Browsing Department of Mathematics by Author "Kalisch, Henrik"
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Admissibility conditions for Riemann data in shallow water theory
Paulsen, Martin Oen; Kalisch, Henrik (Journal article; Peer reviewed, 2020)Consideration is given to the shallowwater 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, 20130314)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, 20181030) 
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.; CarrascoAlvarez, 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 wavebywave variations in meanwater 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 ... 
Nonstandard shocks in the BuckleyLeverett equation
Kalisch, Henrik; Mitrovic, Darko; Nordbotten, Jan Martin (Peer reviewed; Journal article, 201508)It is shown how delta shock waves which consist of Dirac delta distributions and classical shocks can be used to construct nonmonotone 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, 201703)The socalled 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, 20170302)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 the Formulation of Mass, Momentum and Energy Conservation in the KdV Equation
Ali, Alfatih Mohammed A.; Kalisch, Henrik (Peer reviewed; Journal article, 201410)The Kortewegde 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 (Conference object; 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 Kortewegde Vries equation, a system of three ... 
PDE Based Algorithms for Smooth Watersheds
Hodneland, Erlend; Tai, XueCheng; Kalisch, Henrik (Peer reviewed; Journal article, 201604)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 ... 
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, ... 
The Whitham Equation as a model for surface water waves
Moldabayev, Daulet; Kalisch, Henrik; Dutykh, Denys (Peer reviewed; Journal article, 201508)The Whitham equation was proposed as an alternate model equation for the simplified description of unidirectional wave motion at the surface of an inviscid fluid. As the Whitham equation incorporates the full linear ...