Investigation of The Optimum Range of Scaling Parameter in a Proposed Horizontal Eddy Viscosity Formulation for a Hydrodynamic Simulation at Gulf of Kutch

The horizontal eddy viscosity (ε) is a parameter used to attain closure in the two-dimensional Shallow Water Equations (SWE) accounting for turbulence. This parameter drains energy from the system, thus helps to attune the stability in the solution and helps to address the abnormal energy gradients that tend to appear in SWEs. Shallow Water Equations (SWEs) are the basis on which many real time predictions and extenuations of the hydrodynamic events could be explained and various approaches exist for solution of SWEs, mostly depending on the requirement of the problem. In this paper, a hybrid Finite Volume (FV) and Finite Element (FE) based solver, which can efficiently use the depth adaptive unstructured gridding, is developed and applied to simulate the hydrodynamics of the Gulf of Kutch region. Gulf of Kutch is the highly irregular formations with the number of islands, mud flats, creeks, bays, marshes, reefs, tidal flats, about ten small and large ports along with many other natural and anthropogenic morphological features. An empirical relationship for ε based on product of flow velocity and length scale of computational mesh is proposed along with a scaling parameter c
ε
to optimize the range of ε. This paper aims to establish the effective range of c
ε
for the Gulf of Kutch region. To investigate the optimum range of scaling parameter c
ε
, it is introduced to optimize the range of ε, flow field parameter (free surface elevation and velocity magnitude) are analyzed at Kandla and Okha, the finer and coarser gridded locations in the computational mesh, respectively. This study unveils that the effective range of scaling parameter c
ε
is from 0.1 to 10.0 for the Gulf region. Initially, different ranges of c
ε
, between 0.1 to 10.0 has been considered and tested with the same domain and the higher values than 1.5 are excluded to avoid the unrealistic values of eddy viscosity. Based on the statistical analysis, range of c
ε
from 0.6 to 1.5, performed better for the study domain.