Exponential-like decay of the centerline velocity deficit and budget analysis in stratified wake

Thermal stratification and stratified flow are ubiquitous in nature. We conduct direct numerical simulations (DNSs) for temporally evolving stratified wake flows at Re=10,000 to Re=50,000 and Fr = 2 to 50, where Re is the Reynolds number and Fr is the Froude number. Unlike previous DNS studies, 80 to 100 realizations are used for ensemble average to make sure the convergence of higher order statistics. All DNSs continue until the wakes are strongly stratified. The many realizations allow us to get converged statistics and compare these statistics to the previously established scalings. Special attention is given to the decay of the centerline velocity deficit U₀. Instead of a power law decay U₀∼t^0.25,U₀∼t^0.76 in the non-equilibrium regime (NEQ) and the quasi-two-dimensional regime (Q2D) as suggested by the previous studies, our data suggests an exponential-like decay U₀∼exp(-0.008Nt) in two regimes. The budget analysis also supports a unified description of the late NEQ regime and the early Q2D regime.