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In this study, a six-dimensional Lorenz model (6DLM) is derived, based on arecent study using a five-dimensional (5-D) Lorenz model (LM), in order toexamine the impact of an additional mode and its accompanying heating term onsolution stability. The new mode added to improve the representation of thestreamfunction is referred to as a secondary streamfunction mode, while thetwo additional modes, which appear in both the 6DLM and 5DLM but not in theoriginal LM, are referred to as secondary temperature modes. Two energyconservation relationships of the 6DLM are first derived in thedissipationless limit. The impact of three additional modes on solutionstability is examined by comparing numerical solutions and ensemble Lyapunovexponents of the 6DLM and 5DLM as well as the original LM. For the onset ofchaos, the critical value of the normalized Rayleigh number (rc)is determined to be 41.1. The critical value is larger than that in the 3DLM(rc ~ 24.74), but slightly smaller than the one in the5DLM (rc ~ 42.9). A stability analysis and numericalexperiments obtained using generalized LMs, with or without simplifications,suggest the following: (1) negative nonlinear feedback in association withthe secondary temperature modes, as first identified using the 5DLM, plays adominant role in providing feedback for improving the solution's stability ofthe 6DLM, (2) the additional heating term in association with the secondarystreamfunction mode may destabilize the solution, and (3) overall feedbackdue to the secondary streamfunction mode is much smaller than the feedbackdue to the secondary temperature modes; therefore, the critical Rayleighnumber of the 6DLM is comparable to that of the 5DLM. The 5DLM and 6DLMcollectively suggest different roles for small-scale processes (i.e.,stabilization vs. destabilization), consistent with the following statementby Lorenz (1972): "If the flap of a butterfly's wings can be instrumentalin generating a tornado, it can equally well be instrumental in preventing atornado." The implications of this and previous work, as well as futurework, are also discussed

Nonlinear feedback in a six-dimensional Lorenz model: impact of an additional heating term