Vaisala frequency is modelled such that it varies from a constant value outside of the core to zero inside the core over a sharp but continuous transition length.
The lack of stable trapped cores in the field can be explained by the results from dynamic simulations of ISWs with trapped cores which demonstrate that even slight disturbances of the background stratification cause trapped cores to become unstable.
The comparison of the model results with the field observations indicates that the simulated limiting amplitude of the ISWs provides an excellent prediction of the critical wave height above which ISWs break in the field.
This is a somewhat different point of view than that adopted in the recent literature on shear instability in ISWs.
Moreover, there is a linear relationship between wave amplitude and billow growth rate, with increases in wave amplitude resulting in increases in billow growth rate.
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The numerical scheme is not limited by small Richardson number unlike the other alternatives currently available in the literature which appear to be.
However these studies either considered laboratory scales, which do not clearly correspond to the situation in our field measurements (a different stratification, in particular), or focused on instances of strong billow formation in a thermocline located well below the surface.
Shear instabilities and convective instabilities are each responsible for about half of the predicted wave breaking events.
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Our approach is both analytical and numerical; a model valid for relatively thin pycnoclines and suitable for local spectral analysis is devised and used.
Once in the water, Redmond meditated on his children to give him the motivation to complete each swim.
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Redmond and his impressive accomplishments were also featured in the television series Explorers: Adventures of the Century.
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Redmond was able to achieve his Oceans Seven accomplishment, in part, with funds raised through his own Facebook page.
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The Tsugaru Channel was more of a challenge, Redmond stated, due to strong currents and opposing winds creating a powerful tidal flow.
The results are validated against direct numerical simulations and traveling wave exact solutions where the effect of the diffused interface is taken into account.
The complex combination of these modes is shown in the examples: spatially in the video data (Figure 1b) and temporally at discrete locations in the wave gauge data (Figure 1c).
The strength of the stratification in the very top layer is chosen to be sufficient so that waves of depression with trapped cores can be generated.
Our results are representative of geophysical applications in the deep ocean where weakly nonlinear theories fail to capture the characteristics of large amplitude ISWs from field observations.
Despite his extraordinary achievement in being the first person to complete the Oceans Seven, he remains humble.
Energy diagnostics on the simulations are implemented to validate the numerics and illustrate the energy exchanges between background wave flow and its shear.
After Redmond, only five others have completed the Oceans Seven: Anna Carin Nordin, Michelle Macy, Darren Miller, Adam Walker and Kimberly Chambers.
If the instability in the vorticity field is energetic enough, disturbance in the buoyancy field is also seen and fluid exchange takes place across the core boundary.
Helmholtz billows is attributed to the sharp change in the vorticity field at the boundary between the core and the pycnocline.
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In molecular dynamics, by contrast, despite the large numbers of degrees of freedom, structured states are extremely improbable.
The waves are generated by means of a dam break and their evolution is recorded with Laser Induced Fluorescence (LIF) and Particle Image Velocimetry (PIV).
We observe these directly in weather patterns, in the zonal jets on Jupiter and the Great Red Spot, in sunspots and magnetic coronal loops, etc.
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Furthermore, it is proved that if this vorticity is initially zero everywhere in space, then it will remain so for all time.
This results in a stagnant core in which the vorticity is zero and the density is homogeneous and approximately equal to that at the core boundary.
Such fluids and plasmas are very large order dynamical systems, and therefore appear to have ample freedom to explore near endless states or configurations.
Moreover, there is a linear relationship between wave amplitude and billow propagation speed, with increases in wave amplitude resulting in decreases in billow propagation speed.
