Dynamics of Bubble Layer Near the Ocean Surface in the Presence of Internal Wave and Langmuir Circulation

2012 ◽  
Vol 9 (1) ◽  
pp. 76-81
Author(s):  
R. Grimshaw ◽  
L.A. Ostrovsky ◽  
A.S. Topolnikov ◽  
K.R. Khusnutdinovs
Keyword(s):  
Wave Propagation ◽  
Internal Wave ◽  
Field Experiments ◽  
Ocean Surface ◽  
Mechanisms Of Action ◽  
Natural Phenomena ◽  
Langmuir Circulation ◽  
Macro Scale ◽  
Bubble Layer

In the paper the evolution of bubble layer near the ocean surface is studied, which is caused by macro-scale movement of liquid layers. As the origin of such movement there studied such nature phenomena as the internal wave propagation along the pycnocline and Langmuir circulation. On the base of the polydisperse model of bubble layer the influence of different mechanisms of action of the bubble’s dynamics are studied in context to the natural phenomena, which are observed in the field experiments.

A multi-layer model for nonlinear internal wave propagation in shallow water

2012 ◽  
Vol 695 ◽  
pp. 341-365 ◽  
Author(s):  
Philip L.-F. Liu ◽  
Xiaoming Wang
Keyword(s):  
Wave Propagation ◽  
Internal Wave ◽  
Shallow Water ◽  
Internal Waves ◽  
Bottom Topography ◽  
Laboratory Data ◽  
Constant Density ◽  
Layer Model ◽  
Fluid System ◽  
Nonlinear Internal Wave

AbstractIn this paper, a multi-layer model is developed for the purpose of studying nonlinear internal wave propagation in shallow water. The methodology employed in constructing the multi-layer model is similar to that used in deriving Boussinesq-type equations for surface gravity waves. It can also be viewed as an extension of the two-layer model developed by Choi & Camassa. The multi-layer model approximates the continuous density stratification by an $N$-layer fluid system in which a constant density is assumed in each layer. This allows the model to investigate higher-mode internal waves. Furthermore, the model is capable of simulating large-amplitude internal waves up to the breaking point. However, the model is limited by the assumption that the total water depth is shallow in comparison with the wavelength of interest. Furthermore, the vertical vorticity must vanish, while the horizontal vorticity components are weak. Numerical examples for strongly nonlinear waves are compared with laboratory data and other numerical studies in a two-layer fluid system. Good agreement is observed. The generation and propagation of mode-1 and mode-2 internal waves and their interactions with bottom topography are also investigated.

Internal wave propagation in an inhomogeneous fluid of non-uniform depth

1969 ◽  
Vol 38 (2) ◽  
pp. 365-374 ◽  
Author(s):  
Joseph B. Keller ◽  
Van C. Mow
Keyword(s):  
Wave Propagation ◽  
Internal Wave ◽  
Experimental Result ◽  
Bottom Surface ◽  
Radius Of Curvature ◽  
Constant Density ◽  
Trapped Waves ◽  
Inhomogeneous Fluid ◽  
Sloping Beach ◽  
Scale Length

An asymptotic solution is obtained to the problem of internal wave propagation in a horizontally stratified inhomogeneous fluid of non-uniform depth. It also applies to fluids which are not stratified, but in which the constant density surfaces have small slopes. The solution is valid when the wavelength is small compared to all horizontal scale lengths, such as the radius of curvature of a wavefront, the scale length of the bottom surface variations and the scale length of the horizontal density variations. The theory underlying the solution involves rays, a phase function satisfying the eiconal equation, and amplitude functions satisfying transport equations. All these equations are solved in terms of the rays and of the solution of the internal wave problem for a horizontally stratified fluid of constant depth. The theory is thus very similar to geometrical optics and its extensions. It can be used to treat problems of propagation, reflexion from vertical cliffs or from shorelines, refraction, determination of the frequencies and wave patterns of trapped waves, etc. For fluid of constant density, it reduces to the theory of Keller (1958). The theory is applied to waves in a fluid with an exponential density distribution on a uniformly sloping beach. The predicted wavelength is shown to agree well with the experimental result of Wunsch (1969). It is also applied to determine edge waves near a shoreline and trapped waves in a channel.

scholarly journals The Partial Reflection of Tsunami-Generated Gravity Waves

2014 ◽  
Vol 71 (9) ◽  
pp. 3416-3426 ◽  
Author(s):  
Dave Broutman ◽  
Stephen D. Eckermann ◽  
Douglas P. Drob
Keyword(s):  
Wave Propagation ◽  
Gravity Wave ◽  
Gravity Waves ◽  
Vertical Profile ◽  
Turning Points ◽  
Lower Thermosphere ◽  
Ocean Surface ◽  
Wave Transmission ◽  
Sumatra Earthquake ◽  
Partial Reflection

Abstract A vertical eigenfunction equation is solved to examine the partial reflection and partial transmission of tsunami-generated gravity waves propagating through a height-dependent background atmosphere from the ocean surface into the lower thermosphere. There are multiple turning points for each vertical eigenfunction (at least eight in one example), yet the wave transmission into the thermosphere is significant. Examples are given for gravity wave propagation through an idealized wind jet centered near the mesopause and through a realistic vertical profile of wind and temperature relevant to the tsunami generated by the Sumatra earthquake on 26 December 2004.

Internal waves in a horizontally inhomogeneous flow

1984 ◽  
Vol 142 ◽  
pp. 233-249 ◽  
Author(s):  
A. Ya. Basovich ◽  
L. Sh. Tsimring
Keyword(s):  
Wave Propagation ◽  
Internal Wave ◽  
Internal Waves ◽  
Short Wave ◽  
Wave Transformation ◽  
Wave Trapping ◽  
Wave Amplification ◽  
Normal Surfaces ◽  
Inhomogeneous Flow ◽  
Horizontally Inhomogeneous

The effect of horizontally inhomogeneous flows on internal wave propagation in a stratified ocean with a constant Brunt-Väisälä frequency is analysed. Dispersion characteristics of internal waves in a moving fluid and kinematics of wave packets in smoothly inhomogeneous flows are considered using wave-normal surfaces. It is shown that internal-wave blocking and short-wave transformation may occur in longitudinally inhomogeneous flows. For parallel flows internal-wave trapping is possible in the vicinity of the limiting layer where the wave frequency in the locally comoving frame of reference coincides with the Brunt-Väisälä frequency. Internal-wave trapping also takes place in jet-type flows in the vicinity of the flow-velocity maximum. WKB solutions of the equation describing internal-wave propagation in a parallel horizontally inhomogeneous flow in the linear approximation are obtained. Singular points of this equation and the related effect of internal-wave amplification (overreflection) under the action of the flow are investigated. The spectrum and the growth rate of internal-wave localized modes in a jet-type flow are obtained.

scholarly journals Inference of biological and physical parameters in an internal wave using multiple-frequency, acoustic-scattering data

2003 ◽  
Vol 60 (5) ◽  
pp. 1033-1046 ◽  
Author(s):  
Joseph D. Warren ◽  
Timothy K. Stanton ◽  
Peter H. Wiebe ◽  
Harvey E. Seim
Keyword(s):  
Internal Wave ◽  
Field Experiments ◽  
Gulf Of Maine ◽  
Acoustic Scattering ◽  
Primary Source ◽  
Theoretical Work ◽  
Scattering Data ◽  
Physical Parameters ◽  
Multiple Frequency ◽  
Scattering Spectra

Abstract High-frequency sound (>10 kHz) is scattered in the ocean by many different processes. In the water column, marine organisms are often assumed to be the primary source of acoustic backscatter. Recent field experiments and theoretical work suggest that the temperature and salinity microstructure in some oceanic regions could cause acoustic scattering at levels comparable to that caused by marine life. Theoretical acoustic-scattering models predict that the scattering spectra for microstructure and organisms are distinguishable from each other over certain frequency ranges. A method that uses multiple-frequency acoustic data to exploit these differences has been developed, making it possible to discriminate between biological and physical sources of scattering under some conditions. This method has been applied to data collected in an internal wave in the Gulf of Maine. For regions of the internal wave in which the dominant source of scattering is either biological or physical in origin, it is possible to combine the acoustic-scattering data and temperature and salinity profiles with acoustic-scattering models to perform a least-squares inversion. Using this approach, it is possible to estimate the dissipation rate of turbulent kinetic energy for some regions of the internal wave, and the length and numerical abundance of the dominant biological scatterer, euphausiids, in others.

On acoustic transmission in ocean-surface waveguides

1991 ◽  
Vol 335 (1639) ◽  
pp. 513-555 ◽  
Keyword(s):  
Arctic Ocean ◽  
Wave Breaking ◽  
Sound Speed ◽  
Ocean Surface ◽  
Sea Surface ◽  
Speed Profile ◽  
Sound Speed Profile ◽  
Arrival Times ◽  
Extinction Depth ◽  
Bubble Layer

A sound speed profile which increases monotonically with depth below the ocean surface is upward-refractive, acting as a duct in which sound may be transmitted to long ranges with little attenuation. A well-known example is the mixed layer, in which the temperature is uniform and the sound speed approximately scales with the hydrostatic pressure, increasing linearly with depth. The depth of the mixed layer depends on surface conditions, but is of the order of 100 m. Deeper channels are found in ice-covered polar waters, where the temperature and sound speed profiles both show a minimum at the surface. A typical surface duct in the Arctic Ocean may extend to depths of 1000 m or more and is capable of supporting very-low-frequency (VLF) (1-50 Hz) acoustic transmissions with no bottom interactions. On a depth scale that is smaller by several orders of magnitude, wave-breaking events create a bubbly layer one or two metres thick below the sea surface, with the highest concentration of bubbles, and correspondingly the lowest sound speed, at the surface. The bubble layer acts as a waveguide for sound in the audio frequency range, above 2 kHz, although transmission may be severely attenuated due to absorption and scattering by the bubbles, as well as by the irregular geometry of the sea surface and the bubble clouds. Most ocean-surface waveguides can be accurately represented by an inverse-square sound speed profile, which may be monotonic increasing (upward refracting) or decreasing (downward refracting) with depth, and whose detailed shape is governed by just three parameters. An analysis of the sound field below the sea surface in the presence of such a profile shows that it consists of a near-field component, given by a branch-line integral, plus a sum of uncoupled normal modes representing the trapped radiation which propagates to longer ranges. The modal contribution is identically zero in the case of the downward refracting profiles. The properties of the modes emerge from a straightforward theoretical development involving first- and second-order asymptotics: each mode shows an oscillatory region immediately below the surface, terminating at the extinction depth, below which the mode decays exponentially to zero; the extinction depth increases rapidly with both mode number and the reciprocal of the acoustic frequency; a reciprocal relationship exists between the extinction depth and the mode strength; and there is no mode cutoff, nor are there any evanescent modes. On applying the inverse-square theory to VLF Arctic Ocean transmissions, the spectral density of the modal field is found to show a steep positive gradient between 5 and 50 Hz, the rising level occurring as more modes make a significant contribution to the field. This result is compared with observations of infra-sonic ambient noise that have been made in the marginal ice zone of the Greenland Sea, using surface suspended, flow-shielded hydrophones. The measured spectra show a deep minimum at about 5 Hz, in accord with the theoretical prediction. The inverse-square theory also has application to under-ice ocean-acoustic tomography, where the dispersive nature of the upward refractive channel governs the arrival times of the modes at the receivers. A simple expression for the group velocity of the modes gives the arrival times. More generally, the full modal structure of the field across the tomography array may be constructed from the theory. Acoustic signatures of wave-breaking events have recently been observed in the ocean-suiface bubble layer by farmer & Vagle (1989). The spectra show well-defined peaks (La Perouse) or a broader-band structure (FASINEX), both of which are fully explained, in terms of intermode interference, by the inverse-square theory. The differences between the two data-sets are attributed to the different sound speed profiles in the bubble layers at the two sites. The spectral banding in fasinex is a modulation phenomenon, showing a strong dependence on the source depth. A straightforward inverse calculation indicates that the bubble sources in fasinex are located at a depth of 1.5 m, corresponding roughly to the base of the bubble layer, this is a slightly unexpected conclusion, since acoustically active bubbles generated by spilling breakers under wind-free conditions in a laboratory tank are known to be located within a few millimetres of the surface. However, aeration is much more pronounced at the wind-driven surface of the ocean than in a tank, which may be a factor in accounting for the deeper sources. There are practical difficulties in measuring the source distribution using conventional techniques, but the inverse-square transmission theory in conjunction with near-surface measurements of wave-breaking signatures provides an effective means of making such a determination.

Sign in / Sign up

Export Citation Format

Share Document