Far fields of internal gravity waves in a stratified liquid of varying depth

Asymptotic representations of solutions describing the far fields of internal gravity waves in a stratified medium of varying depth are constructed. The effect of space-frequency cutoff of the wave field for a real oceanic shelf is revealed. Depending on frequency characteristics of the wave field and bottom topography, far fields of internal waves either are located in a certain confined space domain (trapped waves) or propagate in the absence of turning points over sufficiently large distances when compared with the sea depth (progressive waves). The space domain where the progressive waves penetrate is fully determined by the presence of turning points whose locations depend on the medium stratification and inhomogeneities of bottom topography.     

Influence of internal gravity waves on meteorological fields and gas constituents near Moscow and Beijing

The influence of internal gravity waves on the spatial coherence and temporal variability of the atmospheric pressure, wind velocity, and gas constituents near Moscow and Beijing is studied in the mesoscale range of periods: from a few tens of seconds to several hours. The results of simultaneous measurements of variations in the atmospheric pressure (using a network of spaced microbarographs), wind velocity at different heights of the atmospheric boundary layer, and gas constituents are given for each city. The wave structures are filtered using a coherence analysis of the atmospheric pressure variations at different measurement sites. The dominant periods and the coherences, phase speeds, and horizontal scales of variations corresponding to these periods are estimated. The general mechanism of the influence of wave structures on meteorological fields and gas constituents is discussed, which is independent of the measurement site and the specificity of meteorological conditions.     

Effects of rotation on self-resonant internal gravity waves in the ocean

The Resonant Triad Model (RTM) developed in (Ibragimov, 2007), is used to study the Thorpe’s problem (Thorpe, 1997) on the existence of self-resonant internal waves, i.e., the waves for which a resonant interaction occurs at second order between the incident and reflected internal waves off slopes. The RTM represents the extension of the McComas and Bretherton’s three wave hydrostatic model (McComas and Bretherton, 1977) which ignores the effects of the earth’s rotation to the case of the non-hydrostatic analytical model involving arbitrarily large number of rotating internal waves with frequencies spanning the range of possible frequencies, i.e., between the maximum of the buoyancy frequency (vertical motion) and a minimum of the inertial frequency (horizontal motion). The present analysis is based on classification of resonant interactions into the sum, middle and difference interaction classes. It is shown in this paper that there exists a certain value of latitude, which is classified as the singular latitude, at which the coalescence of the middle and difference interaction classes occurs. Such coalescence, which apparently had passed unnoticed before, can be used to study the Thorpe’s problem on the existence of self-resonant waves. In particular, it is shown that the value of the bottom slope at which the second-order frequency and wavenumber components of the incident and reflected waves satisfy the internal wave dispersion relation can be approximated by two latitude-dependent parameters in the limiting case when latitude approaches its singular value. Since the existence of a such singular latitude is generic for resonant triad interactions, a question on application of the RTM to the modeling of enhanced mixing in the vicinity of ridges in the ocean arises.     

The generation of plane internal and gyroscopic waves by moving unsteady disturbances

The plane linear problem on the generation of the internal and gyroscopic waves in continuously stratified ocean by a moving area of surface pressures which are harmonic over time is considered. The possible types of the forced waves, the amplitudes and the resonance conditions of generation of the wave fields are determined based on the analytical solution derived for the case of a uniformly stratified ocean.Translated by Mikhail M. Trufanov. UDK 551.466.81.     

Conditions of the propagation of internal gravity waves through wind structures from the troposphere to the ionosphere

We consider the propagation of large-scale internal gravity waves (IGWs) from the troposphere through vertically inhomogeneous wind structures to the ionosphere heights on the basis of an analysis of beam trajectories. We selected different versions of the initial parameters and numerically studied the specific peculiarities of the behavior of beam trajectories related to the location of layers with horizontal and vertical reflection and a critical layer on the pathway of the waves. It was shown that, for sufficiently large-scale IGWs, their propagation from the troposphere to ionosphere heights is possible. We found the characteristic times when the waves generated in the troposphere reach ionosphere heights. We revealed strong variations in these times when the initial parameters of the problem changed. We determined the typical values of the horizontal displacement (relative to the generation source) of the wave packets when they reach the ionosphere.     

Generation of spatial internal waves in a rotating ocean by moving non-stationary disturbances

In a general linear statement, the kinematic structure of spatial internal waves generated by a uniformly moving area of oscillating surface pressures in a continuously stratified ocean of constant depth is studied. The earth's rotation effects are considered. Possible types of ocean wave fields with a constant Brunt-Väisälä frequency are examined. The wave regimes for individual modes of internal and gyroscopic waves are classified on the basis of estimating the integrals asymptotically.Translated by V. Puchkin.     

Generation of internal waves by moving non-stationary disturbances in a real stratified ocean

The plane problem on the generation of linear internal waves by a moving area of time-harmonic surface pressures in a continuously-stratified ocean of constant depth is considered. An analytical relation has been derived for forced internal waves off the site of their generation in the form of an internal wave field superposition corresponding to individual vertical modes. The possible wave regimes are determined. For the Brunt-Väisälä frequency distribution in the North Atlantic, the generation conditions and amplitudes of diverse radiated waves are numerically determined.Translated by Vladimir A. Puchkin.     

Studying internal gravity waves generated by atmospheric fronts over the Moscow region

Internal gravity wave (IGW) data obtained during the passage of atmospheric fronts over the Moscow region in June–July 2015 is analyzed. IGWs were recorded using a group of four microbarographs (developed at the Obukhov Institute of Atmospheric Physics, Russian Academy of Sciences) located at distances of 7 to 54 km between them. Regularities of variations in IGW parameters (spatial coherence, characteristic scales, propagation direction, horizontal propagation velocity, and amplitudes) before, during, and after the passage of an atmospheric front over the observation network, when the observation network finds itself inside the cyclone and outside the front, are studied. The results may be useful in studying the relationships between IGW effects in different physical fields at different atmospheric heights. It is shown that, within periods exceeding 30 min, IGWs are coherent between observation points horizontally spaced at distances of about 60 km (coherence coefficient is 0.6–0.9). It is also shown that there is coherence between wave fluctuations in atmospheric pressure and fluctuations in horizontal wind velocity within the height range 60–200 m. A joint analysis of both atmospheric pressure and horizontal wind fluctuations has revealed the presence of characteristic dominant periods, within which cross coherences between fluctuations in atmospheric pressure and wind velocity have local maxima. These periods are within approximate ranges of 20–29, 37–47, 62–72, and 100–110 min. The corresponding (to these dominant periods) phase propagation velocities of IGWs lie within an interval of 15–25 m/s, and the horizontal wavelengths vary from 52 to 99 km within periods of 35 to 110 min, respectively.     

Numerical analysis and visualization of fine structures of the fields of two-dimensional attached internal waves

In the linear approximation, we compute the patterns of two-dimensional perturbations formed in a viscous exponentially stratified fluid in the process of motion of a plate at an arbitrary angle to the horizon. The exact solution of the problem obtained in quadratures and satisfying the physically meaningful boundary conditions is numerically analyzed. The properties of the fields are computed and described in broad ranges of all parameters of the problem, including the length and velocity of motion of the plate, the characteristics of stratification and viscosity of the medium, and the slope of the path. In the picture of currents, we distinguish two groups of waves and compact nonwave singularities near the edges of a source of generation. The results of comparison with the available data of independently performed calculations and experiments reveal the existing agreement between the computed and observed pictures of the currents.     

Spectra of the above-surface magnetic fields predicted by a canonical model of oceanic internal waves

The various fluctuation spectra associated with the magnetic induction field and its spatial derivatives generated by a canonical model of oceanic internal waves are calculated. The calculations are based upon the well-known canonical distribution from statistical mechanics. While in a general ease it is necessary to consider the details of the strong nonlinear interactions between linear internal waves, it is shown that the spectra of the above-surface magnetic fields are independent of such details. The predictions of the canonical model are compared to those of the Garrett-Munk (GM) model. The two models are found to yield significantly different results. An experiment to test the two models is suggested.     

Interaction of current and flexural gravity waves

The interaction between current and flexural gravity waves generated due to a floating elastic plate is analyzed in two dimensions under the assumptions of linearized theory. For plane flexural gravity waves, explicit expressions for the water particle dynamics and trajectory are derived. The effect of current on the wavelength, phase velocity and group velocity of the flexural gravity waves is analyzed. Variations in wavelength and wave height due to the changes in current speed and direction are analyzed. Effects of structural rigidity and water depth on wavelength are discussed in brief. Simple numerical computations are performed and presented graphically to explain most of the theoretical findings in a lucid manner.     

Generation of long waves by random sources

A statistical approach is applied to solving the problem of long wave generation due to the ocean bottom shift. Various models of random sources are studied. The dependence of the amplitudinal characteristics of long waves on the time scale of random processes is considered. Results of the solution of the dynamic and random source problems are compared.Translated by V. Puchkin.     

On the estimation of surface gravity waves from subsurface pressure records for estuarine basins

According to small-amplitude theory, the surface gravity-wave spectrum can be estimated from a subsurface pressure-fluctuation spectrum by applying a factor (K) that compensates for the attenuation of surface-wave amplitude as the depth below the water surface and the wave frequency increase.There are a number of factors, however, that cause K to be inaccurate over a large portion of the spectrum's frequency range. Numerous attempts have been made to derive an empirical correction factor (n) that could be applied to K to provide a better estimate of the surface-wave spectrum. This paper evaluates some of these empirical factors, specifically for use in an estuarine environment, and recommends Graces' (1978) equation for n as a function of the non-dimensional frequency parameter kh (where $\text{k =}\text{2π}\text{L}$ is the local wavenumber, h the local depth and L the wavelength).The paper also evaluates the maximum limit (K_max) on the magnitude of K suggested by Esteva & Harris (1970), where relative depth $\text{d}\text{h}$ (d is the pressure transducer height above the bottom) and k_oh (a parameter directly related for large values of kh to wave frequency by the dispersion relation) are the independent variables. The choice of K_max may be made unimportant if d is selected beforehand using an equation (Knowles, 1981a) for the minimum $\text{d}\text{h}$ limit affected by the choice of K_max.     

Reflection of long internal waves of small amplitudes from an underwater slope

The dynamics of long waves in the vicinity of a transition point of a two-layer flow into a single-layer one is studied within the linear theory of shallow water. The analogy between this problem and the classical problem of surface wave runup on the shore is shown. Conditions for breaking internal waves on a slope are discussed.     

Particle trajectories of nonlinear gravity waves in deep water

The paper presents a numerical method for calculating the particle trajectories of nonlinear gravity waves in deep water. Particle trajectories, mass-transport velocity and Lagrangian wave period can be accurately determined by the proposed method. The high success rate of the proposed method is examined by comparing the present results with those of (a) Longuet-Higgins, M.S., 1986, 1987. Eulerian and Lagrangian aspects of surface waves. Journal of Fluid Mechanics 173, 683-707 and (b) Lagrangian moments and mass transport in Stokes waves. Journal of Fluid Mechanics 179, 547-555. It is shown that the dimensionless mass-transport velocity can exceed 10% for large waves, and the Lagrangian wave period is much larger than the Eulerian wave period for large waves.     

On the form of crests in limiting gravity waves

Properties of surface singularities and the form of wave crests of limiting gravity waves in steady-state flows of an ideal liquid are considered by analyzing the kinematic boundary condition. It is shown that, for rotational waves, the angle at the crest can have any value from 0° to 180°, while it has the only value 90° in the case of irrotational waves. Two inferences are made from Bernoulli’s integral and the properties of singularities: (i) the Stokes wave is a rotational wave and (ii) no angular points can appear on the profiles of capillary-gravity and capillary waves.