The decay of stably stratified grid turbulence in a viscosity-affected stratified flow regime

The decay of stably stratified turbulence generated by a towed rake of vertical plates is investigated by direct numerical simulations (DNS) of temporally evolving grid turbulence in a linearly stratified fluid. The Reynolds number Re-M = U0M / upsilon is 5000 or 10 000 while the Froude number Fr-M = U-0 / MN is between 0.1 and 6 (U-0: towing speed; M: mesh size; upsilon : kinematic viscosity; : Brunt-Vaisala frequency). The DNS results are compared with the theory of stably stratified axisymmetric Saffman turbulence. Here, the theory is extended to a viscosity-affected stratified flow regime with low buoyancy Reynolds number Re-b, and power laws are derived for the temporal variations of the horizontal velocity scale (U-H) and the horizontal and vertical integral length scales ( L-H amd L-V). Temporal grid turbulence initialized with the mean velocity deficit of wakes exhibits a k(2) energy spectrum at a low-wavenumber range and invariance of (UHLHLV)-L-2-L-2 , which are the signatures of axisymmetric Saffman turbulence. The decay of various quantities follows the power laws predicted for low-Re-b Saffman turbulence when Fr-M is sufficiently small. However, the decay of U-H(2) at Fr-M = 6 is no longer expressed by a power law with a constant exponent. This behaviour is related to the scaling of kinetic energy dissipation rate epsilon, for which alpha = epsilon/ (U-H(3)/LH) is constant during the decay for FrM <= 1while it varies with time for Fr-M = 6. We also examine the experimental data of towed-grid experiments by Praud et al. (J. Fluid Mech., vol. 522, 2005, pp. 1-33), which is shown to agree with the theory of low-Re-b Saffman turbulence.