On entrainment and vertical mixing instably stratified fjords

Abstract

The vertical mixing in some stably stratified fjords with subcritical flow ( F Δ 2 <I, F Δ 2 being the densimetric Froude number) is investigated by means of dye diffusion experiments. Previous interpretation of the obtained results indicates that the wind plays a minor role as energy source for vertical transportation of mass across the pycnocline ( Buch, 1979 ). In this paper the effect of the interfacial shear stress in relation to entrainmenthas been investigated with the following results. o (1) A derivation of a relation between the vertical turbulent diffusioncoefficient and the oceanographical environment: K = R 1 c 1 ( U/N ) 2 du/dzwhere U is the mean velocity of the upper layer, N is the Brünt-Väisälä frequency, R 1 is the flux Richardson number and c 1 the interfacial, drag coefficient. Plotting K vs .( U/N ) 2 du/dz, known from observations, results in a mean value of R 1 c 1 =2·9×10 −4 . (2) For an estimation of the order of magnitude of c 1 , the flux Richardson number, R 1 , is chosen to be 0·10 leading to c 1 =2·9×10 −3 . (3) The order of magnitude of the vertical turbulent diffusion coefficient for the momentum K m is found using the well known formula: K m = K Ri/R 1 , Ri being the Richardson number. (4) Taking start point in the definition of the flux Richardson number,proportionality between the entrainment and the densimetric Froude nember is found: u c /U =2 R t c 1 (I– u 1 / U ) F Δ 2 . Plotting u c /Uvs.F Δ 2 , the constant 2 R 1 c 1 (I- u 1 /U ) is found to be 5·2×10 −4 .