I 10
I). J. ('ARSON .is!) F. R. SMITH
instabilities grow on the crest of the dome, where gradients have been
intensified (Readings cr a/.. 1972). These may then be advccted into the
tongue hy thc wind shear and there play an iinportnnt role in enhancing the
mixing of the tongue into the cotivectivcly unstable houndiiry layer.
It is thcreforc postulated that thc entrainment priwcss and hence .4 of
Eq. (7) are governed not only by H(0. I ) , which partly deterinines the
strength of thc thermals, but also by AU(r) and the magnitude of the wind
shear, AV(r), which relate to the dynamical stability of the interface. On
dimensional grounds. then. the simplest formulation for A is
( 16)
H(h. f)/H(O. I ) 5 - A = - K [ / ) c , , AC' AO/H(O, /)y,
where u, K are two "constants" which must be determined from
ohscrvat ions.
3.2. Dynumicul ('c,risidrrurioris
I t is necessary in our dynamical formulation to include the parameters
ncedcd to dctermine the degree of entrainment as expressed in Eq. (16) and.
as a first uttempt. we construct a simple model based on the idealised wind
profiles of Fig. 2. A right-handed system of axes is chosen such that the
1.'~; 2. Schcmatic rcpre,wntatioii tic thc idcaliscd profiles of potential temperature 0 and the
coniponcnts u. 19 of the horimntal wind velocity V used in the simple thermodynamic model.
Also illlistrated is the nature of the wind velocity shear. AV, across the interface at z = h.
x-axis is directed along the postrophic wind V,. For : < h. the mean wind
components are assumed to be virtually constant with height and, at z = h.
we include a step discontinuity AV in the wind velocity which defines the
angles a and 8, a being the turning of the wind in the boundary layer from
the geostrophic direction. For z > h, the mean wind is assumed to be V,.
I). J. ('ARSON .is!) F. R. SMITH
instabilities grow on the crest of the dome, where gradients have been
intensified (Readings cr a/.. 1972). These may then be advccted into the
tongue hy thc wind shear and there play an iinportnnt role in enhancing the
mixing of the tongue into the cotivectivcly unstable houndiiry layer.
It is thcreforc postulated that thc entrainment priwcss and hence .4 of
Eq. (7) are governed not only by H(0. I ) , which partly deterinines the
strength of thc thermals, but also by AU(r) and the magnitude of the wind
shear, AV(r), which relate to the dynamical stability of the interface. On
dimensional grounds. then. the simplest formulation for A is
( 16)
H(h. f)/H(O. I ) 5 - A = - K [ / ) c , , AC' AO/H(O, /)y,
where u, K are two "constants" which must be determined from
ohscrvat ions.
3.2. Dynumicul ('c,risidrrurioris
I t is necessary in our dynamical formulation to include the parameters
ncedcd to dctermine the degree of entrainment as expressed in Eq. (16) and.
as a first uttempt. we construct a simple model based on the idealised wind
profiles of Fig. 2. A right-handed system of axes is chosen such that the
1.'~; 2. Schcmatic rcpre,wntatioii tic thc idcaliscd profiles of potential temperature 0 and the
coniponcnts u. 19 of the horimntal wind velocity V used in the simple thermodynamic model.
Also illlistrated is the nature of the wind velocity shear. AV, across the interface at z = h.
x-axis is directed along the postrophic wind V,. For : < h. the mean wind
components are assumed to be virtually constant with height and, at z = h.
we include a step discontinuity AV in the wind velocity which defines the
angles a and 8, a being the turning of the wind in the boundary layer from
the geostrophic direction. For z > h, the mean wind is assumed to be V,.