Browsing Department of Mathematics by Author "Kalisch, Henrik"

Now showing items 1-20 of 21

    • Admissibility conditions for Riemann data in shallow water theory 

      Paulsen, Martin Oen; Kalisch, Henrik (Journal article; Peer reviewed, 2020)
      Consideration is given to the shallow-water equations, a hyperbolic system modeling the propagation of long waves at the surface of an incompressible inviscible fluid of constant depth. It is well known that the solution ...

    • Derivation of Boussinesq's shoaling law using a coupled BBM system 

      Kalisch, Henrik; Senthilkumar, Amutha (Peer reviewed; Journal article, 2013-03-14)
      This paper is focused on finding rules for waveheight change in a solitary wave as it runs up a slowly increasing bottom. A coupled BBM system is used to describe the solitary waves. Expressions for energy density and ...

    • Existence and uniqueness of singular solutions for a conservation law arising in magnetohydrodynamics 

      Kalisch, Henrik; Mitrovic, Darko; Teyekpiti, Vincent (Peer reviewed; Journal article, 2018-10-30)

    • Extreme wave runup on a steep coastal profile 

      Bjørnestad, Maria; Kalisch, Henrik (Journal article; Peer reviewed, 2020)
      It is shown that very steep coastal profiles can give rise to unexpectedly large wave events at the coast. We combine insight from exact solutions of a simplified mathematical model with photographs from observations at ...

    • Lagrangian Measurements of Orbital Velocities in the Surf Zone 

      Bjørnestad, Maria; Buckley, M.; Kalisch, Henrik; Streßer, M.; Horstmann, J.; Frøysa, Hege Guldbrandsen; Ige, Olufemi Elijah; Cysewski, M.; Carrasco-Alvarez, R. (Journal article; Peer reviewed, 2021)
      Eulerian and Lagrangian measurements of orbital velocities in waves approaching a beach are analyzed with the goal of understanding the relative influence of wave-by-wave variations in mean-water level, wave height and ...

    • A mathematical justification of the momentum density function associated to the KdV equation 

      Israwi, Samer; Kalisch, Henrik (Journal article; Peer reviewed, 2021)
      Consideration is given to the KdV equation as an approximate model for long waves of small amplitude at the free surface of an inviscid fluid. It is shown that there is an approximate momentum density associated to the KdV ...

    • Non-standard shocks in the Buckley-Leverett equation 

      Kalisch, Henrik; Mitrovic, Darko; Nordbotten, Jan Martin (Peer reviewed; Journal article, 2015-08)
      It is shown how delta shock waves which consist of Dirac delta distributions and classical shocks can be used to construct non-monotone solutions of the Buckley–Leverett equation. These solutions are interpreted using a ...

    • A Nonlinear Formulation of Radiation Stress and Applications to Cnoidal Shoaling 

      Paulsen, Martin Oen; Kalisch, Henrik (Journal article; Peer reviewed, 2021)
      In this article, we provide formulations of energy flux and radiation stress consistent with the scaling regime of the Korteweg–de Vries (KdV) equation. These quantities can be used to describe the shoaling of cnoidal waves ...

    • Numerical bifurcation for the capillary Whitham equation 

      Remonato, Filippo; Kalisch, Henrik (Journal article, 2017-03)
      The so-called Whitham equation arises in the modeling of free surface water waves, and combines a generic nonlinear quadratic term with the exact linear dispersion relation for gravity waves on the free surface of a fluid ...

    • A numerical study of nonlinear dispersive wave models with SpecTraVVave 

      Kalisch, Henrik; Moldabayev, Daulet; Verdier, Olivier (Peer reviewed; Journal article, 2017-03-02)
      In nonlinear dispersive evolution equations, the competing effects of nonlinearity and dispersion make a number of interesting phenomena possible. In the current work, the focus is on the numerical approximation of ...

    • On Existence and Admissibility of Singular Solutions for Systems of Conservation Laws 

      Kalisch, Henrik; Mitrovic, Darko (Journal article; Peer reviewed, 2022)
      A weak notion of solution for systems of conservation laws in one dimension is put forward. In the framework introduced here, it can be shown that the Cauchy problem for any n×n system of conservation laws has a solution. ...

    • On the formulation of energy conservation in the eeKdV equation 

      Norevik, Anders Marifjæren; Kalisch, Henrik (Journal article; Peer reviewed, 2024)
      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 ...

    • On the Formulation of Mass, Momentum and Energy Conservation in the KdV Equation 

      Ali, Alfatih Mohammed A.; Kalisch, Henrik (Peer reviewed; Journal article, 2014-10)
      The Korteweg-de Vries (KdV) equation is widely recognized as a simple model for unidirectional weakly nonlinear dispersive waves on the surface of a shallow body of fluid. While solutions of the KdV equation describe the ...

    • On the shoaling of solitary waves in the KdV equation 

      Khorsand, Zahra; Kalisch, Henrik (Journal article; Peer reviewed, 2014)
      The waveheight change in surface waves with a sufficiently slow variation in depth is examined. Using a new formulation of the energy flux associated to waves modeled by the Korteweg-de Vries equation, a system of three ...

    • PDE Based Algorithms for Smooth Watersheds 

      Hodneland, Erlend; Tai, Xue-Cheng; Kalisch, Henrik (Peer reviewed; Journal article, 2016-04)
      Watershed segmentation is useful for a number of image segmentation problems with a wide range of practical applications. Traditionally, the tracking of the immersion front is done by applying a fast sorting algorithm. In ...

    • Rigorous estimates on mechanical balance laws in the Boussinesq–Peregrine equations 

      Hussien Elkhorbatly, Bashar; Kalisch, Henrik (Journal article; Peer reviewed, 2024)
      It is shown that the Boussinesq–Peregrine system, which describes long waves of small amplitude at the surface of an inviscid fluid with variable depth, admits a number of approximate conservation equations. Notably, this ...

    • Ship wave patterns on floating ice sheets 

      Johnsen, Kristoffer; Kalisch, Henrik; Părău, Emilian I. (Journal article; Peer reviewed, 2022)
      This paper aims to explore the response of a floating icesheet to a load moving in a curved path. We investigate the effect of turning on the wave patterns and strain distribution, and explore scenarios where turning ...

    • Sudden wave flooding on steep rock shores: a clear but hidden danger 

      Kalisch, Henrik; Lagona, Francesco; Roeber, Volker (Journal article; Peer reviewed, 2024)
      It is shown that very steep coastal profiles can give rise to unexpectedly large wave events at the coast. We conduct a statistical analysis of runs from a nearshore Boussinesq-type model to demonstrate that under certain ...

    • Wave Breaking in Undular Bores with Shear Flows 

      Bjørnestad, Maria; Kalisch, Henrik; Abid, Malek; Kharif, Christian; Brun, Mats (Journal article; Peer reviewed, 2021)
      It is well known that weak hydraulic jumps and bores develop a growing number of surface oscillations behind the bore front. Defining the bore strength as the ratio of the head of the undular bore to the undisturbed depth, ...

    • Waves generated by moving loads on ice plates: Viscoelastic approximations 

      Dinvay, Evgueni; Kalisch, Henrik; Părău, Emilian (Journal article; Peer reviewed, 2022)
      The paper investigates waves generated by the moving loads on ice plates floating on an incompressible fluid. Two different viscoelastic approximations are considered for the ice cover: A model depending on the strain-relaxation ...