General Ocean Turbulence Model (GOTM)

Introduction

General Ocean Turbulence Model (GOTM) is an open-source one-dimensional water column model for simulating hydrodynamic and thermodynamic processes related to vertical mixing in natural waters (Burchard, Bolding, and Villarreal 1999; Burchard and Bolding 2001; Umlauf and Burchard 2005). GOTM has been used in many studies, for example, the evolution of thermal stratification in the North Sea and the northern Pacific (Burchard and Bolding 2001), effects of breaking surface waves on surface boundary layer dynamics (Jones and Monismith 2008), mixing in sloping bottom boundary layers (Umlauf and Burchard 2011), and sediment dynamics, etc.

One of the primary strengths of the General Ocean Turbulence Model (GOTM) lies in its extensive collection of well-tested turbulence models integrated within the code to facilitate the calculation of vertical turbulent fluxes. Its fashion contains a range of approaches, spanning from algebraic equations employed to compute turbulence kinetic energy (TKE) and turbulence length-scale to the utilization of two-equation models, in which both mentioned terms are computed from differential transport equations. The second-order model is an essential part of GOTM, with a full or approximate solution of the transport equations for the turbulent momentum fluxes. As an independent module, the turbulence module in GOTM has been integrated into several three-dimensional hydrodynamic models, including the General Estuarine Transport Model (GETM, Burchard and Bolding (2002)), the Regional Ocean Modelling System (ROMS, Haidvogel et al. (2000)), the Nucleus for European Modelling of the Ocean (NEMO, Madec et al. (1991)), the Finite Volume Community Ocean Model (FVCOM, Chen et al. (2003)).

For further information regarding the GOTM, readers should refer to the official GOTM website (https://www.gotm.net). The website provides access to the source code, comprehensive documentation, and various test scenarios, allowing for more detailed model exploration.

GOTM turbulence models interface

From EEMS 12 onward, users are able to build models using turbulence closures from GOTM. A new option named General Ocean Turbulence (GOTM) has been added besides the original EFDC+ options in the Vertical Turbulence Mixing tab as shown in the General Ocean Turbulence Model (GOTM)#Figure 1. Two methods are available to set up the turbulence models from GOTM.

The first method is recommended for users unfamiliar with GOTM. By simply dropdown the Closure Model Presets, users can switch between the options and select the desired one. EE will generate the input file with all the default parameters corresponding to the selected model. The options in Closure Model Presets include:

• Mellor - Yamada
• k - ε
• k - ω
• Generic
  

Figure 1. Vertical Turbulence Mixing Options

The second method is more advanced and allows users to customize the turbulence model following the presetting base. By checking the box Customize GOTM model, the full suite of GOTM turbulence options will be displayed and are able to edit. The Turbulence Closure option includes First-Order and Second-Order. The First-Order method corresponds to models computing the diffusivities from the TKE and the turbulent length scale. TKE and length scale are computed from dynamic PDEs or algebraic relations. The Second-Order method is set by default, corresponds to a second order model for the turbulent fluxes. The second-order models fall into different categories.  As an essential part of GOTM, these models are discussed in detail in (GOTM document https://gotm.net/manual/stable/pdf/a4.pdf).

The TKE equation option specifies the appropriate routines for calculating the turbulent kinetic energy. The user has the choice between:

• Algebraic length scale equation
• Differential equation for TKE (k-epsilon style)
• Differential equation for q2/2 (Mellor-Yamada style

On the Length Scale Method, the user has also the choice between several algebraic equations, and several differential transport equations for a length-scale determining variable, including:

• Algebraic length scale equation (e.g., parabolic, triangular, etc.)
• Dynamic dissipation rate equation
• Dynamic Mellor-Yamada q²l equation
• Generic length scale (GLS)

Figure 2: GOTM Turbulence Options

General Ocean Turbulence Model (GOTM)#Figure 2 illustrates an example of the customizing setup of the k-epsilon model. The boundary conditions for TKE equation and Length Scale method can be setup through GOTM Boundary Conditions tab ( as shown in General Ocean Turbulence Model (GOTM)#Figure 3 ). The turbulence model parameters are given in the tabs Turbulence Parameters, Model Parameters and Second-Order Model as shown in General Ocean Turbulence Model (GOTM)#Figure 4, General Ocean Turbulence Model (GOTM)#Figure 5 and General Ocean Turbulence Model (GOTM)#Figure 6, respectively

Figure 3: GOTM Boundary Conditions

Figure 4: Turbulence Parameters

Figure 5: Model Parameters

Figure 6: Second-Order Model

GOTM turbulence models input file

Since EEMS version 10.2, DSI has taken advantages in applying JSON (JavaScript Object Notation) data format for EFDC+ input files. The format is easy to visualize the information and straightforward to add additional fields for new features. To avoid confusion with conventional JSON files, we have changed this new file extension in EFDC+ to JNP. JSON readers can still read and display this format. Some of the EFDC+ input files that use the new format include those related to MPI, propwash, and the new biota functionality. Following this enhancement, the input file named as gotm_turb.jnp for GOTM turbulence models also uses the JNP format.

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