De Vries Theory Research Articles

Numerical investigation on the interaction between internal solitary wave and self-propelled submersible

Internal solitary waves (ISWs) often seriously threaten the survivability of the underwater submersible. Most of the existing investigations focus on the interaction between ISWs and fixed or suspended submersibles. However, the investigation on the interaction between ISWs and self-propelled submersibles is still scarce, which is a more realistic case in the marine engineering. In this paper, a three-dimensional numerical model for the interaction between ISW and self-propelled submersible is developed. Based on the extended Korteweg–de Vries (eKdV) theory, the ISW is generated in a two-layer fluid numerical wave tank by solving the Navier–Stokes (N–S) equation. By introducing the hydrodynamic loadings provided by the ISW environment into the standard operation equation of the submersible, the six degrees-of-freedom motions of the submersible can be obtained. The dynamic overset mesh technology is adopted to simulate the motions of the self-propelled submersible in the ISW fluid field. The present numerical model is validated by comparing with the experiment on a submerged cylinder in the ISW environment. Using this numerical model, we compare the interaction effects of the fixed, suspended, or the self-propelled submersible in ISW and discuss the influences of propulsive forces of the self-propelled submersible on ISW–structure interaction effects. The numerical results show that the loadings and movements of the submersible change remarkably in the surge, heave, and pitch direction. Especially, the submersible with high propulsive forces can pierce the wave surface and reach a large pitch angle with the amplitude of 36°, which further results in a 35% motion speed decrease in the initial propulsion direction.

Analysis of the Differences in Internal Solitary Wave Characteristics Retrieved from Synthetic Aperture Radar Images under Different Background Environments in the Northern South China Sea

Two internal solitary waves (ISWs) with very long fronts observed by synthetic aperture radar (SAR) images in the northern South China Sea (NSCS) are comparatively analyzed based on oceanic reanalysis data and the Korteweg–de Vries (KdV) theory. The differences in the environmental parameters, wave half-width, and amplitude of the two ISW fronts in the two distinct oceanic environments are studied. In the presence of a weak westward surface current of approximately 0.05 m/s, the values of the linear wave speed increase by up to 0.056 m/s, and the retrieved ISW amplitudes decrease by up to 14 m. On the contrary, for another background oceanic environment considering a relatively strong eastward surface current of approximately 0.2 m/s, there are decreases of up to 0.17 m/s in the linear wave speed and increases of up to 32 m in the retrieved amplitudes. However, the results retrieved from both the SAR observations commonly show that the ISW amplitudes along the fronts reach their maximums at roughly 21°N and decrease toward the southern and northern sides, in spite of their distinct background environments.

Experimental and theoretical study of internal solitary wave loads on a submerged slender body

Based on the extended Korteweg de Vries (eKdV) theory and Morison's equation, a theoretical model of internal solitary wave (ISW) loads on a submerged slender body is investigated, and experimental measurements are further carried out in a large stratified fluid flume. The results show that the theoretical results are in good agreement with the experimental results. The horizontal force of the ISW on the slender body is consists of the horizontal dynamic pressure force and the friction force, in which the horizontal dynamic pressure force plays a dominant role. The vertical force includes the vertical wave force and the reduced gravity during the interaction between a slender body and an ISW. The magnitude of the force increases with increasing ISW amplitude, while its direction remains unchanged, and the force is closely related to the submerged depth of the slender body in the density pycnocline, which affects both the magnitude and the direction of the force.

Weakly nonlinear waves in stratified shear flows

<p style='text-indent:20px;'>We develop a Korteweg–De Vries (KdV) theory for weakly nonlinear waves in discontinuously stratified two-layer fluids with a generally prescribed rotational steady current. With the help of a classical asymptotic power series approach, these models are directly derived from the divergence-free incompressible Euler equations for unidirectional free surface and internal waves over a flat bed. Moreover, we derive a Burns condition for the determination of wave propagation speeds. Several examples of currents are given; explicit calculations of the corresponding propagation speeds and KdV coefficients are provided as well.</p>

Experimental study of elevation- and depression-type internal solitary waves generated by gravity collapse

Gravity collapse in density stratified fluids can excite internal solitary waves (ISWs), which have been studied by creating initial steplike rectangular disturbances in two-layer fluid systems in stratified fluid flumes. The observation of the elevation- and depression-type ISWs has brought detailed insights into the conditions that generate stable propagation of ISWs and the properties thereof. In this work, the results of such experiments are compared with the wave profile, phase velocity, characteristic frequency, and induced flow velocity calculated by using nonlinear theories. In addition, we analyze the capacity of nonlinear theories to accurately predict the characteristics of stable ISWs generated by gravity collapse. The results show that ISWs are generated by the evolution of the propagating vortex that develops from the vertical shear movement in the mixed-density region of the fluid. The length L and depth D of the initial steplike disturbance and the upper- and lower-layer thicknesses h1 and h2 together determine the amplitude, number, and propagation state of the ISWs that are generated. For small-amplitude elevation- and depression-type ISWs (|a/H| < 0.04, where a and H are the amplitude and total depth of the stratified fluid, respectively), the generated ISWs are consistent with the Korteweg de Vries (KdV) theory. Large-amplitude ISWs, however, tend to be consistent with the extended KdV (eKdV) or Miyata–Choi–Camassa (MCC) theories. For larger (smaller) differences |h2 − h1|, the MCC (eKdV) theory provides the best prediction of large-amplitude ISWs.

Triangular temporal-distribution law for disintegrating internal solitons over a step

ABSTRACT Internal solitary waves have been found to disintegrate into a series of solitons over variable bathymetry, with important applications for offshore engineering. Considering realistic background stratification in the South China Sea, internal solitary waves propagating over a step are studied here. By assuming disintegrated solitons propagate independently, a theoretical model, namely a triangular temporal-distribution law based on the Korteweg–de Vries theory, is proposed to describe the fission process of internal solitary waves undergoing disintegration. A parameter is then introduced to quantify the accuracy of the theoretical model. The results indicate that the triangular law predicts the fission process better for a longer travelling distance and a larger amplitude of internal solitary waves.

The Deformation of Shoaling Internal Waves Observed at the Dongsha Atoll in the Northern South China Sea

The deformation of nonlinear internal waves (NLIW) from depression to elevation waves during the shoaling process has been attributed to three key factors: wave amplitude, mixed-layer depth and water depth. This study examined the critical conditions for wave deformation by means of five strings of thermistors deployed at the Dongsha Atoll in the northern South China Sea (SCS). During a two-day experiment, four wave trains consisting of 78 solitone at five sites were identified. The parameters related to soliton transformation were formulated by applying the extended Korteweg—de Vries (eKdV) theory. The results indicated that the soliton energy dispersed dramatically along the sharp bottom slope, likely as a result of bottom friction and turbulence mixing. Large-amplitude depression waves were observed to transform into elevation waves before the thickness of the lower layer became equal to that of the upper layer. The ratio of the wave amplitude to the lower-layer thickness was found to be a good indicator of wave deformation. The critical conditions for the transition of the internal waves (IWs) occurred at the ratio approximately equal to 0.66 ± 0.2. This means that a bottom-trapped elevation wave could form before passing through the theoretical critical point. The solitons felt the bottom and deformed when their amplitudes approached half of the lower-layer thickness. The solitons existed in the form of elevation waves when the waves were in contact with the bottom.

An experimental study of the free evolution of rotating, nonlinear internal gravity waves in a two-layer stratified fluid

AbstractThe temporal evolution of nonlinear large-scale internal gravity waves, in a two-layer flow affected by background rotation, is studied via laboratory experiments conducted in a cylindrical tank, mounted on a rotating turntable. The internal wave field is excited by the relaxation of an initial forced tilt of the density interface ($\eta _{i}$), which generates internal waves, such as Kelvin and Poincaré waves, in response to rotation effects. The behaviour of $\eta _{i}$, in the shore region, is analysed in terms of the background rotation and the nonlinear steepening of the basin-scale waves. The results show that the degeneration of the fundamental Kelvin wave into a solitary-type wave packet is caused by nonlinear steepening and it is influenced by the background rotation. In addition, the physical scales of the leading solitary-type wave are closer to Korteweg–de Vries theory as the rotation increases. Moreover, the nonlinear interaction between the Kelvin wave and the Poincaré wave can transfer energy to higher or lower frequencies than the frequency of the fundamental Kelvin wave, as a function of the background rotation. In particular, a specific normal mode in the off-shore region could be energized by this interaction. Finally, the bulk decay rate of the fundamental Kelvin wave, $\tau _{dk}$, was investigated. The results exhibit that $\tau _{dk}$ is concordant with the Ekman damping time scale when there is no evidence of steepening in the basin-scale waves. However, as nonlinear processes increase, $\tau _{dk}$ shows a strong decrease. In this context, the nonlinear processes play an important role in the decay of the fundamental Kelvin wave, via the energy radiation to other modes. The results reported demonstrate that the background rotation and nonlinear processes are essential aspects in understanding the degeneration and the decay of large-scale internal gravity waves on enclosed basins.

Mutant Utopias: Evening Primroses and Imagined Futures in Early Twentieth-Century America

Hugo de Vries's mutation theory is now little more than a footnote to the history of biology, a failed theory that briefly led a few biologists astray. However, for the first quarter of the twentieth century it attracted considerable attention from both professional biologists and laypeople. De Vries's theory--together with the plant, Oenothera lamarckiana, that had supplied most of his evidence--became the focus of a surprising variety of imaginative hopes. Scientists and their various publics were fascinated by the utopian possibilities that the primrose seemed to offer, and their discussions shaped a public culture around biology that would help define the twentieth century as the "century of the gene." From a conventional history of science perspective (which, in the case of twentieth-century biology, often remains focused on the content of scientific theories and the professional communities that shaped them), the mutation theory seems unimportant. However, while De Vries's new theory of evolution ultimately failed to persuade the scientific community, it was much more important than is now realized, particularly because it helped make biology part of a wide variety of public debates. Understanding the mutation theory's story more fully suggests that we may need to rethink much of the rest of the century of the gene's history, to think less in terms of what happened in the lab and more about how biology came to function as public culture.

Solitary Rossby Waves in the Lower Tropical Troposphere

Weakly nonlinear approximation is used to study the theoretical comportment of large-scale disturbances around the intertropical midtropospheric jet. We show here that the Korteweg de Vries (KdV) theory is appropriated to describe the structure of the streamlines around the African easterly jet (AEJ) region. The introduction of the additional velocity of the soliton C1 permits to search the stage where the configuration of the wave structures is going to emerge out of specified initial conditions and this is the direct and inverse cascade method. It was also shown that the configurations of disturbances can be influenced by this parameter so that we can look if the disturbances are in the control or not of their dispersive effects. This permits to explain the evolution of initial conditions of the Tropical Storm (TS) Debby over West Africa from 20 to 24 August 2006.

Microwave Drying of Food and Agricultural Materials: Basics and Heat and Mass Transfer Modeling

Microwave drying is based on a unique volumetric heating mode facilitated by electromagnetic radiation at 915 or 2,450 MHz. The responses of a lossy food product to dielectric heating result in rapid energy coupling into the moisture and lead to fast heating and drying. A significant reduction in drying time in microwave drying is often accompanied by an improvement in product quality, making it a promising food dehydration technology. The need for improvement in engineering design and process optimization for microwave drying has stimulated the development of computer simulation techniques to predict temperature and moisture history and distribution in the product to be dried. In this article, we present the basics of dielectric heating and drying, examine the heat and mass transfer models developed for the simulation of microwave drying processes, and discuss dielectric properties of selected food products as influenced by moisture, temperature, and porosity. In addition, we analyze nonuniform heating caused by the geometry and composition of the product, as well as by the nonuniform distribution of electromagnetic field in a microwave cavity, followed by a discussion on how to improve the microwave heating uniformity. We focus the discussion on heat and mass transfer models developed over the years to simulate microwave drying, including simplified ones, those based on diffusion theory, and coupled heat and mass transfer analysis with the Philip and de Vries theory, Luikov scheme, Whitaker method, and two-region model. In the end, the determination of the heat source term in the energy equation, numerical schemes used to solve the partial differential equations, and the model validation are also discussed.

The Modified Camassa-Holm Equation

The Camassa–Holm (CH) equation describes pseudo-spherical surfaces and therefore its integrability properties can be studied by geometrical means [Reyes, “Geometric integrability of the Camassa–Holm equation.” Letters in Mathematical Physics 59 (2002): 117–31]. Using this fact, we introduce a “Miura transform” and a “modified” Camassa–Holm (mCH) equation, in analogy with the Korteweg–de Vries theory. We obtain an infinite number of local conservation laws for CH from these data and also an infinite number of (non)local symmetries. We then compute conservation laws for mCH and also show that it describes pseudo-spherical surfaces, so that, in particular, it is the integrability condition of an -valued linear problem. Finally, we investigate mCH analytically: we define weak solutions and prove their existence and uniqueness.

On vorticity waves propagating in a waveguide formed by two critical layers

A theoretical model for long vorticity waves propagating on a background shear flow is developed. The basic flow is assumed to be confined between two critical layers, respectively, located near the lower and upper rigid boundaries. In these critical layers even small disturbances will break, and eventually a thin zone of mixed fluid will appear. We derive a nonlinear evolution equation for the amplitude of a wave-like disturbance in this configuration, based on the assumption that the critical layers are replaced by thin recirculation zones attached to the lower and upper rigid boundaries, where the flow is very weak. The dispersive and time-evolution terms in this equation are typical for Korteweg–de Vries theory, but the nonlinear term is more complicated. It comprises nonlinearity associated with the shear across the waveguide, and the nonlinearity due to the flow over the recirculation zones. The coefficient of the quadratic nonlinear term may change sign, depending on the presence or otherwise of recirculation zones at the upper or lower boundary of the waveguide. We then seek steady travelling wave solutions, and show that there are no such steady solutions if the waveguide contains no density stratification. However, steady solutions including solitary waves and bores can exist if the fluid between the critical layers is weakly density stratified.

Dynamic characteristics and horizontal transports of internal solitons generated at the Columbia River plume front

River plume front-generated internal solitons play an important role in the interaction between the plume and coastal waters. The internal solitons drive a non-harmonic velocity field, resulting in a horizontal transport that carries plume water seaward and redistributes nutrients and sediments. In this study, we present observations of internal solitons generated at the Columbia River plume front that separates the new, tidal plume, older plume and coastal waters. Scale analyses suggest that the plume front-generated internal solitons are highly non-linear waves, and their dynamic properties do not conform to any weakly non-linear theory. Thus, a high-order Korteweg–de Vries (KdV) theory is used to analyze the internal solitons. The comparison between theoretical values and cruise data shows that the high-order KdV model is much better than the weakly non-linear theories for prediction of the soliton dynamic parameters. Based on the model, we develop theoretical and numerical solutions of the soliton-induced upper layer horizontal transport and Lagrangian water parcel transport distance, which shows that the water particle drift, during the internal soliton passage, is as far as 1 km, and demonstrates the role of the internal solitons on the exchange between the plume and ambient coastal water. Energy fluxes caused by the internal solitons are estimated using the high-order KdV theory. The leading soliton fluxes 2.0×10 3 W m −1 per unit crest length, and carries energy of 4.2×10 5 J m −1. The total energy carried by the eight internal solitons is 1.6×10 6 J m −1, about 70% of the total frontal energy.

Modified Korteweg–de Vries theory of non-monotonic double layers in multi-species plasma

AbstractThe analytic solution for the time stationary non-monotonic double layers in multi-species plasma is presented. This solution is the analytic extension of the monotonic double layer and the solitary hole. We have derived the modified Korteweg–de Vries equation in plasmas, taking account of negative ion effects. The effects of negative ion and density on the properties of the non-monotonic double layer are discussed.

A laboratory experiment on internal solitary waves

A simple laboratory experiment is designed to show the properties of internal solitary waves. The procedure and analysis are suited for a senior undergraduate laboratory course, though the techniques described may also be used for demonstration purposes in a fluid mechanics course. The measurements collected can be compared to the weakly nonlinear Korteweg–deVries (KdV) theory for the wave shape, lengthscale-amplitude relationship, and phase speed. The experiment provides a good introduction to internal solitary waves in the ocean, along with an exploration of error analysis and the limits of applicability of a theory.

The Short-Wave Limit of Linear Equatorial Kelvin Waves in a Shear Flow

Abstract The effects of latitudinal shear on equatorial Kelvin waves in the one-and-one-half-layer model are examined through a mixture of perturbation theory and numerical solutions. For waves proportional to exp(ikx), where k is the zonal wavenumber and x is longitude, earlier perturbation theories predicted arbitrarily large distortions in the limit k → ∞. In reality, the distortions are always finite but are very different depending on the sign of the equatorial jet. When the mean jet is westward, the Kelvin wave becomes very, very narrow. When the mean jet flows eastward, the Kelvin wave splits in two with peaks well off the equator and exponentially small amplitude at the equator itself. The phase speed is always a bounded function of k, asymptotically approaching a constant. This condition has important implications for the nonlinear behavior of Kelvin waves. Strong nonlinearity cannot be balanced by contracting longitudinal scale, as in the author’s earlier Korteweg–deVries theory for equatorial solitons: for sufficiently large amplitude, the Kelvin wave must always evolve to a front.

Numerical Simulation of the Propagation of a Solitary Wave over Underwater Barriers

The problem on the behavior of a solitary wave passing over different types of underwater barriers is considered. The problem has been solved numerically using the method of the correction of flows. The parameters of the method of solution have been selected. The results are compared with the Korteweg–de Vries theory. The interaction of two solitary waves is simulated and it is shown that they possess the properties of solitons. After the interaction, their shape and velocity remain constant; it is only the phase that undergoes a change. The case of disintegration of the initial perturbation in a cylindrically symmetric problem is considered.

Soil Water Heat of Transport

Competing theories used to describe coupled transport of heat and water in soil are irreversible thermodynamics (IT) and the Philip–de Vries (PD) theory. In practice, PD has dominated the field and advanced understanding through models used to predict the thermal status of soil and soil-atmosphere interaction. However, the principle of Onsager reciprocity in IT has also found considerable acceptance in thermal physics. The applicability of IT reciprocity to soil physics has been extensively scrutinized without substantial agreement being reached. Examination of PD equations reveals that they do not satisfy Onsager reciprocity. One coefficient is missing from PD that would produce equations consistent with reciprocity. The coefficient is associated with the thermal water flux, but it fails to appear a second time in the heat flux equation as expected with reciprocity. This missing coefficient can be readily calculated for inclusion in models based on PD. The value of the coefficient varies with temperature...

Excitation and propagation of negative-potential solitons in an electronegative plasma

The excitation, propagation, and interaction of planar negative-potential solitary waves in a plasma containing positive ions, negative ions, and electrons (i.e., an electronegative plasma) are studied using a hybrid simulation with kinetic, particle ions, and Boltzmann electrons. Solitary waves are launched into the plasma when the potential on an initially unbiased electrode is stepped downward. They then propagate self-consistently through the ambient plasma. Results are shown for excitation and propagation as well as for overtaking collisions. During overtaking collisions, the solitons preserve their shape and speed, though they are not necessarily described by the Korteweg–deVries theory. These solitons may provide a useful diagnostic of the negative ion concentration in electronegative plasmas.