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An intermediate solution between diagnostic exchange coefficients and prognostic TKE methods for vertical turbulent transport

Method: It is often claimed that searching the stationary solution of a full prognostic Turbulent Kinetic Energy (TKE) scheme should in principle give a computation for vertical turbulent exchange coefficients close to that of schemes simply inferring those coefficients from the local vertical gradients of wind and potential temperature. We implicitly refer here either to the methods solving the Monin-Obukhov (MO) implicit set of equations or to those using a local Richardson number, in the wake of the Louis (1979) paper. To our knowledge however, there has never been an attempt to inverse the proposal, i.e. to find the TKE prognostic equations that would have for stationary solution some already computed exchange coefficients Km (for momentum) and Kh (for energy).

turbulence parametrisation mixing length

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