p.8
Vertical Fine Structure Generation
What does the correction to density ρ ∆ indicate?
It is determined by the vertical fine structure generated by an internal wave and is irreversible.
p.6
Hydrodynamic Equations
What methods were used to solve the dispersion equation?
Asymptotic and numerical methods.
p.13
Vertical Wave Fluxes of Mass
How do the first mode vertical wave mass fluxes compare in homogeneous vs. inhomogeneous cases?
They are higher in the case that is horizontally inhomogeneous in average density.
p.1
Vertical Fine Structure Generation
What is the main purpose of the study conducted by Slepyshev and Ankudinov?
To study the wave mechanism of fine structure generation and determine the vertical wave fluxes of mass.
p.8
Experimental Observations in the Black Sea
What does Figure 1 illustrate?
The time course of temperature isolines obtained by four gradient-distributed temperature sensors.
p.4
Hydrodynamic Equations
What does ρ and P represent in the context of wave disturbances?
Density and pressure wave disturbances.
p.13
Vertical Wave Fluxes of Mass
What is shown in Fig. 9?
The dependence on the vertical coordinate of wave mass flux and generated fine structure for the internal wave of the second mode in both horizontally inhomogeneous and homogeneous cases.
p.9
Hydrodynamic Equations
What numerical method is used to solve the boundary value problem?
The implicit Adams scheme of third order accuracy.
p.14
Vertical Fine Structure Generation
What effect does considering horizontal inhomogeneity of the average density field have?
It increases both vertical wave mass fluxes and generated fine structure.
p.11
Vertical Wave Fluxes of Mass
What frequencies are considered for the second mode of internal waves?
4, 1, and 12 cycles per hour (cph).
p.17
Experimental Observations in the Black Sea
What role does Nikita O. Ankudinov play in the research?
Leading Engineer-Researcher responsible for numerical calculations and graphical presentation of results.
What does the Coriolis parameter f depend on?
It depends on the angular velocity of Earth's rotation and latitude.
p.7
Vertical Wave Fluxes of Mass
What is the significance of integrating equation (25) over time?
It allows for the derivation of relationships between wave density and other wave parameters over time.
p.1
Vertical Fine Structure Generation
What new approach is proposed for forming fine structure by internal waves?
Determining the vertical wave fluxes of mass in the field of an inertia-gravity internal wave without breaking.
What type of waves are considered in the study on the Black Sea northwestern shelf?
Inertia-gravity internal waves.
What does Figure 3, b reveal?
The dependence of the imaginary part of frequency on the wave number.
p.1
Nonlinear Effects in Wave Propagation
What is the relationship between wave frequency and the generation of fine structure?
The indicated fluxes and generated fine structure for waves of different frequencies are close, and the effect is enhanced in their presence.
p.13
Vertical Wave Fluxes of Mass
What does Fig. 8 illustrate regarding internal waves?
The vertical distribution of wave fluxes of mass and generated fine structure for the second mode in both horizontally inhomogeneous and homogeneous cases.
p.6
Brunt-Väisälä Frequency
What type of functions are used to obtain a solution at constant Brunt–Väisälä frequency?
Imaginary order modified Bessel functions.
Under what conditions are the vertical wave mass fluxes nonzero?
For inertia-gravity internal waves in the presence of a flow where the velocity component normal to wave propagation depends on the vertical coordinate.
p.4
Hydrodynamic Equations
In which direction is the 3 x axis directed?
Opposite to the gravitational acceleration vector g.
p.4
Brunt-Väisälä Frequency
What is the purpose of the linear approximation in the equations?
To find solutions under the condition of horizontal homogeneity of Brunt-Väisälä frequency.
p.3
Vertical Wave Fluxes of Mass
What are the vertical wave fluxes of heat, salt, and momentum?
Nonzero and lead to the formation of irreversible fine structure.
What do the two horizontal components of the Stokes drift velocity depend on?
They are determined by specific formulas involving wave frequency.
p.2
Hydrodynamic Equations
What happens to internal waves in a dissipative medium?
They attenuate and form boundary layers near boundaries.
p.15
Vertical Wave Fluxes of Mass
What is the focus of the 2017 study by Podymov et al.?
Vertical Turbulent Exchange in the Black Sea Pycnocline and its Relation to Water Dynamics.
p.14
Hydrodynamic Equations
How are vertical velocity shifts balanced in the flow?
By the horizontal gradient of the average density field.
p.8
Experimental Observations in the Black Sea
What was the purpose of the third stage of the 44th cruise of R/V Mikhail Lomonosov?
To calculate the vertical fine structure generated by internal waves in the Black Sea.
p.6
Nonlinear Effects in Wave Propagation
What happens to the dispersion curves due to flow?
They exhibit noticeable anisotropy, with frequency isolines potentially opening up.
p.9
Nonlinear Effects in Wave Propagation
What is the characteristic of the imaginary part of the first-mode frequency?
It is negative, indicating that the wave is slightly attenuated.
p.16
Inertia-Gravity Waves
What is the subject of Jones's 1967 study?
Propagation of Internal Gravity Waves in Fluids with Shear Flow and Rotation.
What is the vertical component of the Stokes drift velocity determined by?
A formula involving complex frequency.
p.4
Hydrodynamic Equations
What does the operator D Dt represent in the equations?
It represents the material derivative.
p.5
Hydrodynamic Equations
What is the role of the horizontal wavenumber 'k'?
It characterizes the spatial frequency of the wave.
p.5
Hydrodynamic Equations
Why does the wave frequency have a small imaginary part?
It indicates that the wave solution may involve damping or growth.
p.15
Vertical Fine Structure Generation
What do Kuzmina et al. (2011) study in the Arctic Ocean?
The Structure and Dynamical Features of Intrusive Layering in the Eurasian Basin.
What is the attenuation decrement for 15-minute internal waves of the second mode?
It is equal to 8 × 10^(-4) rad/s.
p.14
Hydrodynamic Equations
What is assumed about the flow in relation to the average density field?
The flow is assumed to be geostrophically balanced.
p.13
Vertical Fine Structure Generation
What mechanism does the paper present?
A mechanism for generating vertical fine structure due to vertical wave mass fluxes.
p.7
Vertical Wave Fluxes of Mass
What does the final expression (27) represent?
It represents a relationship involving wave density, Stokes drift velocity, and other wave parameters.
p.16
Vertical Wave Fluxes of Mass
What is the main topic of Slepyshev and Nosova's 2022 research?
Vertical Transfer of Momentum by Internal Waves in the Western Part of the Mediterranean Sea.
p.17
Experimental Observations in the Black Sea
What do the authors declare regarding conflicts of interest?
They declare that they have no conflict of interest.
p.9
Nonlinear Effects in Wave Propagation
What is the nature of the resulting solution for wave frequency?
It is complex, with a small imaginary part.
p.1
Vertical Fine Structure Generation
What kind of structures are studied in the context of fine structure generation?
Structures that arise when solids move in a liquid or when a liquid drop falls onto another liquid.
p.3
Hydrodynamic Equations
How is the boundary value problem for vertical velocity amplitude solved in this work?
Numerically using the implicit Adams scheme of third order accuracy.
p.15
Nonlinear Effects in Wave Propagation
What is the main topic of the 2009 study by Rudels et al.?
Double-Diffusive Convection and Interleaving in the Arctic Ocean.
What does Kistovich and Chashechkin's 1998 study focus on?
Linear Theory of the Propagation of Internal Wave Beams in an Arbitrarily Stratified Liquid.
p.10
Vertical Fine Structure Generation
Which mode has a greater intensity of generated vertical fine structure of the density field?
The first mode has greater intensity than the second mode at the same maximum wave amplitude.
p.7
Vertical Wave Fluxes of Mass
How is the average wave density corrected in the equations?
The correction is accurate to terms quadratic in the wave amplitude and does not oscillate on a time scale.
p.14
Hydrodynamic Equations
What relations are used to find the gradient of the average density field?
The 'thermal wind' relations.
p.11
Vertical Wave Fluxes of Mass
What does Fig. 5 illustrate regarding internal waves?
Profiles of the vertical wave mass flux and fine structure of the density field for the first and second modes of internal waves.
What effect do one-hour periods have on internal waves?
They enhance the effect when summed up.
p.1
Hydrodynamic Equations
What approximation is used in the study to describe the flow?
The f-plane approximation.
p.2
Vertical Fine Structure Generation
What are salt fingers?
Convective cells formed when temperature and salinity decrease with depth.
p.11
Vertical Fine Structure Generation
What is the relationship between wave period and fine-structure corrections to density?
Fine-structure corrections to density decrease with shorter wave periods.
p.5
Hydrodynamic Equations
What does the wave phase equation θ = ωk x - t represent?
It describes the phase of the wave, where k is the horizontal wavenumber and ω is the wave frequency.
p.2
Brunt-Väisälä Frequency
What is the relationship that determines the vertical scale of corrections produced by internal wave trains?
/ g c N, where g c is group velocity and N is Brunt–Väisälä frequency.
What phenomenon does the 2005 study by Falina and Volkov investigate?
The influence of Double Diffusion on the General Hydrological Structure of the Deep Waters in the Black Sea.
p.15
Hydrodynamic Equations
What do Kistovich and Chashechkin (2007) discuss in their study?
Regular and Singular Components of Periodic Flows in the Fluid Interior.
p.7
Vertical Wave Fluxes of Mass
What is the equation for vertical wave mass flux based on the provided formulas?
The equation incorporates terms for wave density and oscillation, accounting for various parameters like wave amplitude and velocity.
p.17
Experimental Observations in the Black Sea
What is the primary contribution of Aleksandr A. Slepyshev to the work?
Problem statement and theoretical part of the work, including mathematical formulation of the model and derivation of formulas.
p.4
Hydrodynamic Equations
What is the significance of 0 ρ in the equations?
It is the unperturbed average density.
p.14
Vertical Wave Fluxes of Mass
How do wave mass fluxes and fine-structure corrections relate for different frequencies?
They are very close for waves of 1 and 4 cph frequencies, intensifying the overall effect.
p.1
Vertical Wave Fluxes of Mass
What is the significance of the vertical wave fluxes of mass in this study?
They lead to the generation of vertical fine structure which is irreversible.
p.5
Hydrodynamic Equations
What is the significance of the term 'complex-conjugate' in wave equations?
It refers to terms that are paired in complex analysis, often used in the context of wave functions.
p.5
Hydrodynamic Equations
What does the term 'Doppler shift' refer to in the context of wave frequency?
It describes the change in frequency due to the relative motion between the source and observer.
p.15
Vertical Fine Structure Generation
What does the 1977 study by Leonov et al. calculate?
The Fine Structure of the Density and Velocity Fields in the Baltic Sea.
p.10
Vertical Wave Fluxes of Mass
How do the wave fluxes of the first and second modes compare at greater depths?
They are comparable in absolute value.
p.7
Vertical Wave Fluxes of Mass
What happens to the equation in the horizontally homogeneous case?
It simplifies to a form that relates wave density and various wave parameters without oscillation.
What aspect of internal waves does Slepyshev's 2022 paper address?
Vertical Momentum Transfer in a Shear Flow with Turbulent Viscosity and Diffusion.
p.11
Vertical Wave Fluxes of Mass
How do the vertical wave mass fluxes of the second mode behave with different wave periods?
They are co-directed and decrease in absolute value with decreasing wave period.
How does the presence of a two-dimensional shear flow affect fine structure generation?
It enhances the effect of generation of vertical fine structure by inertia-gravity internal waves.
p.12
Vertical Wave Fluxes of Mass
What does Fig. 9 illustrate regarding the first mode of internal waves?
Profiles of the vertical mass flux and generated fine structure in homogeneous and inhomogeneous cases.
p.5
Hydrodynamic Equations
What does the equation (14) represent in the context of wave dynamics?
It describes the behavior of the vertical velocity component under complex coefficients.
p.15
Hydrodynamic Equations
What does the 2007 study by Zatsepin et al. examine?
The influence of the Dynamics of Currents on the Hydrophysical Structure of the Waters in the Black Sea.
p.16
Vertical Fine Structure Generation
What phenomenon does Slepyshev's 2016 paper discuss?
Vertical Momentum Transfer by Internal Waves considering Eddy Viscosity and Diffusion.
p.8
Brunt-Väisälä Frequency
What does Figure 2 show regarding Brunt–Väisälä frequency?
It shows the dependence on the vertical coordinate.
p.3
Vertical Fine Structure Generation
What do boundary flows generate in the context of internal waves?
Fine structure of the periodic flow.
p.12
Vertical Fine Structure Generation
Where do the differences in vertical wave mass fluxes become noticeable?
In the pycnocline for waves with 12 cph frequency.
p.5
Brunt-Väisälä Frequency
What is the squared Brunt–Väisälä frequency 'N'?
It is a measure of the stability of a fluid column, defined as N² = - (g/ρ) dρ/dz.
p.15
Vertical Fine Structure Generation
What is the focus of the study by Falina and Volkov in 2003?
The Fine Structure and Thermohalinic Stability of the Abyssal Water in the Black Sea.
p.15
Inertia-Gravity Waves
What is the main focus of the 2019 study by Ivanov et al.?
Modeling and Observation of Internal Waves on the Black Sea Shelf near the Heracles Peninsula.
p.3
Vertical Fine Structure Generation
What forms boundary layers in internal waves?
Discontinuities in the buoyancy frequency or its derivatives.
p.6
Brunt-Väisälä Frequency
Under what condition are the wave frequency and eigenfunction of internal waves real?
When the Richardson number is larger than 1/4.
p.16
Vertical Wave Fluxes of Mass
What does Longuet-Higgins's 1969 paper focus on?
The Transport of Mass by Time Varying Ocean Current.
p.12
Vertical Fine Structure Generation
How does the amplitude of fine-structure oscillations in the inhomogeneous case compare to the homogeneous case?
It is higher in the inhomogeneous case.
p.5
Hydrodynamic Equations
What boundary conditions are applied to the vertical velocity component 'u30'?
The boundary conditions are u30(0) = 0 and H = 0.
p.15
Vertical Fine Structure Generation
What does the 2003 study by Panteleev and Okhotnikov focus on?
Intrusive Stratification of the Gulf-Stream Frontal Zone.
What does Figure 3, a show regarding frequency?
The dependence of the real part of frequency on the wave number for the first two modes.
p.2
Vertical Fine Structure Generation
What additional factor contributes to fine structure generation in measurements?
The kinematic effect of internal waves.
What does the second term in the expression for average Lagrangian velocity represent?
The Stokes drift velocity.
p.8
Experimental Observations in the Black Sea
How were the temperature sensors deployed during the cruise?
They were hung from the board of the vessel at various depths.
What is neglected in the horizontally homogeneous case?
Terms containing horizontal gradients of the average density.
What is the significance of the horizontal average density gradient in geostrophically balanced flow?
It was not considered in previous studies, affecting the analysis.
p.15
Nonlinear Effects in Wave Propagation
What contribution do Samodurov et al. (1995) discuss regarding internal waves?
Breaking Internal Waves' contribution to Structure Formation, Energy Dissipation, and Vertical Diffusion in the Ocean.
What is the relationship between Euler and Lagrange representations of flow velocities?
They are related up to second-order terms in wave steepness.
p.3
Nonlinear Effects in Wave Propagation
What factors lead to the attenuation of internal waves?
Turbulent viscosity and diffusion.
p.2
Vertical Fine Structure Generation
Do internal waves need to break to generate fine structure?
No, they do not necessarily have to break.
p.15
Vertical Fine Structure Generation
What do Navrotsky et al. (2007) study regarding internal waves?
Internal Waves and Formation of Hydrophysical Fields Fine Structure in the Shelf Zone.
p.10
Vertical Wave Fluxes of Mass
In which layer does the vertical wave mass flux of the first mode predominate significantly?
In the upper 40-meter layer.
What boundary condition is applied at the sea surface?
The 'rigid lid' condition.
p.12
Vertical Wave Fluxes of Mass
How do vertical wave mass fluxes and fine-structure corrections compare for 1 and 4 cph frequencies?
They are almost the same.
p.3
Vertical Fine Structure Generation
What additional factors contribute to vertical fine structure generation aside from turbulent viscosity and diffusion?
Earth rotation and inhomogeneous average flows.
p.3
Hydrodynamic Equations
What is the f-plane approximation used for?
To analyze horizontal gradients of average density from geostrophic relations.
p.15
Vertical Fine Structure Generation
What is the subject of the 2016 study by Golovin et al.?
Intrusive Layering of the Antarctic Slope Front.
How does the first-mode damping decrement compare to the second-mode damping decrement?
The first-mode damping decrement is greater in absolute value than the second-mode damping decrement for a fixed wave number.
p.12
Vertical Wave Fluxes of Mass
What is shown in Fig. 7 regarding the first mode of internal waves?
Graphs of the vertical wave mass flux and generated fine density structure for different frequencies.
p.11
Vertical Wave Fluxes of Mass
What are the wave periods analyzed for the second mode in Fig. 6?
15-minute, one-hour, and 5-minute internal waves.
p.2
Vertical Fine Structure Generation
What can double diffusion lead to in the ocean?
The formation of step structures.
p.2
Vertical Fine Structure Generation
What mechanism has been proposed to explain fine structure formation?
Internal waves breaking and hydrodynamic instability of flows.
What phenomenon is investigated by Samodurov in 1993?
Intrusion Layering and Vertical Diffusion in the Ocean due to Tidal Mixing.
What occurs in the high-frequency region for the second mode?
The imaginary part of the frequency becomes positive, indicating weak amplification.
p.2
Vertical Fine Structure Generation
What phenomenon allows for intrusive layering in the area of fronts?
Mutual penetration of waters with different temperature and salinity characteristics.
p.3
Hydrodynamic Equations
What approximation is used for free internal waves in this study?
The Boussinesq approximation with regard to Earth rotation.
p.2
Hydrodynamic Equations
What occurs when a beam of three-dimensional internal waves reflects from a layer?
Reflection occurs with energy losses.
p.15
Vertical Fine Structure Generation
What aspect of ocean thermocline is discussed in the 1983 study by Zhurbas and Ozmidov?
The Internal Structure of the Fine Stepped Structure of the Main Ocean Thermocline.
p.15
Inertia-Gravity Waves
What is the focus of the 2022 study by Chashechkin and Ochirov?
Periodic Waves and Ligaments on the Surface of a Viscous Exponentially Stratified Fluid.
What happens to the imaginary part of the frequency for the second mode when frequency is less than 12 cph?
It is negative, indicating weak attenuation.
