In this paper, a new analysis of the known topographic models of Rossby waves for piecewise exponential topography profiles is performed. A mathematical method is proposed that allows us to find analytically the group velocity and variance. A numerical comparison is made of the relations presented in the study of Buchwald and Adams and the dependencies obtained within the framework of a new analytical approach. Numerical comparative analysis showed that the discrepancy for the phase velocities lies in the range of five percent. For group speeds, the discrepancy reaches nineteen percent for the first mode and decreases for higher mode numbers. We also consider long-wave asymptotics of eigenfunctions. It is established that the long-wave limit for Rossby shelf waves has specifics: the longitudinal wave number tends to zero, and the transverse wave number reaches a certain finite positive constant, which is the greater the higher the mode number. It is shown that in the long-wave limit, Rossby shelf waves transform into shelf topographic currents, while there is a certain self-similarity for the phase and group velocities of shelf currents depending on the value of the topography gradient.

The paper presents an interpretation of the results of spectral wave-forecast model using the phase-resolving model. Spectral models provide the information on the evolution of the potential energy distribution in terms of angle and frequency though the information about the geometry and statistical wave characteristics in such models are not available. This information has to be extracted through the additional, often unsubstantiated, hypotheses. The proposed computational procedure transforms spectral information into a two-dimensional wave field which consists of a set of linear modes with randomly distributed phases is proposed. The wave field is not realistic since it does not have non-linear properties, for example, various asymmetry properties such as increased kurtosis. Afterwards the linear wave field reproduced on the basis of the wave spectrum is set as the initial condition for the exact phase-resolving model. The exact models formally suitable for such calculations are cumbersome and inefficient and that practically restricts their broad and regular application. This restriction can be overcome by using a new type of 3D wave simulation based on 2D equations. The 2D model reproduces the statistical characteristics of the wave field similar to the results of the 3D exact model and runs several times faster. The examples of using the developed method of interpretation of the spectral wave forecast in the Baltic Sea are demonstrated.

The paper focuses on the validation of the accelerated method for simulation of 2D-surface waves with a use of 2D-model derived by simplifications of 3D-equations for potential periodic waves at infinite depth. The separation of the velocity potential into nonlinear and linear components is used. A derivation of the equation for the total kinetic energy calculation in the surface-following coordinate system is given for the first time. The spectral characteristics of the wave field calculated with the accelerated model are compared with the results from the equivalent full 3D-model. The 3D-model is based on the numerical solution of the 3D-Poisson equation written in surface coordinates for the nonlinear component of the velocity potential. The similarity of the results obtained from the two versions of the model confirms that the new accelerated model can be used to quickly reproduce the wave field dynamics and thereby increase a speed of calculations by about two orders.

The research involves the examination of modeling outcomes regarding the density structure and baroclinic dynamics of Antarctic shelf waters (ASW) within the shelf-slope area, encompassing a wide range of extreme weather conditions. We used a small-scale non-hydrostatic Fluidity-ICOM model to understand the formation and persistence of quasi-stationary polynyas in the Antarctic, which play a role in enhancing the formation of ASW. The salt fluxes, or buoyancy, are calculated for different forms of ice formation, namely static ice formation in young ice-covered polynyas and dynamic intra-water ice formation, which is considered the most effective and occurs in open water polynyas. Based on the intensification of ASW formation and its spread, three distinct modes of propagation along the continental slope have been identified: non-wave or subcritical mode, vortex mode, and wave or supercritical mode, which is characterized by rapid flow. The classification into different modes is determined by the internal Froude number (Fr) estimates. At the moment when the most developed stage of near-bottom density currents are transformed on a slope, the spatial dimensions of meanders, eddies, or frontal waves were found to be similar in magnitude, as well as their thickness. This observation aligns with model calculations of the local baroclinic Rossby deformation radius (Rd_L) for these currents. These findings agree with comparable assessments of the baroclinic Rossby deformation radius (Rd_L) for the Antarctic Slope Front (ASF) in the Commonwealth Sea, which were based on field observations. Additionally, the calculated propagation velocities of density currents and the density gradients at their boundaries coincide with the data obtained from field measurements. By estimating the volumetric fluxes (q_v) and specific fluxes (q_l) of ASW along the continental slope near the Cape Darnley coastal polynya area in the Commonwealth Sea, we can determine the contribution of ASW cascading to the formation of bottom waters under different flux regimes. The precision and accuracy of the q_v and q_l estimates are ensured through small-scale calculations using the non-hydrostatic Fluidity-ICOM model. These calculations consider the occurrences of intensified ASW formation in open water polynyas. Numerical experiments have revealed that a four-fold increase in a spatial step X results in an underestimation of q_v by approximately 30%. As a consequence, in large-scale and even mesoscale hydrostatic models, such underestimation of q_v and q_l may be unsatisfactory (several times lower).

In the framework of a high-resolving version of the 3D finite-element hydrostatic model QUODDY-4 we have simulated the fields of dynamic characteristics (amplitudes and phases of tidal elevations and barotropic tidal velocity ellipses) corresponding to the surface semidiurnal M₂ tide in the no-ice East-Siberian Sea. It is shown that the obtained tidal chart has a complex structure, determined by 4 real amphidromes of left rotation which are induced by interference of counter-coming progressive Poincare waves in the southern part of the sea, 1 fake amphidrome with the center upon the Novaya Sibir Isl. and 4 small-scale amphidromes caused by interference of counter-coming Kelvin waves, from which 3 are formed in the narrow straits in the region of Bolshoy and Maly Lyahovsky Isls. and 1 near the entrance of the Chaunskaya Guba. Tidal amplitudes in the vicinity of the Novaya Sibir Isl. achieve 20–30 cm, whereas in the remaining part of the sea they are comparatively small and do not exceed 5–10 cm. Accordingly, the field of barotropic tidal velocities in the north-western part of the sea basically consists of high values (they are tens of cm/s), but in the other parts of the sea barotropic velocities are small (lower then 10 cm/s) and their field has a band structure. The fields of the averaged (over a tidal cycle) integrated in depth constituents of the barotropic tidal energy budget (namely, the barotropic tidal energy density, the advective transport and the horizontal wave flux per unit length of this energy and the rate of its dissipation due to the bottom friction) are presented. Also, a comparison of predicted tidal elevations with the mareographic level measurement data states that an estimate of their agreement may be considered as satisfactory taking into account that the tidal amplitudes in the sea as a whole are small.

The paper presents the results of studying the mixing of the water mass of a small forest dimictic lake at the stage of summer heating. The wind effect is limited by the small area of the mirror (the size of the lake is 80–110 by 400 m) and the forested shores, so in summer the convective mixing mechanism prevails when the lake surface cools at night. Evaluation of the mixing efficiency η was carried out by the integral energy method, based on the calculations of energy pumping and changes in the background potential energy according to the temperature profile transformation. For this purpose, a chain with 13 highly sensitive temperature sensors was used; the measurements were carried out in the middle of summer 2022 for 35 days with a time interval of one minute. Acoustic current profiler’s data were used to estimate turbulent velocity fluctuations and calculate the energy dissipation rate, which made it possible to make an alternative assessment of the mixing efficiency. The value of η ~0,4 was obtained, which significantly exceeds the “canonical” value of 0,17 for the case of wind mixing.

The provocation of the hydroacoustic communication interaction of Tursiops truncatus dolphins based on cognitive empathy showed that they use packets of ultrashort pulses (USPs) in the process of “dialogue”. The duration of bursts varies from 40 ms to 3000 ms with modulation of the interval between USPs from ~1 to ~120 ms and pauses between bursts. The interval modulation pattern is structured using various modulation laws. The communication signals were obtained in an experiment with theparticipation of three animals, who knew the main task of sequential acoustic differentiation of two objective stimuli. The impetus for hydroacoustic interaction is the resolution of uncertainty when teaching the respondent the inverse differentiation problem. This generates emotional empathy in observers and provokes vocalization between individuals. The advantages and disadvantages of methodological methods of provoking hydroacoustic interaction are considered in detail, starting the process of cognitive empathy. In the method under consideration, echolocation and communication signals are spaced apart in time and space, which allows them to be uniquely identified.

Based on the mathematical definition of a non-self-adjoint operator and the physical meaning of a specific boundary value problem, a non-self-adjoint model statement of boundary value problems in acoustics is formulated. As an example, boundary value problems for the reflection of a plane wave and a spherical wave at the interface between two liquid media are considered. A new definition of the reflection coefficient of a spherical wave is introduced. In the region of subcritical angles of incidence, the new definition takes into account the appearance in the total sound field of converging recoil waves corresponding to the eigenfunctions of the adjoint operator. In the region of supercritical angles of incidence, the participation of the eigenfunctions of two conjugate operators in the total sound field forms a nonzero power flux through the interface and its transformation into the vortex component of the intensity vector at the total internal reflection horizon. The definition of the total internal reflection horizon is given. Experimental data are presented that confirm the new definition of the reflection coefficient and the physical correctness of the non-self-adjoint model statement.

To detect and classify objects, the source trajectories detected in the process of hydroacoustic observation are used, which contain information about the measured parameters of objects, which are their classification attributes. The analysis of these attributes allows to make a decision about the class of the observed object, for example, a surface or underwater source. As the measured object parameters are used their energy characteristics, parameters of the observed trajectory (bearing, speed of change in bearing and other possible trajectory parameters). In this case, the correctness and speed of the decision on classification depends on the quantity and quality of used classification signs, which are determined by both parameters of the observed object, and the features of sound propagation from the source to the observation device.
For signal detection and resolution, we further consider fast projective adaptive algorithms, the use of which, as applied to the problems of in-situ experimental signal detection was considered in [1], [4]. The goal of this class of algorithms is to provide a high probability of detection and accurate measurement of the parameters of the source trajectories under the conditions of a model of multi-beam propagation and scattering in the real ocean environment [5]-[8]. The proposed work is a continuation of the work [1], [4], and aims to ensure the use of experimental field data not only for detection, but also for the classification of the observed sources.
The subject of the study are the results of the full-scale experiment of hydroacoustic noise direction finding, given earlier and described in detail in [1], [4]. For the experiment was used antenna of L = 56 vertical daisy chains (of 10 elements each), equidistantly spaced horizontally. The antenna was installed at a depth of 200 meters in the coastal marine zone of the coastal wedge near the shipping lanes. The elements of the flat antenna were affected by signals from surface ships moving ncontrollably in the observation area and one underwater source.
A singular decomposition of sampled antenna element data was used to construct adaptive algorithms. Modification of the initial results of singular decomposition allows to create algorithms that provide priority conditions for extraction of separate components of the observed (e. g., weakest) signals when constructing direction finding terrain.
In this regard, in addition to the non-adaptive direction finding relief, it is proposed to form three variants of direction finding relief, each of which solves part of the general problem of selection and classification of individual varieties of observed signals:
– Initial, corresponding to the energy of the signals of the input sample with amplified components of the weakest signals (overview algorithm);
– direction finding relief, which uses an algorithm to detect weak and scattered signals;
– direction finding terrain, which highlights the coherent components of signals.
Analysis of the trajectories of more than 30 sources in the episode of two hours and forty minutes has been carried out, which increased the reliability of the detection and measurement accuracy of the parameters of the observed objects. Joint analysis of the trajectories of sources based on different variants of the bearing relief allowed to improve the conditions for the detection of weak signals and to make classification decisions using the classification attribute of the width of the area of fluctuations of the surface target trajectory for signals with a strong scattered component.