Characterizing plume dispersion in the diabatic surface layer by trajectory analysis

Abstract

Theory is developed to describe the vertical structure of a continuous plume emitted from a ground-based source in the diabatic surface layer. It was found that the mean height z ( x) and the root-mean square width σ z ( x) could each be represented by solutions of the base equations dz i/ dt = b iu ∗ φ(z i/L) and d x/d t = u( z i )( i = 1, 2). The case i = 1 depicts the z variation (z 1 ≡ z) and i = 2 signifies the σ z variation ( z 2 ≡ σ z ). Terms u, u ∗, t signify the wind speed, friction velocity and time, respectively; φ i are stability functions dependent on the Monin-Obukhov length ( L), with φ i = (1 − α iz i/L) 1 2 and (1 + β iz i/L) −1 for L ⩽ 0 and L ⩾ 0, respectively; remaining parameters are coefficients, e.g. b 1 = 0.4, b 2 = 0.57. The base equations ( i = 3) were also used to examine the trajectory of the plume “height”, z max; this is defined by the position χ( z max) = 0.1 χ(0) in which χ( z) is the gaseous concentration at height z. In unstable conditions, the vertical propagation d z max/d t was adequately specified by a velocity w = σ w , where σ w is the standard deviation of the vertical fluctuating component in the horizontal wind speed. In stable conditions, experimental evidence suggested that w = 1.2(4)u ∗/(1 + βz max /L) with β ≈ 2 . Amongst the conclusions, it was shown that σ z(x/z 0, z 0/L) = z((b 2/b 1)(x/z 0), z 0/L) provided φ 1 = φ 2 and that σ z/ z ≈ (b 2/b 1) q in which √ 2⩽q⩽2 and z 0 is the roughness length.