Pseudospectral Bound and Transition Threshold for the 3D Kolmogorov Flow

In this paper, we study pseudospectral bounds for the linearized operator of the Navier-Stokes equations around the 3D Kolmogorov flow. Using the pseudospectral bound and the wave operator method introduced in [22], we prove the sharp enhanced dissipation rate for the linearized Navier-Stokes equations. As an application, we prove that if the initial velocity satisfies parallel to U-0-k(f)(-2)sin(k(f)y), 0,0 parallel to(H2) <= c nu(7/4) (nu the viscosity coefficient) and k(f) is an element of (0, 1), then the solution does not transition away from the Kolmogorov flow. (c) 2019 Wiley Periodicals, Inc.