Center for Ocean-Atmospheric Prediction Studies Internal wave generation and propagation: analytical and numerical computations Flavien Gouillon and Eric Chassignet Center for Ocean-Atmospheric Prediction Studies November 13th, 2008 Flavien Gouillon (COAPS)

Internal Wave Modeling Internal waves matter! Internal waves occur in stably stratified fluid when a water parcel is displaced by external forces and restored by buoyancy forces. Knowledge of internal wave generation and propagation is crucial to understand ocean mixing and the large scale ocean circulation (Munk and Wunsch, 98). Spain Internal wave surface signature at the strait of Gibraltar From J. Nash Maintain the strength of the thermohaline circulation Half of the energy to vertically mix the abyssal ocean Flavien Gouillon (COAPS) Internal Wave Modeling November 13, 2008 1/9

Internal Wave Modeling Internal wave modeling background Their spatial scales (m to few km) are not resolved in Oceanic General Circulation Models that are 1° to 1/12° horizontal resolution at best. The dynamic of internal wave is non-hydrostatic and thus cannot be well resolved in Oceanic General Circulation Models that usually make the hydrostatic approximation. 3 types of model vertical discretization (z-, σ- and ρ-) Numerical models that use fixed vertical coordinate (z- and σ- levels) have a spurious diapycnal mixing associated with the transport of density. z ρ σ Flavien Gouillon (COAPS) Internal Wave Modeling November 13, 2008 2/9

Internal Wave Modeling Internal wave mixing parameterization To represent the internal wave breaking mixing in models we need to use a sub grid scale parameterization. Numerical models assume a quasi-uniform internal wave mixing in the deep interior. Unrealistic since it depends mostly on the geography (topography) and the dynamic of the internal wave. In Oceanic General Circulation Models we need, first, to well understand: Internal-Tide Generation Garrett and Kunze 07 Processes that transfer energy into small scale turbulence mixing Flavien Gouillon (COAPS) Internal Wave Modeling November 13, 2008 3/9

Internal Wave Modeling My PhD Objectives To investigate the internal wave representation in Oceanic General Circulation Models as a function of model grid spacing. To document and quantify the numerically induced mixing in the fixed coordinate ocean model. Flavien Gouillon (COAPS) Internal Wave Modeling November 13, 2008 4/9

Internal Wave Modeling My PhD Objectives To investigate the internal wave representation in Oceanic General Circulation Models as a function of model grid spacing. To document and quantify the numerically induced mixing in the fixed coordinate ocean model. Flavien Gouillon (COAPS) Internal Wave Modeling November 13, 2008 4/9

Schematic of the situation being modeled Internal Wave Modeling Approach We compare the results for the same simple problem From an analytical point of view. From 2 numerical models: The HYbrid Coordinate Ocean Model (HYCOM, ρ-level) and the Regional Ocean Model System (ROMS, σ-level). Schematic of the situation being modeled Flavien Gouillon (COAPS) Internal Wave Modeling November 13, 2008 5/9

Internal Wave Modeling The only slide with equations… Analytical solution derived by Khatiwala (2003). Conditions: the baroclinic response needs to be weaker than the barotropic forcing. Wave mode structure The vertical velocities: Moving frame Topography System Properties with Flavien Gouillon (COAPS) Internal Wave Modeling November 13, 2008 6/9

Internal Wave Modeling Analytic vs. Numeric (snapshot, linear regime) m.s-1 m.s-1 m.s-1 Δx =1.5km 25 layers U0=0.02 m.s-1 N=Constant f=0 No mixing No bottom friction 1h Output m.s-1 Flavien Gouillon (COAPS) Internal Wave Modeling November 13, 2008 7/9

The impact of the model horizontal resolution (animation) Cross vertical section of the zonal baroclinic velocities using ROMS Δx = 1.5 km Δx = 30 km m.s-1 Depth (m) -2000 -600 km 0 km 600 km Low modes (fastest) are well represented (carry ~70% of the energy away). Higher modes (slowest) at the tip of the ridge are not (responsible for the turbulent mixing). Flavien Gouillon (COAPS) Internal Wave Modeling November 13, 2008 8/9

Internal Wave Modeling Conclusions Internal wave modeling matters for the global ocean circulation. From the barotropic tide to the turbulent processes, steps are not well understood. Numerical models seem to well represent the internal wave if the horizontal resolution is high enough (what is high enough?). If the grid is too coarse, higher modes are not well represented. “The Graal”: Can we derived a physically based internal wave breaking mixing parameterization to implement in numerical models? Flavien Gouillon (COAPS) Internal Wave Modeling November 13, 2008 9/9