Implications of conservation equations for the determination of absolute velocities

The consequences of assuming that density is conserved in the problem of determining absolute velocities are investigated. Two questions are considered: (i) the constraints that the density must satisfy to be compatible with the assumed geostrophic and hydrostatic dynamics and (ii) whether and to what extent the indeterminacy in this dynamics is removed by this additional assumption

Internal solitary waves in the ocean: Analysis using the periodic, inverse scattering transform

The periodic, inverse scattering transform (PIST) is a powerful analytical tool in the theory of integrable, nonlinear evolution equations. Osborne pioneered the use of the PIST in the analysis of data form inherently nonlinear physical processes. In particular, Osborne's so-called nonlinear Fourier analysis has been successfully used in the study of waves whose dynamics are (to a good approximation) governed by the Korteweg--de Vries equation. In this paper, the mathematical details and a new application of the PIST are discussed. The numerical aspects of and difficulties in obtaining the nonlinear Fourier (i.e., PIST) spectrum of a physical data set are also addressed. In particular, an improved bracketing of the "spectral eigenvalues" (i.e., the +/-1 crossings of the Floquet discriminant) and a new root-finding algorithm for computing the latter are proposed. Finally, it is shown how the PIST can be used to gain insightful information about the phenomenon of soliton-induced acoustic resonances, by computing the nonlinear Fourier spectrum of a data set from a simulation of internal solitary wave generation and propagation in the Yellow Sea.Comment: 10 pages, 4 figures (6 images); v2: corrected a few minor mistakes and typos, version accepted for publication in Math. Comput. Simu

Wind-driven secondary circulation in ocean mesoscale

A two-dimensional, numerical circulation model is used to study the response of a stratified, f-plane ocean current to wind stress forcing at the surface. Nonhydrostatic, primitive equations are integrated on a 3 m vertical and 400 m horizontal grid in a periodic domain perpendicular to the ocean current. Initially, a geostrophically balanced current [Vi(x, z)] with a maximum Rossby number of 0.16–0.8 is maintained against horizontal and vertical diffusion by a body force. A spatially uniform wind is applied along and across this jet. A secondary circulation is created as a result of the nonlinear interaction between the jet and wind-driven flow in the Ekman layer. We present results from seven numerical experiments. When the wind blows in the direction of the jet (against the jet), a narrow upwelling (downwelling) area and broad downwelling (upwelling) area are formed. This secondary circulation pattern extends well below the mixed layer. When the wind blows perpendicular to the jet, the secondary circulation does not extend below the mixed layer. The fully nonlinear secondary circulation is 50% weaker than the circulation produced by the semi-linearized calculation around the basic state, Vi. Near-inertial fluctuations appear and are confined to the negative relative vorticity side of the circulation (dV/dx \u3c 0). The time-averaged vertical velocity can be as high as 1.5 m/day with a wind stress of 1 dyne/cm2 over a jet and a maximum Rossby number of 0.16. The magnitude of the vertical circulation in this symmetric basic state is dependent on the Rossby number and the horizontal and vertical mixing coefficients

Shoaling of large-amplitude nonlinear internal waves at Dongsha Atoll in the northern South China Sea

Author Posting. © The Author(s), 2012. This is the author's version of the work. It is posted here by permission of Elsevier B.V. for personal use, not for redistribution. The definitive version was published in Continental Shelf Research 37 (2012): 1-7, doi:10.1016/j.csr.2012.01.010.Shoaling of large-amplitude (~100 m) nonlinear internal waves over a steep slope (~3°) in water depths between 100 m and 285 m near Dongsha Atoll in the northern South China Sea is examined with an intensive array of thermistor moorings and a bottom mounted Acoustic Doppler Current Profiler. During the 44 h study period in May 5–7, 2008, there were four groups of large internal waves with semidiurnal modulation. In each wave group a rapid transition occurred during the shoaling, such that the front face of the leading depression wave elongated and plunged to the bottom and the rear face steepened and transformed into a bottom-trapped elevation wave. The transitions occur in water depths of 200 m and deeper, and represent the largest documented internal wave shoaling events. The observations repeatedly capture the detailed temperature and velocity structures of the incident plunging waves. Strong horizontal convergence and intense upward motion are found at the leading edge of transformed elevation waves, suggesting flow separation near the bottom. The observations are compared with the previous observations and model studies. The implication of the shoaling internal waves on coral reef ecology also is discussed.Support for LS and HS came from the US Office of Naval Researc

Observations and simulation of a bottom Ekman layer on a continental shelf

A numerical model was used to simulate the bottom Ekman layer of a continental shelf region. The basis for the model was the Mellor and Yamada level 2 « turbulence closure scheme. Conservation equations for momentum, turbulent kinetic energy, and turbulent length scale were utilized in the model. The model was used to simulate data taken from a Cyclesonde mooring on the Peruvian continental shelf in May 1976 as part of the Joint II Coastal Upwelling Ecosystems Analysis program. The Cy-clesonde provided mean horizontal velocity, temperature, salinity, and pressure data. An intense pole-ward undercurrent drove the bottom flow regime. The most striking feature of the data was the clockwise Ekman veering of velocity vectors as the bottom was approached. A 48-hour period was chosen for the model simulations. The vertical profile of speed (48 hours mean) simulated by the model fell within the error bars of the data. The corresponding Ekman spiral display of the model results also showed good agreement with the observati. ons

A finite-volume module for simulating global all-scale atmospheric flows

This paper was accepted for publication in the Journal of Computational Physics and the definitive published version is available at http://dx.doi.org/10.1016/j.jcp.2016.03.015.The paper documents the development of a global nonhydrostatic finite-volume module designed to enhance an established spectral-transform based numerical weather prediction (NWP) model. The module adheres to NWP standards, with formulation of the governing equations based on the classical meteorological latitude-longitude spherical framework. In the horizontal, a bespoke unstructured mesh with finite-volumes built about the reduced Gaussian grid of the existing NWP model circumvents the notorious stiffness in the polar regions of the spherical framework. All dependent variables are co-located, accommodating both spectral-transform and grid-point solutions at the same physical locations. In the vertical, a uniform finite-difference discretisation facilitates the solution of intricate elliptic problems in thin spherical shells, while the pliancy of the physical vertical coordinate is delegated to generalised continuous transformations between computational and physical space. The newly developed module assumes the compressible Euler equations as default, but includes reduced soundproof PDEs as an option. Furthermore, it employs semi-implicit forward-in-time integrators of the governing PDE systems, akin to but more general than those used in the NWP model. The module shares the equal regions parallelisation scheme with the NWP model, with multiple layers of parallelism hybridising MPI tasks and OpenMP threads. The efficacy of the developed nonhydrostatic module is illustrated with benchmarks of idealised global weather

Two-dimensional numerical simulations of shoaling internal solitary waves at the ASIAEX site in the South China Sea

The interaction of barotropic tides with Luzon Strait topography generates some of the world's largest internal solitary waves which eventually shoal and dissipate on the western side of the northern South China Sea. Two-dimensional numerical simulations of the shoaling of a single internal solitary wave at the site of the Asian Seas International Acoustic Experiment (ASIAEX) have been undertaken in order to investigate the sensitivity of the shoaling process to the stratification and the underlying bathymetry and to explore the influence of rotation. The bulk of the simulations are inviscid; however, exploratory simulations using a vertical eddy-viscosity confined to a near bottom layer, along with a no-slip boundary condition, suggest that viscous effects may become important in water shallower than about 200 m. A shoaling solitary wave fissions into several waves. At depths of 200–300 m the front of the leading waves become nearly parallel to the bottom and develop a very steep back as has been observed. The leading waves are followed by waves of elevation (pedestals) that are conjugate to the waves of depression ahead and behind them. Horizontal resolutions of at least 50 m are required to simulate these well. Wave breaking was found to occur behind the second or third of the leading solitary waves, never at the back of the leading wave. Comparisons of the shoaling of waves started at depths of 1000 and 3000 m show significant differences and the shoaling waves can be significantly non-adiabatic even at depths greater than 2000 m. When waves reach a depth of 200 m, their amplitudes can be more than 50% larger than the largest possible solitary wave at that depth. The shoaling behaviour is sensitive to the presence of small-scale features in the bathymetry: a 200 m high bump at 700 m depth can result in the generation of many mode-two waves and of higher mode waves. Sensitivity to the stratification is considered by using three stratifications based on summer observations. They primarily differ in the depth of the thermocline. The generation of mode-two waves and the behaviour of the waves in shallow water is sensitive to this depth. Rotation affects the shoaling waves by reducing the amplitude of the leading waves via the radiation of long trailing inertia-gravity waves. The nonlinear-dispersive evolution of these inertia-gravity waves results in the formation of secondary mode-one wave packets

Internal gravity waves in the Strait of Luzon: Dispersion studies using Fourier and continuous wavelet transforms

Investigation of the dynamics of internal gravity waves often includes the interrelationship between wave amplitudes, wave speeds, and wavelengths. These relationships are commonly thought of as dispersion relations. Because internal gravity waves are the result of nonlinear dynamics dispersion relations are a challenge to obtain in a quantitative sense. Model data for internal gravity waves in the Strait of Luzon are examined using Fourier and continuous wavelet transforms. Dispersion is qualitatively evident in the results and the investigation is extended to include quantitative assessment of the dispersion. The results are compared to results from Korteweg D'Vries theory. Good agreement is obtained for dispersion estimates using wavelet analysis and those from KdV theory