On an inverse problem of ship-induced internal waves

An inverse problem for trapped internal waves is considered in an attempt to provide a practical tool for estimating the density stratification in the sea from the wake pattern behind a moving vessel. The ambient stratification is represented by Barber's (1993) exponential series and the coefficients are found by matching the first mode dispersion relation to the one found from the wake data. A fast algorithm for calculating the dispersion relation is derived. It is shown that when the series converges with a low number of coefficients, the inverse profile is adequate, as happens for example for typical sea loch profiles. In more general circumstances the predicted maximum stratification still provides a reasonable approximation as a result of Barber's (1993) theorem.     

On an inverse problem of ship-induced internal waves

An inverse problem for trapped internal waves is considered in an attempt to provide a practical tool for estimating the density stratification in the sea from the wake pattern behind a moving vessel. The ambient stratification is represented by Barber's (1993) exponential series and the coefficients are found by matching the first mode dispersion relation to the one found from the wake data. A fast algorithm for calculating the dispersion relation is derived. It is shown that when the series converges with a low number of coefficients, the inverse profile is adequate, as happens for example for typical sea loch profiles. In more general circumstances the predicted maximum stratification still provides a reasonable approximation as a result of Barber's (1993) theorem.     

声学法深海热液速度场测量重建算法研究

介绍了利用声学法测量深海热液速度场的基本原理.利用往返飞渡时间差与流场速度的关系,应用反问题求解技术重建测量区域的速度场.应用最小二乘法对两种典型的热液口速度场模型进行了仿真重建,分析了换能器数量、实验测量误差以及换能器的布放对重建结果的影响,并对重建结果进行了流量分析.仿真重建的绝对误差、相对误差以及流量分析结果表明...     

An inverse method for reconstructing the density and sound speed profiles of a layered ocean bottom

A standard inverse problem in underwater acoustics is the reconstruction of the ocean subbottom structure (e.g., the density and sound speed profiles) from an aperture- and bandlimited knowledge of the reflection coefficient. In this paper we describe an inverse solution method due to Candel et al. [12] which is based on the scattering of acoustic plane waves by a one-dimensional inhomogeneous medium. As a consequence of applying the forward scattering approximation to a local wave representation of the acoustic field, they obtain an expression for the reflection coefficient in the form of a nonlinear Fourier transform of the logarithmic derivative of the local admittance. Inversion of this integral transform enables the recovery of the admittance profile via the numerical integration of two first-order differential equations which require as reflection data a single impulse response of the medium. Separate recovery of both the density and sound speed profiles requires two impulse responses for two different grazing angles. In this case, four differential equations need to be integrated instead of two. To illustrate the capability of the method, we present numerical reconstructions which are based on synthetic reflection data for a geoacoustic model that represents the acoustic properties of the surficial sediments for a site in the Hatteras Abyssal Plain.     

Generation of quasiinertial internal waves in the process of evolution of local perturbations in the ocean

Within the framework of a linear model of long waves in a two-layer ocean, we obtain the analytic solution of the problem of evolution of an axially symmetric initial displacement of the jump of density. In the process of adaptation of the fields, internal waves in the form of a decaying (in time) wave packet are emitted from the zone of initial perturbation. These waves are quasiinertial and their dispersion is conditioned by Earth’s rotation. We study the time evolution of the wave packet and the dependence of its characteristics on the width of the zone of initial perturbation and the depth of the jump of density. __________ Translated from Morskoi Gidrofizicheskii Zhurnal, No. 2, pp. 12–23, March–April, 2006.     

提高航迹计算精度的方法研究

分析了传统的航迹计算方法存在的系统误差,引入了符号形式的子午线弧长正反解公式,推导出了可以消除该误差进而提高航迹计算精度的精确墨卡托航法。算例分析表明,该方法可以解决航海上不同地球参考椭球下的航迹计算问题,反解精度高达10^-4 m。     

Similitude of the hydraulic model experiment for tidal mixing

The treatment of diffusion due to the tidal current in the near-shore ocean, and the similitude in the hydraulic model experiment are studied.In broad and shallow tidal bays and in the coastal seawaters near irregular boundaries, horizontal eddy-currents induced geometrically and turbulence caused by their cascading have predominant effect on dispersion of river and waste waters. These turbulent diffusion processes are similarly reproduced in the Froude models of turbulent resume, by adding the similitude for the self-similar structure of the spectral density of turbulence, or the eddy diffusivity. The similitude means to take the scale ratios of the time and the vertical length as the two-thirds power of the scale ratio of the horizontal length.Similitudes are also derived for the system of the gravitational circulation, the stratification and the salt-mass transport in partially and well-mixed estuaries. Generally, the vertical eddy diffusivity must be exaggerated by a half power of the model distortion externally by some methods of agitation. When the tidal bay is broad and very shallow, the Rayleigh number and the Hansen number are small, and the effect of density current and stratification on the flushing is small. Instead the effect of local eddies, geometrically induced tidal residual circulations become predominant. In this special case, there is no need to satisfy the similitude for density difference and vertical shear effects on dispersion.     

Nonlinear effects occurring during the propagation of trapped topographic waves

Baroclinic topographic waves trapped by a sloping bottom in the case of a real stratification are considered. The dispersion properties of these waves are studied. The characteristic scales and amplitudes of trapped topographic waves observed in the Norwegian Sea are determined. The asymptotic method of multi-scale expansions is used to study nonlinear effects occurring during the propagation of these waves. The wave-induced mean flow is determined in the second order of smallness in the wave amplitude. The evolution equation for the envelope—the nonlinear Schrödinger equation—is derived. Modulation instability of these waves is examined. It is shown that trapped topographic waves are modulationally unstable.     

Retrieving of the biooptical characteristics of Black-Sea waters under the conditions of constant reflectance at a wavelength of 400 nm

We consider a method used for the solution of the inverse problem of biooptics of the sea according to the spectrum of upwelling radiation and propose a procedure for the correction of the data of measurement by fixing the value of reflectance at a wavelength of 400 nm. The influence of this assumption on the results of retrieving of the concentrations of admixtures in seawater is analyzed. The computed values of the concentration of chlorophyll correspond to the data of direct biological measurements, and the reconstructed spectra of the absorption coefficient of phytoplankton have local maxima typical of biological particles. The applied correction allows us to decrease the influence of measurement errors on the results of retrieving and to increase the stability of solution of the inverse problem. __________ Translated from Morskoi Gidrofizicheskii Zhurnal, No. 1, pp. 38–50, January–February, 2008.     

A mathematical representation of random gravity waves in the ocean

We give a mathematical representation of random ocean surface waves in the gravity-wave regime. The so-called random gravity waves are treated as an asymptotic phenomenon when the wind pressure acting on the surface and the dissipation become negligible. We adopt a phenomenological model for the wind pressure such that it excites a surface consisting of wind-driven sea and swell. Starting from the Navier-Stokes equations, we derive a general system of the first-order perturbation equations governing the surface waves, and solve them with this wind pressure as the excitation. The resulting solution is decomposed into a part which is asymptotically dominant and another which is asymptotically negligible. The former consists of two groups: one which is a sum of superpositions of uncorrelated plane waves having approximate dispersion relations and the other a sum of random plane waves with their wavenumbers and frequencies approximately satisfying the dispersion relation. They correspond to the dominant parts of the wind-driven sea and the swell, respectively. Finally, we derive a limiting form of the directional-frequency spectrum in the gravity-wave regime.     

Absorption of infrasonic waves in a cloudy medium

We study the absorption of infrasonic waves when they are propagating in cloud media. In this case, the main mechanism of absorption is the relaxation processes associated with vapor-drop phase transitions caused by infrasonic waves. For frequencies comparable to the inverse relaxation time, the acoustic waves in a cloud medium were shown to have a noticeable dispersion. We derive an expression for the frequency-dependent effective adiabatic index linking the oscillations of pressure and density in the wave, the dispersion equation, and the expression for the absorption coefficient. For typical values of cloud parameters, the absorption coefficient was estimated to be around 0.1 km^?1. We discuss observation data which indirectly confirm that clouds can considerably absorb infrasonic waves.     

Statistical analysis of a global photochemical model of the atmosphere

This is a study of the sensitivity of model results (atmospheric content of main gas constituents and radiative characteristics of the atmosphere) to errors in emissions of a number of atmospheric gaseous pollutants. Groups of the model variables most dependent on these errors are selected. Two variants of emissions are considered: one without their evolution and the other with their variation according to the IPCC scenario. The estimates are made on the basis of standard statistical methods for the results obtained with the detailed onedimensional radiative—photochemical model of the Main Geophysical Observatory (MGO). Some approaches to such estimations with models of higher complexity and to the solution of the inverse problem (i.e., the estimation of the necessary accuracy of external model parameters for obtaining the given accuracy of model results) are outlined.     

A boundary-value problem for the parameterized mesoscale eddy transport

We present a physically and numerically motivated boundary-value problem for each vertical ocean column, whose solution yields a parameterized mesoscale eddy-induced transport streamfunction. The new streamfunction is a nonlocal function of the properties of the fluid column. It is constructed to have a low baroclinic mode vertical structure and to smoothly transition through regions of weak stratification such as boundary layers or mode waters. It requires no matching conditions or regularization in unstratified regions; it satisfies boundary conditions of zero transport at the ocean surface and bottom; and it provides a sink of available potential energy for each vertical seawater column, but not necessarily at each location within the column. Numerical implementation of the methodology requires the solution of a one-dimensional tridiagonal problem for each vertical column. To illustrate the approach, we present an analytical example based on the nonlinear Eady problem and two numerical simulations.     

Observations and modelling of the travel time delay and leading negative phase of the 16 September 2015 Illapel,Chile tsunami

The systematic discrepancies in both tsunami arrival time and leading negative phase (LNP) were identified for the recent transoceanic tsunami on 16 September 2015 in Illapel, Chile by examining the wave characteristics from the tsunami records at 21 Deep-ocean Assessment and Reporting of Tsunami (DART) sites and 29 coastal tide gauge stations. The results revealed systematic travel time delay of as much as 22 min (approximately 1.7％ of the total travel time) relative to the simulated long waves from the 2015 Chilean tsunami. The delay discrepancy was found to increase with travel time. It was difficult to identify the LNP from the near-shore observation system due to the strong background noise, but the initial negative phase feature became more obvious as the tsunami propagated away from the source area in the deep ocean. We determined that the LNP for the Chilean tsunami had an average duration of 33 min, which was close to the dominant period of the tsunami source. Most of the amplitude ratios to the first elevation phase were approximately 40％, with the largest equivalent to the first positive phase amplitude. We performed numerical analyses by applying the corrected long wave model, which accounted for the effects of seawater density stratification due to compressibility, self-attraction and loading (SAL) of the earth, and wave dispersion compared with observed tsunami waveforms. We attempted to accurately calculate the arrival time and LNP, and to understand how much of a role the physical mechanism played in the discrepancies for the moderate transoceanic tsunami event. The mainly focus of the study is to quantitatively evaluate the contribution of each secondary physical effect to the systematic discrepancies using the corrected shallow water model. Taking all of these effects into consideration, our results demonstrated good agreement between the observed and simulated waveforms. We can conclude that the corrected shallow water model can reduce the tsunami propagation speed and reproduce the LNP, which is observed for tsunamis that have propagated over long distances frequently. The travel time delay between the observed and corrected simulated waveforms is reduced to <8 min and the amplitude discrepancy between them was also markedly diminished. The incorporated effects amounted to approximately 78％ of the travel time delay correction, with seawater density stratification, SAL, and Boussinesq dispersion contributing approximately 39％, 21％, and 18％, respectively. The simulated results showed that the elastic loading and Boussinesq dispersion not only affected travel time but also changed the simulated waveforms for this event. In contrast, the seawater stratification only reduced the tsunami speed, whereas the earth's elasticity loading was responsible for LNP due to the depression of the seafloor surrounding additional tsunami loading at far-field stations. This study revealed that the traditional shallow water model has inherent defects in estimating tsunami arrival, and the leading negative phase of a tsunami is a typical recognizable feature of a moderately strong transoceanic tsunami. These results also support previous theory and can help to explain the observed discrepancies.     

On the effect of spray on the dynamics of the marine atmospheric surface layer in strong winds

A nonlinear analytical model of the near-water air layer is considered. In the model, the effect of spray droplets on turbulent exchange is taken into account through their effect on density stratification. To close the system of equations, a semiempirical turbulence theory in the Kolmogorov-Monin form is used. Unlike previous publications, we use an alternative closure scheme that seems more appropriate. A version is also proposed for generalizing the model to the case where heavy admixture particles (spray droplets) make a dominant contribution to the average density of a medium. This model allows a general analytical solution that, in principle, describes non-linear effects such as a decrease in the effective friction and “self-closure” of the heavy admixture in the near-surface layer because of turbulence suppression due to the strengthening of stratification stability. As the current data show, however, the intensity of spray production is probably insufficient to explain the recently discovered phenomenon of the aerodynamic-drag decrease (saturation) in storm winds.     

Calculation of the initial elevation at the tsunami source using analytical solutions

We have obtained an analytical solution to the problem of determining the initial elevation at the tsunami source, which was formed by small residual deformations of a flat sloping bottom. This solution, which is newly derived, is compared with the known analytical solution of an equivalent problem over a horizontal bottom. It is shown that applying an analytical solution over a horizontal bottom for calculating the initial perturbations in the sources of realistic tsunami provides sufficient accuracy.     

Perturbed solution of sea-air oscillator for the El Niño/La Niña-Southern Oscillation mechanism

A class of coupled system of the El Niño/La Niña-Southern Oscillation (ENSO) mechanism is studied. Using the perturbed theory, the asymptotic expansions of the solution for ENSO model are obtained and the asymptotic behavior of solution for corresponding problem is considered.     

Baroclinic seiches in rotating basins of variable depth in the case of two-layer density stratification

We solve a plane problem of linear baroclinic seiches in closed rotating basins of variable depth with two-layer density stratification. In the long-wave approximation, we get a boundary-value problem for a system of ordinary differential equations and propose a numerical procedure for finding internal seiches. The analytic solutions of the problem are obtained for a basin of constant depth. The numerical analysis of seiches is performed for the distributions of depth corresponding to the zonal and meridional sections of the Black Sea and model basins including the cases of a shelf zone and an underwater ridge. It is shown that the baroclinic seiches become more intense in shallow-water regions and that the intense longshore currents caused by Earth’s rotation are formed in the shelf zones and over the underwater ridges.     

Peculiarities of Polluted Water Spreading from a Submarine Source in Stratified Coastal Environment

We study the spreading of wastewaters from an underwater source in a stratified coastal environment using the results of satellite monitoring and mathematical modeling. The problem is considered as applied to deepwater discharge in the region of Golubaya Bay of the Black Sea near Sebastopol. The main factors preventing upwelling of pollution to the sea surface are analyzed on the basis of a numerical model. It is shown that peculiarities of wastewater spreading depend on the character of stratification and velocity of the background current. The main factor influencing the uplift of these waters to the surface is the existence of water layers with high vertical gradients of water density. We reveal the structure of the wastewater field consisting of a plume and a jet extended in the direction of the background current, which is located in the density interface. If stratification is weak, the plume may reach the sea surface and form a local region of water pollution, which is recorded in multispectral satellite images. It is found that the mass of polluted waters is characterized by negative anomalies of temperature and salinity.     

A numerical study on the generation of the small meander of the Kuroshio off southern Kyûshû

The generation of small meanders of the Kuroshio off southern Kyûshû is investigated. Basing on the fact that the small meanders tend to follow an increase in velocity of the Kuroshio in the Satsunan region (Sekine andToba, 1981), the influence of this velocity increase on the quasi-stationary path of the Kuroshio is studied numerically. Simplified bottom and coastal topographies are employed in a two layer model ocean. A quasi-stationary numerical solution with a constant inflow is used for the initial condition, and a temporal increase in the inflow with corresponding leakage is employed as the boundary condition to investigate nonlinear effects due to the increase in current velocity. Experiments for four different physical models are carried out to determine the specific roles of the continental slope, the planetary-effect, and density stratification. Temporal increase in the inflow tends to cause offshore shift of the current path. But the topographic effect of the continental slope is strong enough that no significant shift of the current path occurs in the case of the barotropic ocean. However, in the case of a baroclinic ocean, temporal increase in the inflow does cause generation of small meanders, because density stratification diminishes the topographic effect. A larger density stratification provides more favorable condition for the appearance of the small meander, and a cyclonic eddy is formed on the continental side of the small meander path.