scholarly journals Strongly nonlinear, simple internal waves in continuously-stratified, shallow fluids

2011 ◽  
Vol 18 (1) ◽  
pp. 91-102 ◽  
Author(s):  
L. A. Ostrovsky ◽  
K. R. Helfrich

Abstract. Strongly nonlinear internal waves in a layer with arbitrary stratification are considered in the hydrostatic approximation. It is shown that "simple waves" having a variable vertical structure can emerge from a wide class of initial conditions. The equations describing such waves have been obtained using the isopycnal coordinate as a variable. Emergence of simple waves from an initial Gaussian impulse is numerically investigated for different density profiles, from two- and three-layer structure to the continuous one. Besides the first mode, examples of second- and third-mode simple waves are given.

2003 ◽  
Vol 15 (10) ◽  
pp. 2934 ◽  
Author(s):  
Lev A. Ostrovsky ◽  
John Grue

2011 ◽  
Vol 41 (5) ◽  
pp. 994-1008 ◽  
Author(s):  
W. J. Teague ◽  
H. W. Wijesekera ◽  
W. E. Avera ◽  
Z. R. Hallock

Abstract Closely spaced observations of nonlinear internal waves (NLIWs) were made on the outer continental shelf off New Jersey in June 2009. Nearly full water column measurements of current velocity were made with four acoustic Doppler current profilers (ADCPs) that were moored about 5 km apart on the bottom along a line approximately normal to the bathymetry between water depths of 67 and 92 m. Density profiles were obtained from two vertical strings of temperature and conductivity sensors that were deployed near each of the interior ADCP moorings. In addition, a towed ScanFish provided profiles and fixed-level records of temperature and salinity through several NLIW packets near the moorings. Several case studies were selected to describe the propagation of the NLIWs. One to three solitary waves of depression were observed in five selected packets. There were also occurrences of multiple-phase dispersive wave packets. The average propagation speed corrected for advection of the observed waves was 0.51 ± 0.09 m s−1. The waves were directed primarily shoreward (~northwestward) along the mooring line with average wavelengths and periods of about 300 m and 10 min, respectively. Wave amplitudes and energies decreased with decreasing water depth. The observed wave parameters can be locally described by a two-layer Korteweg–de Vries (KdV) model, except for the decreasing amplitudes, which may be due to shear-induced dissipation and/or bottom drag. The various complementary observations utilized in this study present a unique description of NLIWs.


2021 ◽  
Vol 11 (1) ◽  
Author(s):  
R. Mendes ◽  
J. C. B. da Silva ◽  
J. M. Magalhaes ◽  
B. St-Denis ◽  
D. Bourgault ◽  
...  

AbstractInternal waves (IWs) in the ocean span across a wide range of time and spatial scales and are now acknowledged as important sources of turbulence and mixing, with the largest observations having 200 m in amplitude and vertical velocities close to 0.5 m s−1. Their origin is mostly tidal, but an increasing number of non-tidal generation mechanisms have also been observed. For instance, river plumes provide horizontally propagating density fronts, which were observed to generate IWs when transitioning from supercritical to subcritical flow. In this study, satellite imagery and autonomous underwater measurements are combined with numerical modeling to investigate IW generation from an initial subcritical density front originating at the Douro River plume (western Iberian coast). These unprecedented results may have important implications in near-shore dynamics since that suggest that rivers of moderate flow may play an important role in IW generation between fresh riverine and coastal waters.


2010 ◽  
Vol 10 (21) ◽  
pp. 10639-10654 ◽  
Author(s):  
C. S. Bretherton ◽  
R. Wood ◽  
R. C. George ◽  
D. Leon ◽  
G. Allen ◽  
...  

Abstract. Multiplatform airborne, ship-based, and land-based observations from 16 October–15 November 2008 during the VOCALS Regional Experiment (REx) are used to document the typical structure of the Southeast Pacific stratocumulus-topped boundary layer and lower free troposphere on a~transect along 20° S between the coast of Northern Chile and a buoy 1500 km offshore. Strong systematic gradients in clouds, precipitation and vertical structure are modulated by synoptically and diurnally-driven variability. The boundary layer is generally capped by a strong (10–12 K), sharp inversion. In the coastal zone, the boundary layer is typically 1 km deep, fairly well mixed, and topped by thin, nondrizzling stratocumulus with accumulation-mode aerosol and cloud droplet concentrations exceeding 200 cm−3. Far offshore, the boundary layer depth is typically deeper (1600 m) and more variable, and the vertical structure is usually decoupled. The offshore stratocumulus typically have strong mesoscale organization, much higher peak liquid water paths, extensive drizzle, and cloud droplet concentrations below 100 cm−3, sometimes with embedded pockets of open cells with lower droplet concentrations. The lack of drizzle near the coast is not just a microphysical response to high droplet concentrations; smaller cloud depth and liquid water path than further offshore appear comparably important. Moist boundary layer air is heated and mixed up along the Andean slopes, then advected out over the top of the boundary layer above adjacent coastal ocean regions. Well offshore, the lower free troposphere is typically much drier. This promotes strong cloud-top radiative cooling and stronger turbulence in the clouds offshore. In conjunction with a slightly cooler free troposphere, this may promote stronger entrainment that maintains the deeper boundary layer seen offshore. Winds from ECMWF and NCEP operational analyses have an rms difference of only 1 m s−1 from collocated airborne leg-mean observations in the boundary layer and 2 m s−1 above the boundary layer. This supports the use of trajectory analysis for interpreting REx observations. Two-day back-trajectories from the 20° S transect suggest that eastward of 75° W, boundary layer (and often free-tropospheric) air has usually been exposed to South American coastal aerosol sources, while at 85° W, neither boundary-layer or free-tropospheric air has typically had such contact.


2006 ◽  
Vol 03 (02) ◽  
pp. 269-295 ◽  
Author(s):  
OLIVIER GUES ◽  
JEFFREY RAUCH

Semilinear hyperbolic problems with source terms piecewise smooth and discontinuous across characteristic surfaces yield similarly piecewise smooth solutions. If the discontinuous source is replaced with a smooth transition layer, the discontinuity of the solution is replaced by a smooth internal layer. In this paper we describe how the layer structure of the solution can be computed from the layer structure of the source. The key idea is to use a transmission problem strategy for the problem with the smooth internal layer. That leads to an anastz different from the obvious candidates. The obvious candidates lead to overdetermined equations for correctors. With the transmission problem strategy we compute infinitely accurate expansions.


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