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Mark Schlutow

slowly such that the waves persist in their overall structure over several more wavelengths. However, turbulence is produced. Lindzen (1970) modeled the effect of turbulence on the wave by harmonic damping with a constant kinematic eddy viscosity. The eddy viscosity is exactly such that it saturates the wave, meaning that viscous damping and anelastic amplification are balanced ( Lindzen 1981 ; Fritts 1984 ; Dunkerton 1989 ; Becker 2012 ). Pitteway and Hines (1963) referred to this instance as

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Jannik Wilhelm, T. R. Akylas, Gergely Bölöni, Junhong Wei, Bruno Ribstein, Rupert Klein, and Ulrich Achatz

energy-conserving equation system of linear Boussinesq equations for the mesoscale, and one-dimensional ray equations for the submesoscale dynamics. Subsequently, our numerical models are described in section 3 ; the initial conditions of the numerical experiments are motivated in section 4a , and section 4b briefly discusses the postprocessing of the model output data. In section 4c , a kinematic analysis similar to ship wake theory is used to predict the geometry of the induced mesoscale wave

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Junhong Wei, Gergely Bölöni, and Ulrich Achatz

. 2015 ) a turbulent Smagorinsky coefficient C S 2 is determined, then averaged for stability reasons over a local five-point smoothing window along all the available spatial directions, and finally a turbulent kinematic viscosity is determined via (45) ν t = C S 2 Δ 2 S , where (46) Δ = { ⁡ ( Δ x Δ y Δ z ) 1 / 3 , 3 D   case ⁡ ( Δ x Δ z ) 1 / 2 , 2 D   case and (47) S = ∑ i , j ⁡ ( ∂ υ i ∂ x j + ∂ υ j ∂ x i ) 2 . The turbulent viscosity is then used in the dynamic shear viscosity coefficient via

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