase speed and the empirical model proposed by (2). After the selection procedure, the tool provides initial and boundary conditions for non-hydrostatic numerical models. The numerical models run in 2D-V configuration (vertical slices) with horizontal and vertical resolutions ranging from 50 to 200 m and 5 to 10 m, respectively. Examples are provided for an open ocean location over the Mascarene Plateau in the Indian Ocean. Validation of diagnostics and prognostics are provided against ADCP and satellite data.

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