TRR181 - T4: Surface wave-driven energy fluxes at the air-sea interface
The transfer of energy by the free-surface waves is important for the coupled atmosphere-ocean system. In this project, we numerically examine the details of the energy transfer mechanisms in the vicinity of the ocean surface using hybrid scale-resolving Cahn-Hilliard-VoF two-phase flow approaches. Different from all previous approaches, the present computational model is not confined to the single air phase using an assumed free surface evolution together with an arbitrarily chosen interface roughness, but a true two-phase flow representation. Efforts are supplemented by analogue experimental two-phase work and jointly aim to identify the physics controlling air-sea energy fluxes and to quantify the mechanical energy budget within the coupled atmospheric and oceanic boundary layers. Related results should finally feed into an improved model of phase-averaged momentum equations, to be used in future general circulation models.
The computational model is based on a finite volume Navier-Stokes procedure and consists of the following ingredients:
1. The wind-wave-interaction is modeled by a simplified version of the diffusive interface CH-VoF. The latter is always compared to conventional VoF models that are predominately used in maritime air-water simulations. The CH-VoF approach features a number of theoretical advantages, e.g. with regards to an efficient (natural) interface compression, relevant for computing the dynamic interplay between two virtually immiscible fluid phases.
2. A hybrid RANS/LES (DES) turbulence model has been introduced to the numerical wind-wave tank. The model features optional DDES and IDDES capabilities. Different from the traditional DES approach, the formulation of the turbulent length scale follows from a dynamic free surface distance instead of the (usually steady) wall distance, which required the implementation of an efficient, HPC-capable distance calculation procedure. The latter is also essential for post processing (cf. 4.), and is computed from a PDE-based approach.
3. A numerical wind-wave flume was set up. Related work aims at the reproduction of experimentally observed wave properties under wind forcing. Experimentally observed (averaged) wind-wave conditions are introduced using an implicit forcing of flow properties (velocity, density, turbulence) in an inlet zone extracted from measurements. The latter spans approximately a typical wave length from the inlet into the interior and involves both, the air and the water phase. Water phase forcing refers to the linear wave theory. In the air phase, a logarithmic velocity profile is imposed. At the outlet, the grid is sufficiently stretched to obtain a numerical beach and thereby damping the wave field to suppress reflections.
4. A comprehensive post-processing using phase averaged, wave-following coordinates has been established which is able to connect numerical results with experimental data. The wave coherent velocities play an important role for the investigation of different wave parameters on the energy budget at the air-sea interface. They can be calculated by a triple decomposition, including the phase independent mean velocity, the wave coherent velocity and the turbulent fluctuation. The wave-following coordinates are completely unlinked from the employed unstructured spatial/temporal discretization. The procedure supports averaging the data based upon substantial (dynamic) data identification (binning).
First wind-wave computations where performed for two cases previously measured in a wind-wave flume. The cases were used to assess the predictive performance of mathematical and computational model described above against data published for two particular wind-wave configurations, which seem least costly to resolve.
Fig. (1) illustrates the normalized wave coherent velocity contours over the surface elevation for both cases (simulations left, experiments (PIV) right). The results of the CH-VoF model are a fairly good approximation to the experimental data, both qualitatively and quantitatively.
A simulation of a wind-wave scenario, with propagating non-linear waves and strong wind forcing can be found in: https://youtu.be/gSiOBW6nNzM
- University of Hamburg - Center for Earth System Research and Sustainability (CEN)
- University of Bremen - Center for Marine Environmental Sciences (MARUM)
- Constructor University
- Goethe University Frankfurt
- Catholic University of Eichstätt-Ingolstadt
- Max Planck Institute for Meteorology
- Leibniz Institute for Baltic Sea Research Warnemünde
- Leibniz Institute of Atmospheric Physics
- Alfred Wegener Institute for Polar and Marine Research
- Helmholtz-Zentrum Hereon
This project (''Surface Wave-Driven Energy Fluxes at the Air-Sea Interface'') is part of the Collaborative Research Centre TRR 181 ''Energy Transfers in Atmosphere and Ocean'' funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - Grant number 274762653.