Some algebraic length-scale relations

*INTERFACE:*

subroutine algebraiclength(method,nlev,z0b,z0s,depth,h,NN)

This subroutine computes the vertical profile of the turbulent
scale from different types of analytical expressions. These
range from simple geometrical forms to more complicated expressions
taking into account the effects of stratification and shear. The
users can select their method in the input file `gotmturb.nml`.
For convenience, we define here and as the distance
from the bottom and the surface, respectively. The water
depth is then given by , and and
are the repective roughness lengths. With these
abbreviations, the expressions implemented in GOTM are as follows.

- The parabolic profile is defined according to
(175)

where it should be noted that only for large water depth this equation converges to near the bottom or near the surface. - The triangular profile is defined according to
(176)

which converges always to near the bottom or near the surface. - A distorted parabola can be constructed by
using a slightly modified form of the equation
used by Xing and Davies (1995),
(177)

where it should be noted that only for large water depth this equation converges to near the bottom or near the surface. The constant is a form parameter determining the distortion of the profile. Currently we use in GOTM. - A distorted parabola can be constructed by
using a slightly modified form of the equation
used by Robert and Ouellet (1987),
(178)

where it should be noted that only for large water depth this equation converges to near the bottom. Near the surface, the slope of is always different from the law of the wall, a fact that becomes important when model solutions for the case of breaking waves are computed, see section 4.7.4. - Also the famous formula of Blackadar (1962) is based on
a parabolic shape, extended by an extra length-scale .
Using the form of Luyten et al. (1996), the algebraic relation
is expressed by
(179)

where(180)

is the natural kinetic energy scale resulting from the first moment of the rms turbulent velocity. The constant usually takes the value . It should be noted that this expression for converges to at the surface and the bottom only for large water depth, and when plays only a minor role. - The so-called ISPRAMIX method to compute the length-scale is described in detail in section 4.22.

*USES:*

use turbulence, only: L,eps,tke,k_min,eps_min use turbulence, only: cde,galp,kappa,length_lim IMPLICIT NONE

type of length scale integer, intent(in) :: method number of vertical layers integer, intent(in) :: nlev surface and bottom roughness (m) REALTYPE, intent(in) :: z0b,z0s local depth (m) REALTYPE, intent(in) :: depth layer thicknesses (m) REALTYPE, intent(in) :: h(0:nlev) buoyancy frequency (1/s^2) REALTYPE, intent(in) :: NN(0:nlev)

integer, parameter :: Parabola=1 integer, parameter :: Triangle=2 integer, parameter :: Xing=3 integer, parameter :: RobertOuellet=4 integer, parameter :: Blackadar=5 integer, parameter :: ispra_length=7

Original author(s): Manuel Ruiz Villarreal, Hans Burchard

Karsten Bolding 2012-12-28