Similarity scaling of turbulence spectra and cospectra in a shallow tidal flow

Abstract

Measured turbulence power spectra, cospectra, and ogive curves from a shallow tidal flow were scaled using Monin-Obukhov similarity theory to test the applicability to a generic tidal flow of universal curves found from a uniform, neutrally stable atmospheric boundary layer (ABL). While curves from individual 10 min data bursts deviate significantly from similarity theory, averages over large numbers of sufficiently energetic bursts follow the general shape. However, there are several differences: (1) Variance in the measured curves was shifted toward higher frequencies, (2) at low frequencies, velocity spectra were significantly more energetic than theory while cospectra were weaker, and (3) spectral ratios of momentum flux normalized by turbulent kinetic energy (TKE) indicate decreased fluxes and/or elevated TKE levels. Several features of the turbulence structure may explain these differences. First, turbulent dissipation exceeded production, indicating nonequilibrium turbulence, possibly from advection of TKE. Indeed, using the production rate rather than dissipation markedly improves agreement in the inertial subrange. Second, spectral lag of the largest eddies due to inhomogeneous boundary conditions and decaying turbulence could explain spectral deviations from theory at low frequencies. Finally, since the largest eddies dominate momentum transfer, the consequence of the cospectra difference is that calculated ogive curves produced smaller total momentum fluxes compared to theory, partly because of countergradient fluxes. While ABL similarity scaling applied to marine bottom boundary layers (MBBLs) will produce curves with the general shape of the universal curves, care should be taken in determining details of turbulent energy and stress estimates, particularly in shallow and inhomogeneous MBBLs.