Sea Of Constant Depth Research Articles

Generation of a Vertical Fine Structure by Internal Waves on the Sea Shelf

Free internal waves are considered in the Boussinesq approximation with account of horizontal turbulent viscosity and diffusion in a two-dimensional flow in the sea of constant depth. In the linear approximation the boundary-value problem for the amplitude of vertical velocity has complex coefficients and is solved numerically using the third-order implicit Adams method. The vertical component of the Stokes drift velocity and the vertical wave fluxes of mass and salt are found in the second order in the wave amplitude. These fluxes lead to generation of a vertical fine structure that has an irreversible nature.

On the propagation of acoustic–gravity waves due to a slender rupture in an elastic seabed

The propagation of waves from a vertical uplift of a slender rectangular fault in a sea of constant depth is discussed, accounting for water compressibility, gravity and seabed elasticity. The compressed water column results in the generation of acoustic–gravity waves that travel at the speed of sound in water. Acoustic–gravity waves are found to terminate after a finite time, with the decay time most influenced by seabed rigidity, which is in contrast to the rigid stationary-phase model where signals persist indefinitely. At certain frequencies acoustic–gravity waves couple with the elastic seabed and travel at the shear velocity (speed of sound in an elastic solid). Improved estimates of the critical frequencies are derived. Moreover, besides the usual tsunami, a second – very small amplitude – surface wave mode travelling at the speed of sound arises under certain frequencies. We derive the cut-off frequency for this mode. The acoustic modes possess a frequency spectrum which depends on the time evolution and spatial properties of the rupture. We find that appropriate filtering of the acoustic–gravity wave signal can reveal characteristic peaks that encode information on the fault's geometry and dynamics.

Acoustic–gravity waves from multi-fault rupture

Abstract

Asymptotic analysis of dispersive tsunami from a slender fault

An approximate theory is developed for the two-dimensional propagation of tsunami emanated from a slender fault of fine length. Assuming significant contrasts between the sea depth, fault width, fault length and the bathymetric length scales, we invoke parabolic approximation to deduce a linear Kademtsev-Petviashivili (K-P) equation governing the two-dimensional propagation of dispersive long waves over great distances. Analytical techniques are employed to explore the far-field radiation in the forward and spanwise directions in a sea of constant depth. The solution can be used as a convenient input for predicting local variations of wave scattering and possibly breaking along a coast.

A Cliffed Cape Does Not Trap Water Waves in the Sea of Constant Depth

The water wave problem is considered for a class of semi-infinite domains each having its shore shaped as a cliffed cape. In particular, the free surface of a water domain is supposed to be an infinite sector whose vertex angle is greater than π, whereas the water layer lying under the free surface is of constant depth. Under these assumptions it is shown that there are no trapped mode solutions of the problem for all values of a non-dimensional spectral parameter; in other words, no point eigenvalues are embedded in the continuous spectrum of the problem.

An Analytic Solution for Wave Scattering by a Circular Cylinder Mounted on a Conical Shoal

In this paper, the combined refraction-diffraction of plane monochromatic waves by a circular cylinder mounted on a conical shoal in an otherwise open sea of constant depth is solved analytically based on the mild-slope equation. At first, Hunt's approximate direct solution for the wave dispersion equation [Hunt, 1979] is used to transform the mild-slope equation with implicit coefficients into an equation with all coefficients being explicitly expressed. This equation is then solved analytically in terms of combined Fourier series and Taylor series. Comparisons are made between the present method and the analytical solutions based on the linear shallow-water equation [Zhu and Zhang, 1996] and the Helmholtz equation [MacCamy and Fuchs, 1954] for long waves and short waves, respectively, and excellent agreements are obtained. For waves in intermediate water depth, comparisons are made with numerical results based on the mild-slope equation and an equally good quality of agreement is achieved. By varying the shoal size, it is found that the wave amplification normally enhances with the increase of shoal, due to the increased contribution from wave refraction. For relatively short wave, the trapped waves by refraction in front of the island interact with the reflected waves and form the partial-standing waves there.

Second-order refraction and diffraction of surface water waves

The mild-slope equation is an effective approximation for treating the combined effects of refraction and diffraction of infinitesimal water waves, for it reduces the spatial dimension of the linear boundary-value problem from three to two. We extend this approximation to nonlinear waves up to the second order in wave steepness, in order to simplify the inherently three-dimensional task. Assuming that the geometrical complexity is restricted to a finite, though large, horizontal domain, the hybrid-element method designed earlier for linearized problems is modified for the two-dimensional elliptic boundary-value problems at the second order. In the special case of a semi-circular peninsula (or a vertical cylinder on a cliff) in a sea of constant depth, the solution is analytical. Effects of the angle of incidence are examined for the free-surface height along the cylinder. For a cylinder standing on a shoal of radially varying depth, numerical results are discussed.

Variation of the polarization characteristics of electromagnetic waves in a horizontally-inhomogeneous environment

The paper considers the propagation of the electromagnetic fields having a range of tens of cycles per second in a horizontally-inhomogeneous ocean. The TM-wave characteristics in the presence of a horizotal conductivity jump are estimated. The amplitudinal and phase values of the electric intensity's vertical component are provided for various conductivities of a two-segment sea of constant depth. A conclusion is made that marine environment inhomogeneities can he studied through electromagnetic techniques.

Laboratory Models of Bay-Type Continental Shelves in the Winter

Abstract A laboratory experiment consisting of a shallow sea of constant depth bounded by a deep ocean through a uniformly sloping continental rise was conducted. The experiment is cooled from above, and there is a region that exhibits sinking convection cells which form the coldest water. This water then spills off the rhs of the shallow sea as a density current (looking downstream for counterclockwise rotation) and forms bottom water in the deep experimental ocean. There are three regimes: for very slow (scaled) rotations there is one big gyre in the shallow sea, and the sinking (convection) region is near the coast; for faster rotations, there are two or three gyres, and for even faster rotations, there are many gyres. In this latter case, the sinking regions are very patchy and sporadic. Comparison with theoretical estimates of temperature difference between the coldest shelf water and the offshore water (based upon the assumption that the density current removes all the cold water) was good but yield...

Laboratory models of circulation in shallow seas

Three laboratory experiments are described. The first was made to observe the flow field of circulation in a model given by Stommel & Leetmaa (1972). The experiment consisted of a very shallow (1 or 2 cm deep) annulus with an inner heated wall of radius 25 cm and a cooled outer wall of radius 57 cm, all mounted on a turntable. When the Ekman number was large the flow was steady and resembled the solutions for a non-rotating estuary given by Hansen & Rattray (1965), but when the Ekman number was small the flow became time-dependent. Values of shear and stratification obtained from theory indicate that the flowing water probably underwent baroclinic instability. It appears that such instability may develop on real shelves. The second experiment consisted of a shallow sea of constant depth bounded by a deep ocean through a uniformly sloping continental rise. The experiment is cooled from above and there is a region that exhibits sinking convection cells, which form the coldest water. This water then spills off the right-hand side of the shallow sea (looking downstream for counterclockwise rotation) and forms bottom water in the deep experimental ocean. The third experiment is a rotating version of the dam-break problem in which a density current is generated after a barrier has been removed. The rotation causes the current to lean against the right-hand wall (looking downstream for counterclockwise rotation) and turbulent eddies are detrained to the side rather than vertically.

Storm surges in stratified seas

The theory of storm surges along a straight coast in case of a continuously stratified sea of constant depth is considered. The stratification is shown to have no appreciable effect on the surge at the coast, which therefore is mainly a barotropic response. The internal response at the coast which depends strongly on stratification is found to be extremely sensitive to how the turbulent stress depends on depth. Moreover, it is argued that in relatively deep water the internal response is substantially influenced by bottom friction, whereas the storm surge is not. A solution based on this assumption is presented. DOI: 10.1111/j.2153-3490.1979.tb00912.x

Longshore circulation around a conical island

This paper is concerned with the averaged circulation caused by waves breaking along the beach of a constant slope around a circular island in a sea of constant depth. It is reasoned that the refraction pattern determines the extent of longshore circulation. In particular, for an island so large that there is a lee shore which is not affected by the refracting waves, two current cells are found on two sides of the island with respect to the wave direction, without significant penetration in the lee shore region. This enhances the creation of two sand spits which may grow to form a looped bar, or two tombolos to connect with the neighboring mainland. For an island so small that the extent of the lee shore vanishes, the two current cells collide at the center of the island lee and form a single rip current. This is used to explain the presence of a single tombolo.