In many ocean general circulation models, the background value of the vertical eddy viscosity coefficient is typically set to around Ab = 1.0 cm²s^-1. However, in straits with complex topography and strong currents, subgrid-scale wave motions such as internal waves and lee waves are frequently generated, and thus enhanced vertical viscosity may be required. For example, in the Tsushima Strait, Hirose et al. (2021) inversely estimated Ab to be the order of 100 cm²s^-1, implying that Ab = 1.0 cm²s^-1 may also be insufficient for the Kuroshio through the Tokara Strait.
  This study investigates an appropriate vertical viscosity model for representing subgrid-scale turbulence in the Tokara Strait. Numerical experiments are conducted using the DREAMS_Ep model for the ocean south of Kyushu, with a horizontal resolution of approximately 1.5 km. In addition to the conventional constant-viscosity formulation, the Smagorinsky (1963) turbulence model is applied to calculate the vertical eddy viscosity coefficient. Model performance is evaluated using both moored and shipboard ADCP data.
  The original viscosity coefficient Ab = 1.0 cm²s^-1 has produced excessively strong vertical shear of horizontal velocity and the locally unstable structures. These noisy small-scale structures are suppressed by applying larger Ab, leading to a smoother and more realistic velocity structure compared to the moored ADCP data.
  Furthermore, several parameters in the momentum equations are inversely estimated using Green's function method constrained by the shipboard ADCP data. When the Smagorinsky turbulence model is not applied, Ab is estimated to be 70–80 cm²s^-1. If the constant background value of Ab is fixed at 1.0 cm²s^-1, the estimated Smagorinsky constant Cs is around 0.1 or 0.2. This range is consistent with values adopted in many CFD model studies. These results suggest that, even in a hydrostatic model, it is appropriate to adopt the Smagorinsky turbulence model as a vertical eddy viscosity scheme.

vertical viscosity coefficient,Kuroshio,Tokara Strait,ADCP