Related papers: Inverse non-linear problem of the long wave run-up…
We formulate a new approach to solving the initial value problem of the shallow water-wave equations utilizing the famous Carrier-Greenspan transformation [G. Carrier and H. Greenspan, J. Fluid Mech. 01, 97 (1957)]. We use a Taylor series…
We put forward a simple but effective explicit method of recovering initial data for the nonlinear shallow water system from the reading at the shoreline. We then apply our method to the tsunami waves inverse problem.
The runup of tsunami waves on the coasts of the barrow bays, channels and straits is studied in the framework of the nonlinear shallow water theory. Using the narrowness of the water channel, the one-dimensional equations are applied; they…
We investigate the inverse tsunami wave problem within the framework of the 1D nonlinear shallow water equations (SWE). Specifically, we focus on determining the initial displacement $\eta_0(x)$ and velocity $u_0(x)$ of the wave, given the…
We discuss the following inverse problem: given the run-up data of a tsunami wave, can we recover its initial shape? We study this problem within the framework of the non-linear shallow water equations, a model widely used to study tsunami…
We put forward a solution to the initial boundary value (IBV) problem for the nonlinear shallow water system in inclined channels of arbitrary cross-section by means of the generalized Carrier-Greenspan hodograph transform (Rybkin et al.,…
Long linear wave transformation in the basin of varying depth is studied for a case of a convex bottom profile in the framework of one-dimensional shallow water equation. The existence of travelling wave solutions in this geometry and the…
Long waves in shallow water propagating over a background shear flow towards a sloping beach are being investigated. The classical shallow-water equations are extended to incorporate both a background shear flow and a linear beach profile,…
The estimate of individual wave run-up is especially important for tsunami warning and risk assessment as it allows to evaluate the inundation area. Here as a model of tsunami we use the long single wave of positive polarity. The period of…
The problem of the sea wave runup on a beach is discussed in the framework of the rigorous solutions of the nonlinear shallow-water theory. Key and novel moment here is the accounting of the asymmetric waves when the face slope steepness…
The description of gravity waves propagating on the water surface is considered from a historical point of view, with specific emphasis on the development of a theoretical framework and equations of motion for long waves in shallow water.…
The paper studies inverse problems of determining unknown coefficients in various semi-linear and quasi-linear wave equations. We introduce a method to solve inverse problems for non-linear equations using interaction of three waves, that…
The problem of the long wave runup on a beach is discussed in the framework of the rigorous solutions of the nonlinear shallow-water theory. The key and novel moment here is the analysis of the runup of a certain class of asymmetric waves,…
The reconstruction of water wave elevation from bottom pressure measurements is an important issue for coastal applications, but corresponds to a difficult mathematical problem. In this paper we present the derivation of a method which…
Wave shoaling of water waves over mild bottom slopes is well described by linearized theories. However, the analytical treatment of nonlinear wave shoaling subject to rapidly varying bottoms has proven to be elusive in the past decades. As…
Nonlinear initial-boundary value problem on deep-water gravity waves of finite amplitude is solved approximately (up to small terms of higher order) assuming that the waves are generated by an initial disturbance to the water and the…
In the present study a mathematical model of long-crested water waves propagating mainly in one direction with the effect of Earth's rotation is derived by following the formal asymptotic procedures. Such a model equation is analogous to…
The Green-Naghdi equations are a nonlinear dispersive perturbation of the nonlinear shallow water equations, more precise by one order of approximation. These equations are commonly used for the simulation of coastal flows, and in…
The problem of interest in this article are waves on a layer of finite depth governed by the Euler equations in the presence of gravity, surface tension, and vertical electric fields. Perturbation theory is used to identify canonical…
Long waves bring many important challenges in the ocean and coastal engineering, including but are not limited to harbor resonance and run-up. Therefore, understanding and modeling their dynamics is crucially important. Although their…