The effect of temperature on CDOM fluorescence was investigated in dystrophic freshwaters Wisconsin and aqueous standards. Laboratory experiments with two commercial situ fluorometers showed that intensity decreased as ambient water increased. A compensation equation derived to standardize measurements a specific reference temperature. form the is: r = m /[1 + ρ(T − T )], where is (°C), ρ temperature‐specific coefficient (°C −1 ), subscripts stand for measured values. (We note an analogous...

After we derive the Serre system of equations water wave theory from a generalized variational principle, present some its structural properties. We also propose robust and accurate finite volume scheme to solve these in one horizontal dimension. The numerical discretization is validated by comparisons with analytical experimental data or other solutions obtained highly pseudo-spectral method.

The problem of waves propagating on the surface a two-dimensional ideal fluid infinite depth bounded above by an elastic sheet is studied with asymptotic and numerical methods. We use nonlinear model that has been used to describe dynamics ice sheets. Particular attention paid forced unforced having near-minimum phase speed. For problem, we find wavepacket solitary bifurcate from periodic minimum When moving load, that, for small-amplitude forcing, steady responses are possible at all...

A millimetric droplet bouncing on the surface of a vibrating fluid bath can self-propel by virtue resonant interaction with its own wave field. This system represents first known example pilot-wave form envisaged Louis de Broglie in his double-solution theory. We here develop model hydrodynamics coupling recent models droplet’s dynamics more realistic weakly viscous quasi-potential generation and evolution. The resulting is to capture number features reported experiment, including rapid...

The purpose of this work is to explore in detail the structure interior flow generated by periodic surface waves on a fluid with constant vorticity. problem mapped conformally strip and solved numerically using spectral methods. Once solution known, streamlines, pressure particle paths can be found back physical domain. We find that beneath contains zero, one, two or three stagnation points frame moving wave speed, describe bifurcations between these flows. When vorticity sufficiently...

In this paper, the unsteady evolution of two-dimensional fully nonlinear free-surface gravity–capillary solitary waves is computed numerically in infinite depth. Gravity–capillary wavepacket-type were found previously for full Euler equations, bifurcating from minimum linear dispersion relation. Small and moderate amplitude elevation waves, which known to be linearly unstable, are shown evolve into stable depression together with a radiated wave field. Depression certain large robust...

Eddi et al. [Phys. Rev Lett. 102, 240401 (2009)] presented experimental results demonstrating the unpredictable tunneling of a classical wave-particle association as may arise when droplet walking across surface vibrating fluid bath approaches submerged barrier. We here present theoretical model that captures influence bottom topography on this and so enables us to investigate its interaction with barriers. The coupled wave-droplet dynamics in events. As reported experiments by is case...

A droplet may ‘walk’ across the surface of a vertically vibrating bath same fluid, due to propulsive interaction with its wave field. This hydrodynamic pilot-wave system exhibits many dynamics previously believed exist only in quantum realm. Starting from first principles, we derive discrete-time fluid model, whereby bath–droplet interactions are modelled as instantaneous. By analysing stability fixed points system, explain walking and capture quantisations for multiple-droplet interactions....

Abstract We study nonlinear free‐surface rotational waves generated through the interaction of a vertically sheared current with topography. Equivalently, may be by pressure distribution along free surface. A forced Korteweg–de Vries equation (fKdV) is deduced incorporating these features. The weakly nonlinear, dispersive reduced model valid for small amplitude topographies. To effect gradually increasing topography amplitude, surface Euler equations are formulated in presence variable depth...

An algorithm for the solution of general isotropic nonlinear wave equations is presented. The based on a symmetric factorization linear part operator, followed by its exact integration through an integrating factor in spectral space. remaining and forcing terms can be handled with any standard pseudospectral procedure. Solving operator exactly effectively eliminates stiffness original problem, characterized wide range temporal scales. tested applied to several problems three-dimensional long...

A model equation governing the primitive dynamics of wave packets near an extremum linear dispersion relation at finite wavenumber is derived. In two spatial dimensions, we include effects weak variation in direction transverse to propagation. The resulting contrasted with Kadomtsev–Petviashvilli and Nonlinear Schrödinger (NLS) equations. derived as approximation equations for deep water gravity‐capillary waves, but has wider applications. Both line solitary waves which decay both...

Steady periodic and solitary waves propagating in a 2D fluid bounded above by flexible sheet—which may be viewed as modelling an ice sheet—are considered deep water. The non-linear elastic model is based on the special Cosserat theory of hyperelastic shells proposed Toland (2008, hydroelastic waves. Arch. Ration. Mech. Anal., 189, 325–362) for this problem. Numerical solutions are computed via conformal mapping pseudo-spectral method. New found using continuation method to follow branch...

Abstract The dynamics of solitary gravity–capillary water waves propagating on the surface a three-dimensional fluid domain is studied numerically. In order to accurately compute complex time-dependent solutions, we simplify full potential flow problem by using variables and taking particular cubic truncation possessing Hamiltonian with desirable properties. This approximation agrees remarkably well equations for bifurcation curves, wave profiles two-dimensional domain, higher-order...

Waves propagating on the surface of a three–dimensional ideal fluid arbitrary depth bounded above by an elastic sheet that resists flexing are considered in small amplitude modulational asymptotic limit. A Benney–Roskes–Davey–Stewartson model is derived, and we find fully localized wavepacket solitary waves (or lumps) may bifurcate from trivial state at minimum phase speed problem for range depths. Results using linear two nonlinear models compared. The stability these wave solutions...

Hydrodynamic quantum analogs is a nascent field initiated in 2005 by the discovery of hydrodynamic pilot-wave system [Y. Couder, S. Protière, E. Fort, and A. Boudaoud, Nature 437, 208 (2005)]. The consists millimetric droplet self-propeling along surface vibrating bath through resonant interaction with its own wave [J. W. M. Bush, Annu. Rev. Fluid Mech. 47, 269-292 (2015)]. There are three critical ingredients for like-behavior. first "path memory" [A. Eddi, Sultan, J. Moukhtar, Rossi, Y....

We develop a time-dependent conformal method to study the effect of viscosity on steep surface waves. When tension is included, numerical solutions are found that contain highly oscillatory parasitic capillary ripples. These small-amplitude ripples associated with high curvature at crest underlying viscous-gravity wave, and display asymmetry about wave crest. Previous inviscid studies waves have calculated intricate bifurcation structures appear for small tension. show numerically suppresses...

We study the evolution of small‐amplitude water waves when fluid motion is three dimensional. An isotropic pseudodifferential equation that governs free surface a with arbitrary, uniform depth derived. It shown to reduce Benney‐Luke equation, Korteweg‐de Vries (KdV) Kadomtsev‐Petviashvili (KP) and nonlinear shallow theory in appropriate limits. compute, numerically, doubly periodic solutions this equation. In weakly two‐dimensional long wave limit, computed patterns dispersion relations...

A millimetric droplet may bounce and self-propel on the surface of a vertically vibrating bath, where its horizontal “walking” motion is induced by repeated impacts with accompanying Faraday wave field. For ergodic long-time dynamics, we derive relationship between droplet’s stationary statistical distribution mean field in very general setting. We then focus case subjected to harmonic potential confined line. By analyzing system’s periodic states, reveal number dynamical regimes, including...

Steady solitary and generalized waves of a two-fluid problem where the upper layer is under flexible elastic sheet are considered as model for internal an ice-covered ocean. The fluid consists two layers constant densities, separated by interface. resists bending forces mathematically described fully nonlinear thin shell model. Fully localized computed via boundary integral method. Progression along various branches solutions shows that barotropic (i.e. surface modes) wave-packet wave end...

Three-dimensional solitary waves or lump solitons are known to be solutions the Kadomtsev--Petviashvili I equation, which models small-amplitude shallow-water when Bond number is greater than $\frac{1}{3}$. Recently, Pego and Quintero presented a proof of existence such for Benney--Luke equation with surface tension. Here we establish an explicit connection between these two equations numerically compute their speed-amplitude relation. Furthermore, collide illustrate soliton wave character....

A model equation for gravity-capillary waves in deep water is proposed. This a quadratic approximation of the potential flow equations and has wavepacket-type solitary wave solutions. The supports line which are spatially localized direction propagation constant transverse direction, lump both directions. Branches computed via numerical continuation method. stability each type examined. instability predicted by similar nonlinear Schrödinger equation. spectral lumps using waves' speed energy...

We present a fully predictive model for the impact of smooth, convex and perfectly hydrophobic solid onto free surface an incompressible fluid bath infinite depth in regime where tension is important. During impact, we impose natural kinematic constraints along portion interface that pressed by solid. This provides mechanism generation linear waves simultaneously yields pressure applied on impacting masses. The compares remarkably well with data spheres bouncing droplet experiments,...