Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userIn a book Tsunami and Nonlinear Waves: Numerical Verification of the Hasselmann equation
72
0
0.0
(
0
)
Added by
Alexander O. Korotkevich
Publication date
2007
fields
Physics
and research's language is
English
Authors
Alexander O. Korotkevich
Ask ChatGPT about the research
No Arabic abstract
The purpose of this article is numerical verification of the thory of weak turbulence. We performed numerical simulation of an ensemble of nonlinearly interacting free gravity waves (swell) by two different methods: solution of primordial dynamical equations describing potential flow of the ideal fluid with a free surface and, solution of the kinetic Hasselmann equation, describing the wave ensemble in the framework of the theory of weak turbulence. Comparison of the results demonstrates pretty good applicability of the weak turbulent approach.
rate research
Read More
By performing two parallel numerical experiments -- solving the dynamical Hamiltonian equations and solving the Hasselmann kinetic equation -- we examined the applicability of the theory of weak turbulence to the description of the time evolution of an ensemble of free surface waves (a swell) on deep water. We observed qualitative coincidence of the results. To achieve quantitative coincidence, we augmented the kinetic equation by an empirical dissipation term modelling the strongly nonlinear process of white-capping. Fitting the two experiments, we determined the dissipation function due to wave breaking and found that it depends very sharply on the parameter of nonlinearity (the surface steepness). The onset of white-capping can be compared to a second-order phase transition. This result corroborates with experimental observations by Banner, Babanin, Young.
The problem of tsunami wave run-up on a beach is discussed in the framework of the rigorous solutions of the nonlinear shallow-water theory. We present an analysis of the run-up characteristics for various shapes of the incoming symmetrical solitary tsunami waves. It will be demonstrated that the extreme (maximal) wave characteristics on a beach (run-up and draw-down heights, run-up and draw-down velocities and breaking parameter) are weakly dependent on the shape of incident wave if the definition of the significant wave length determined on the 2/3 level of the maximum height is used. The universal analytical expressions for the extreme wave characteristics are derived for the run-up of the solitary pulses. They can be directly applicable for tsunami warning because in many case the shape of the incident tsunami wave is unknown.
The mass balance of mountain glaciers is of interest for several applications (local hydrology or climate projections), and turbulent fluxes can be an important contributor to glacier surface mass balance during strong melting events. The underlying complex terrain leads to spatial heterogeneity and non-stationarity of turbulent fluxes. Due to the contribution of thermally-induced flows and gravity waves, exchange mechanisms are fully three-dimensional, instead of only vertical. Additionally, glaciers have their own distinct microclimate, governed by a down-glacier katabatic wind, which protects the glacier ice and interacts with the surrounding flows on multiple scales. In this study, we perform large-eddy simulations with the WRF model with dx=48 m to gain insight on the boundary-layer processes over an Alpine valley glacier, the Hintereisferner (HEF). We choose two case studies from a measurement campaign (August 2018) with different synoptic wind directions (South-West and North-West). Model evaluation with an array of eddy-covariance stations on the glacier tongue and surroundings reveals that WRF is able to simulate the general glacier boundary-layer structure. Under southwesterly airflow, the down-glacier wind is supported by the South-Western synoptic wind direction, a stable boundary layer is present over the ice surface, and local processes govern the turbulence kinetic energy production. Under northwesterly airflow, a cross-glacier valley flow and a breaking gravity wave lead strong turbulent mixing and to the subsequent erosion of the glacier boundary layer. Stationarity analyses of the sensible heat flux suggest non-stationary behaviour for both case study days, while non-stationarity is highest on the NW day during the gravity-wave event. These results suggest that the synoptic wind direction has, in addition to upstream topography and the atmospheric stability, a strong impact on whether a local glacier boundary layer can form or not, influencing whether a glacier is able to maintain its own microclimate.
In the vast literature on tsunami research, few articles have been devoted to energy issues. A theoretical investigation on the energy of waves generated by bottom motion is performed here. We start with the full incompressible Euler equations in the presence of a free surface and derive both dispersive and non-dispersive shallow-water equations with an energy equation. It is shown that dispersive effects only appear at higher order in the energy budget. Then we solve the Cauchy-Poisson problem of tsunami generation for the linearized water wave equations. Exchanges between potential and kinetic energies are clearly revealed.
The development of a set of high-order accurate finite-volume formulations for evaluation of the pressure gradient force in layered ocean models is described. A pair of new schemes are presented, both based on an integration of the contact pressure force about the perimeter of an associated momentum control-volume. The two proposed methods differ in their choice of control-volume geometries. High-order accurate numerical integration techniques are employed in both schemes to account for non-linearities in the underlying equation-of-state definitions and thermodynamic profiles, and details of an associated vertical interpolation and quadrature scheme are discussed in detail. Numerical experiments are used to confirm the consistency of the two formulations, and it is demonstrated that the new methods maintain hydrostatic and thermobaric equilibrium in the presence of strongly-sloping layer-wise geometry, non-linear equation-of-state definitions and non-uniform vertical stratification profiles. Additionally, one scheme is shown to maintain high levels of consistency in the presence of non-linear thermodynamic stratification. Use of the new pressure gradient force formulations for hybrid vertical coordinate and/or terrain-following general circulation models is discussed.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
