Search

The Serre–Green–Naghdi equations of water wave theory have been widely employed to study undular bores. In this study, we introduce a modified Serre–Green–Naghdi system incorporating the effect of an artificial term that results in dispersive and dissipative dynamics. We show that the modified system effectively approximates the classical Serre–Green–Naghdi equations over sufficiently extended time intervals and admits dispersive–diffusive shock waves as traveling wave solutions. The traveling waves converge to the entropic shock wave solution of the shallow water equations when the dispersion and diffusion approach zero in a moderate dispersion regime. These findings contribute to an understanding of the formation of dispersive shock waves in the classical Serre–Green–Naghdi equations and the effects of diffusion in the generation and propagation of undular bores. [ABSTRACT FROM AUTHOR]

The Korteweg-de Vries (KdV) equation is a well-known model equation for unidirectional shallow-water (long) surface waves. The equation includes dispersion and weak non-linearity. The derivation of the equation originates in assuming that the velocity potential takes the form of an asymptotic expansion, and applying this in the classical surface wave problem. While a typical assumption on the relative size of non-dimensional key parameters introduced in the derivation will give the KdV equation as a final result, one can change the assumption on the relative size of parameters, and end up with an equation including terms in higher orders in desired parameters. The present article presents the derivation of an extended form referred to as the eeKdV equation. Information regarding various properties of the flow can be found by studying the derivation of the eeKdV equation itself, and some of the relations found can be used for studying the energy balance of a system modeled by the equation. In line with previous work for the KdV equation, we present here corresponding formulations of energy balance laws for an inertial reference frame, in context of the eeKdV equation. We also present a partial verification of the KdV and eeKdV energy flux expressions by looking at a far-field, uniform flow situation, as well as performing a numerical study to confirm the assumed behaviour of the error in the eeKdV energy equation in the context of a undular bore flow setup. Further, conserved integrals for the eeKdV equation are presented and numerically checked. [ABSTRACT FROM AUTHOR]

We consider a dissipative, dispersive system of the Boussinesq type, which describes wave phenomena in scenarios where dissipation plays a significant role. Examples include undular bores in rivers or oceans, where turbulence-induced dissipation significantly influences their behavior. In this study, we demonstrate that the proposed system admits traveling wave solutions known as diffusive-dispersive shock waves. These solutions can be categorized as oscillatory and regularized shock waves, depending on the interplay between dispersion and dissipation effects. By comparing numerically computed solutions with laboratory data, we observe that the proposed model accurately captures the behavior of undular bores over a broad range of phase speeds. Traditionally, undular bores have been approximated using the original Peregrine system, which, even though it doesn't possess these as traveling wave solutions, tends to offer accurate approximations within suitable time scales. To shed light on this phenomenon, we demonstrate that the discrepancy between the solutions of the dissipative Peregrine system and the non-dissipative counterpart is proportional to the product of the dissipation coefficient and the observation time. [ABSTRACT FROM AUTHOR]

In this study, a speed parameter is introduced into the steady Korteweg–de Vries (KdV)–Burgers equation which enables the theoretical undular bore profiles to be adjustable with a proper combination of the speed parameter and the viscous damping parameter. A new criterion for identifying the above two bores is then proposed with respect to these two parameters, whose influence on the undular bore profile is then discussed. For the theoretical solution with a small damping, error after introducing the variable speed parameter is limited. A large speed parameter corresponds to a wide range of acceptable dampings. From the energy perspective, it is confirmed that the speed parameter also denotes the nonlinearity effect. In addition, comparison between the theoretical and experimental results shows the superiority of the present model over the traditional model, which also reveals the physical meanings of the present model. [ABSTRACT FROM AUTHOR]

The addition of higher order asymptotic corrections to the Korteweg--de Vries equation results in the extended Korteweg--de Vries (eKdV) equation. These higher order terms destabilize the dispersive shock wave solution, also termed an undular bore in fluid dynamics, and result in the emission of resonant radiation. In broad terms, there are three possible dispersive shock wave regimes: radiating dispersive shock wave (RDSW), cross-over dispersive shock wave (CDSW) and travelling dispersive shock wave (TDSW). While there are existing solutions for the RDSW and TDSW regimes obtained using modulation theory, there is no existing solution for the CDSW regime. Modulation theory and the associated concept of a Whitham shock are used to obtain this CDSW solution. In addition, it is found that the resonant wavetrain emitted by the eKdV equation with water wave coefficients has a minimal amplitude. This minimal amplitude is explained based on the developed Whitham modulation theory. [ABSTRACT FROM AUTHOR]

We study the evolution of the longitudinal release wave that is generated by induced tensile fracture as it propagates through solid rectangular polymethylmethacrylate (PMMA) bars of different constant cross-section. High-speed multi-point photoelasticity is used to register the strain wave at three distances from the fracture site in each experiment. In all cases, oscillations develop at the bottom of the release wave that exhibit the qualitative features of an undular bore. The pre-strain, post-strain, strain rate of the release wave and the cross-section dimensions determine the evolution of the oscillations. From the wave speed and strain rate close to the fracture site, we estimate the strain rate of the release wave as well as the growth of the amplitude and duration of the leading oscillation away from the fracture site by using formulae derived from the simple analytical solution of the linearized Gardner equation (linearized near the pre-strain level at fracture). Our estimates are then compared to experimental data, where good agreements of these three parameters are found between the predictions of the model and the experimental observations. Thus, we developed an approach to estimating the key characteristics of the developing unsteady undular bore based on the measured initial speeds of the longitudinal and shear waves. This does not require a prior knowledge of the elastic moduli for the conditions of the experiments, which in PMMA are known to be strain rate dependent. [ABSTRACT FROM AUTHOR]

In this study, the problem of surface waves induced by water flow in a flow channel was investigated. The mathematical model based on the potential wave theory was established, and a new analytic solution to the corresponding initial and boundary value problem was proposed. To confirm our analytic solution, the mathematical model was applied to simulate experiments conducted in a flow channel in the laboratory. Using our analytic solution, water surface elevations and flow velocities at certain locations in the channel were compared with experimental results. Comparisons between our analytic solution and experimental results confirmed our theory that amplitudes and propagating phases are in very close agreement. Our analytic solution can be used to calculate variations in pressure and velocity along the water depth, which are expensive to calibrate and obtain in experiments. Although our analytic solution was established based on linear theory, it is very practical for applications studying the basic properties of surface elevation, velocity, and pressure of the flow field induced by water current both in space and time. [ABSTRACT FROM AUTHOR]

In this work, the dispersive shock wave (DSW) solution of a Boussinesq Benjamin–Ono (BBO) equation, the standard Boussinesq equation with dispersion replaced by nonlocal Benjamin–Ono dispersion, is derived. This DSW solution is derived using two methods, DSW fitting and from a simple wave solution of the Whitham modulation equations for the BBO equation. The first of these yields the two edges of the DSW, while the second yields the complete DSW solution. As the Whitham modulation equations could not be set in Riemann invariant form, the ordinary differential equations governing the simple wave are solved using a hybrid numerical method coupled to the dispersive shock fitting which provides a suitable boundary condition. The full DSW solution is then determined, which is found to be in excellent agreement with numerical solutions of the BBO equation. This hybrid method is a suitable and relatively simple method to fully determine the DSW solution of a nonlinear dispersive wave equation for which the (hyperbolic) Whitham modulation equations are known, but their Riemann invariant form is not. [ABSTRACT FROM AUTHOR]

In this study, the problem of surface waves induced by water flow in a flow channel was investigated. The mathematical model based on the potential wave theory was established, and a new analytic solution to the corresponding initial and boundary value problem was proposed. To confirm our analytic solution, the mathematical model was applied to simulate experiments conducted in a flow channel in the laboratory. Using our analytic solution, water surface elevations and flow velocities at certain locations in the channel were compared with experimental results. Comparisons between our analytic solution and experimental results confirmed our theory that amplitudes and propagating phases are in very close agreement. Our analytic solution can be used to calculate variations in pressure and velocity along the water depth, which are expensive to calibrate and obtain in experiments. Although our analytic solution was established based on linear theory, it is very practical for applications studying the basic properties of surface elevation, velocity, and pressure of the flow field induced by water current both in space and time.

A tidal bore is a natural phenomenon usually occur in bays with large tidal waves. Sometimes this large tidal inflow are channeled deep into a river. In Indonesia, this natural phenomenon is found in the Kampar River, which is known as the tidal bore Bono. Sometimes, these tidal bore phenomena disappear, as happened to the Mascaret, tidal bore on the River Seine France. Through an understanding of the formation of tidal bore mechanism, there is hope that the tidal bore Bono in Kampar River can be preserved. In this paper, the occurrence of tidal bore Bono is simulated using the non-hydrostatic Saint-Venant equation under a staggered grid formulation. To test the accuracy of the implementation, several scenarios of hydraulic jumps were simulated first. The numerical results have shown to quantitatively confirm the analytical formula of bore height and velocity, two parameters that are important to characterize a bore wave. Further, by adopting a model that incorporates the non-hydrostatic pressure, our simulation shows the appearance of an undular bore accompanying the shock front. Finally, by using tidal current data measured along Kampar River estuary, our simulation that employs the actual river topography can show the appearance of tidal bore Bono. Our simulations were shown to be in fair agreement with the measurement.

A uniform flow on an open channel is studied in this paper. Shallow water equations are used as the model by involving the bottom topography. In this problem, we focus on incline bottom and put a bump on it, so that the flow generates a surface wave. The model is extended by energy dissipation through tangential shear and the energy dissipation by shearing normal to the flow. In non-dimensional variables, the profile of the fluid surface is observed as waves growing to split and propagating, depending on the type of the bump, parameters angle of the channel, Froude number and Reynolds number. When the angle is not zero, we found that the waves propagate downward and possible appearing secondary waves or undular bore, that does not occur for zero angles but agrees to the model of Boussinesq equations. To get the accurate result with purely showing the damping effect from the equation, the finite volume method has been applied on a staggered grid that is free from damping error to solve the equations numerically. [ABSTRACT FROM AUTHOR]

It is known from linear theory that bottom oscillations in uniform open-channel flow can produce resonant surface waves with zero group velocity and diverging amplitude (Tyvand and Torheim 2012). This resonance exists for Froude numbers smaller than one, at a critical frequency dependent on the Froude number. This resonance phenomenon is studied numerically in the time domain, with fully nonlinear free-surface conditions. An oscillatory 2D bottom source is started, and the local elevation at resonance grows until it may reach a saturation amplitude. Four waves exist at subcritical Froude numbers, where resonance represents the third and the fourth wave merging. In the zero-frequency limit, the dispersive second and fourth wave merge into a steady wave with finite group velocity and amplitude, and no other periodic waves exist. In the time-dependent nonlinear analysis at zero frequency, a transient undular bore may emerge as the dominating phenomenon. [ABSTRACT FROM AUTHOR]

When tsunami waves propagate into shallow and gentle continental shelves, the effects of submarine topography and wave dispersion lead to the appearance of undular bore. This kind of wave is quite different from the initial tsunami wave in the waveform, and its amplitude is enhanced significantly. The undular bore will cause great and repeated runups on the beach, which brings larger destruction to the coastal region. In order to investigate the characteristics of the propagation of undular bore, this paper simulates the evolution from the sinusoidal long wave to the undular bore and analyzes the influencing factors. The beach slope has an important effect on the development of undular bores in terms of the undulation form, amplitude, wave length and occurrence time. The influence of bottom friction and submarine topography on the undulations and soliton fissions are discussed. These bottom conditions will lead to great change of the waveform and amplitude of undular bores. [ABSTRACT FROM AUTHOR]

A tidal bore is a natural phenomenon usually occur in bays with large tidal waves. Sometimes this large tidal inflow are channeled deep into a river. In Indonesia, this natural phenomenon is found in the Kampar River, which is known as the tidal bore Bono. Sometimes, these tidal bore phenomena disappear, as happened to the Mascaret, tidal bore on the River Seine France. Through an understanding of the formation of tidal bore mechanism, there is hope that the tidal bore Bono in Kampar River can be preserved. In this paper, the occurrence of tidal bore Bono is simulated using the non-hydrostatic Saint-Venant equation under a staggered grid formulation. To test the accuracy of the implementation, several scenarios of hydraulic jumps were simulated first. The numerical results have shown to quantitatively confirm the analytical formula of bore height and velocity, two parameters that are important to characterize a bore wave. Further, by adopting a model that incorporates the non-hydrostatic pressure, our simulation shows the appearance of an undular bore accompanying the shock front. Finally, by using tidal current data measured along Kampar River estuary, our simulation that employs the actual river topography can show the appearance of tidal bore Bono. Our simulations were shown to be in fair agreement with the measurement. [ABSTRACT FROM AUTHOR]

The secondary wave field associated with undular tidal bores (known as whelps) has been barely studied in field conditions: the wave field can be strongly non-hydrostatic, and the turbidity is generally high. In situ measurements based on pressure or acoustic signals can therefore be limited or inadequate. The intermittent nature of this process in the field and the complications encountered in the downscaling to laboratory conditions also render its study difficult. Here, we present a new methodology based on LiDAR technology to provide high spatial and temporal resolution measurements of the free surface of an undular tidal bore. A wave-by-wave analysis is performed on the whelps, and comparisons between LiDAR, acoustic and pressure-derived measurements are used to quantify the non-hydrostatic nature of this phenomenon. A correction based on linear wave theory applied on individual wave properties improves the results from the pressure transducer (Root mean square error, RMSE of 0.19 m against 0.38 m); however, more robust data is obtained from an upwards-looking acoustic sensor despite high turbidity during the passage of the whelps ( RMSE of 0.05 m). Finally, the LiDAR scanner provides the unique possibility to study the wave geometry: the distribution of measured wave height, period, celerity, steepness and wavelength are presented. It is found that the highest wave from the whelps can be steeper than the bore front, explaining why breaking events are sometimes observed in the secondary wave field of undular tidal bores. [ABSTRACT FROM AUTHOR]

Two implicit and two explicit schemes preserving the local momentum conservation laws exactly on any time–space region are proposed for the regularized long-wave equation. With appropriate boundary conditions, the schemes will be energy- and mass-preserving globally. Combining with the momentum conservation laws, we obtain the priori estimates of the numerical solution and the error estimates in l ∞ norm for the proposed implicit schemes. Numerical experiments show the excellent performance of the proposed schemes and the numerical results coincide with the theoretical ones. [ABSTRACT FROM AUTHOR]

Hydraulic transients with the movement of an interface between pressurized flow and free surface flow can be observed in rapid water emptying in the pipes. This study focuses on air cavity intrusion into horizontal and inclined circular pipes. Laboratory experiments were carried out to observe the negative surge during depressurization in a circular pipe. In order to generate the undular bore in a circular pipe, in some cases a sharp-crested weir at the open end of the horizontal pipe was used. Various behaviors of air cavity were observed for a series of weir heights. A numerical model is proposed and applied to the cavity flow in a circular pipe. To reproduce the undular bore in circular pipes (when water depth is greater than pipe radius), this study derived the depth-averaged shallow water equations with the effects of vertical acceleration using the Boussinesq equation. In this study, the continuity and the momentum equations of free surface and pressurized flows with the hydrostatic and the Boussinesq pressure assumptions have been used. The results from the model showed good agreement with the experimental results. [ABSTRACT FROM AUTHOR]

The 2011 Tohoku tsunami entered the Kitakami river and propagated there as a train of shock waves, recorded with a 1-min interval at water level stations at Fukuchi, Iino, and the weir 17.2 km from the mouth, where the bulk of the wave was reflected back. The records showed that each bore kept its shape and identity as it traveled a 10.9-km-path Fukuchi-Iino-weir-Iino. Shock handling based on the cross-river integrated classical shock conditions was applied to reconstruct the flow velocity time histories at the measurement sites, to estimate inflow into the river at each site, to evaluate the wave heights of incident and reflected tsunami bores near the weir, and to estimate propagation speed of the individual bores. Theoretical predictions are verified against the measurements. We discuss experiences of exercising the shock conditions with actual tsunami measurements in the Kitakami river, and test applicability of the shallow-water approximation for describing tsunami bores with heights ranging from 0.3 to 4 m in a river segment with a depth of 3-4 m. [ABSTRACT FROM AUTHOR]

The paper reports unique high-resolution observations of meteotsunami by a large array of oceanographic instruments deployed on the Atchafalaya Shelf (Louisiana, USA) in 2008 with the primary aim to study wave dissipation in muddy environments. The meteotsunami event on March 7, 2008, was caused by the passage of a cold front which was monitored by the NOAA NEXRAD radar. The observations of water surface elevations on the shelf show a highly detailed textbook picture of an undular bore (solibore) in the process of its disintegration into a train of solitons. The picture has a striking feature never reported before not only for the meteotsunamis but in other contexts of disintegration of a long-wave perturbation into a sequence of solitons as well-the persistent presence of a single soliton, well ahead of the solibore. Data analysis and simulations based on the celebrated variable-coefficient KdV (vKdV) equation first proposed by Ostrovsky and Pelinovsky (Izv Atmos Ocean Phys 11:37-41, 1975) explain the physics of this phenomenon and suggest that the formation of the lone soliton ahead of the solibore is very likely to be the result of the specific interplay of natural meteotsunami forcing and nearshore bathymetry. The analysis strongly suggests that the patterns of coexisting lone solitons and packets of cnoidal waves should be quite common for meteotsunamis. They were not observed before only because of the scarcity of high-resolution observations. The results highlight the effectiveness of the vKdV equation in providing understanding of the fundamental mechanisms of the complex natural phenomenon that would otherwise require computationally very expensive numerical models. [ABSTRACT FROM AUTHOR]

Gerald Beresford (GB) Whitham, FRS, (13th December, 1927–26th January, 2014) was one of the leading applied mathematicians of the twentieth century whose work over forty years had a profound, formative impact on research on wave motion across a broad range of areas. Many of the ideas and techniques he developed have now become the standard tools used to analyse and understand wave motion, as the papers of this special issue of Physica D testify. Many of the techniques pioneered by GB Whitham have spread beyond wave propagation into other applied mathematics areas, such as reaction–diffusion, and even into theoretical physics and pure mathematics, in which Whitham modulation theory is an active area of research. GB Whitham’s classic textbook Linear and Nonlinear Waves , published in 1974, is still the standard reference for the applied mathematics of wave motion. In honour of his scientific achievements, GB Whitham was elected a Fellow of the American Academy of Arts and Sciences in 1959 and a Fellow of the Royal Society in 1965. He was awarded the Norbert Wiener Prize for Applied Mathematics in 1980. [ABSTRACT FROM AUTHOR]

Internal tidal wave entering shallow waters transforms into an undular bore and this process can be described in the framework of the Gardner equation (extended version of the Korteweg–de Vries equation with both quadratic and cubic nonlinear terms). Our numerical computations demonstrate the features of undular bore developing for different signs of the cubic nonlinear term. If cubic nonlinear term is negative, and initial wave amplitude is large enough, two undular bores are generated from the two breaking points formed on both crest slopes (within dispersionless Gardner equation). Undular bore consists of one table-top soliton and a group of small soliton-like waves passing through the table-top soliton. If the cubic nonlinear term is positive and again the wave amplitude is large enough, the breaking points appear on crest and trough generating groups of positive and negative soliton-like pulses. This is the main difference with respect to the classic Korteweg–de Vries equation, where the breaking point is single. It is shown also that nonlinear interaction of waves happens similarly to one of scenarios of two-soliton interaction of “exchange” or “overtake” types with a phase shift. If small-amplitude pulses interact with large-amplitude soliton-like pulses, their speed in average is negative in the case when “free” velocity is positive. Nonlinear interaction leads to the generation of higher harmonics and spectrum width increases with amplitude increase independently of the sign of cubic nonlinear term. The breaking asymptotic k 4 / 3 predicted within the dispersionless Gardner equation emerges during the process of undular bore development. The formation of soliton-like perturbations leads to appearance of several spectral peaks which are downshifting with time. [ABSTRACT FROM AUTHOR]

This paper carries out the numerical simulation of tsunami propagation based on the fully nonlinear and highly dispersive Boussinesq model. The numerical results indicate that the waveforms of a tsunami are quite different on steeply and mildly sloping beaches, which cannot be predicted by the analytical solution of the nonlinear shallow water equations. Long wave trains form on the steeply sloping beaches while undular bores emerge on the mildly sloping beaches. The simulation of hypothesized tsunamis in the China Seas provide different wave patterns in the near shore regions, including long wave trains, undular bores, and solitons. In order to study the propagation and run-up of undular bores, a series of undular bores is proposed by sinusoidal and attenuation functions. The properties of the run-up and energy budget of these undular bores are investigated. [ABSTRACT FROM AUTHOR]

We consider the step Riemann problem for the system of equations describing the propagation of a coherent light beam in nematic liquid crystals, which is a general system describing nonlinear wave propagation in a number of different physical applications. While the equation governing the light beam is of defocusing nonlinear Schrödinger (NLS) equation type, the dispersive shock wave (DSW) generated from this initial condition has major differences from the standard DSW solution of the defocusing NLS equation. In particular, it is found that the DSW has positive polarity and generates resonant radiation which propagates ahead of it. Remarkably, the velocity of the lead soliton of the DSW is determined by the classical shock velocity. The solution for the radiative wavetrain is obtained using the Wentzel--Kramers--Brillouin approximation. It is shown that for sufficiently small initial jumps the nematic DSW is asymptotically governed by a Korteweg--de Vries equation with the fifth-order dispersion, which explicitly shows the resonance generating the radiation ahead of the DSW. The constructed asymptotic theory is shown to be in good agreement with the results of direct numerical simulations. [ABSTRACT FROM AUTHOR]

The secondary wave field associated with undular tidal bores (known as whelps) has been barely studied in field conditions: the wave field can be strongly non-hydrostatic, and the turbidity is generally high. In situ measurements based on pressure or acoustic signals can therefore be limited or inadequate. The intermittent nature of this process in the field and the complications encountered in the downscaling to laboratory conditions also render its study difficult. Here, we present a new methodology based on LiDAR technology to provide high spatial and temporal resolution measurements of the free surface of an undular tidal bore. A wave-by-wave analysis is performed on the whelps, and comparisons between LiDAR, acoustic and pressure-derived measurements are used to quantify the non-hydrostatic nature of this phenomenon. A correction based on linear wave theory applied on individual wave properties improves the results from the pressure transducer (Root mean square error, R M S E of 0 . 19 m against 0 . 38 m); however, more robust data is obtained from an upwards-looking acoustic sensor despite high turbidity during the passage of the whelps ( R M S E of 0 . 05 m). Finally, the LiDAR scanner provides the unique possibility to study the wave geometry: the distribution of measured wave height, period, celerity, steepness and wavelength are presented. It is found that the highest wave from the whelps can be steeper than the bore front, explaining why breaking events are sometimes observed in the secondary wave field of undular tidal bores.

The formation of undular bores in Riemann problems of the good generalized Kaup–Boussinesq equation is investigated by Whitham modulation theory. Firstly, the Whitham equations associated with the one-phase and two-phase periodic wave solutions are given by the finite-gap averaging method. Secondly, the basic structures of rarefaction wave and dispersive shock wave are discussed by considering the self-similar solutions of the Whitham equations. Then we propose a complete classification of all possible wave patterns for the initial discontinuity of the good generalized Kaup–Boussinesq equation, in which it has been shown that the theoretical results from Whitham modulation theory are in good agreement with the full numerical simulations. The correspondences between the soliton frontiers of the dispersive shock waves and the exact soliton solution of the good generalized Kaup–Boussinesq equation are considered, and exotic undular bores are found. Finally, the dam break problem and piston problem are explored to show the important physical applications of the theoretical results, from which certain inspiring phenomena of wave breaking are discovered for the first time. • The Riemann problems of the generalized KB equation are investigated. • The Whitham equations are derived by the finite-gap averaging method. • The basic structures of rarefaction wave and dispersive shock wave are proposed. • A classification of all possible wave patterns for the initial discontinuity is given. • The dam break problem and piston problem are explored by Whitham modulation theory. [ABSTRACT FROM AUTHOR]

In this article, we intend to use quadratic and cubic B-spline quasi-interpolants to develop higher order numerical methods for some Sobolev type equations in one space dimension. Our aim is also to compare the performance of the proposed methods in terms of the accuracy and the rate of convergence. We also discuss another approach to the cubic B-spline quasi-interpolation based method, where we achieve fourth order of accuracy in space. We theoretically establish the order of accuracy for the three proposed methods and also establish the L 2 -stability in the linear case using von Neumann analysis. As a particular case of the Sobolev type equations, we take the equal width and the Benjamin–Bona–Mahony–Burgers equations, and perform several numerical experiments to support our theoretical results. [ABSTRACT FROM AUTHOR]

Field data on undular and breaking bores observed in a coastal zone and river estuaries were collected. The existing criteria of distinction of these two regimes of bores, which depend on the ratio between the bore height and unperturbed water depth, are applied to the collected data. It is shown that criterion H/ h > 1.5 (where H is bore height measured from the bottom and h is unperturbed depth of reservoir) is sufficient for the rough separation of the bores by their type. [ABSTRACT FROM AUTHOR]