In this letter, the spectrum of high Schmidt number passive scalar in forced homogeneous isotropic turbulence is studied through direct numerical simulations. A hybrid spectral-particle method is used with a finer resolution of the scalar than of the momentum and large time-steps. This approach enables to perform a systematic analysis over a wide range of Schmidt numbers. Our results recover th...

This paper aims to present some inequalities for unitarily invariant norms. In section 2, we give a refinement of the Cauchy-Schwarz inequality for matrices. In section 3, we obtain an improvement for the result of Bhatia and Kittaneh [Linear Algebra Appl. 308 (2000) 203-211]. In section 4, we establish an improved Heinz inequality for the Hilbert-Schmidt norm. Finally, we present an inequality...